tag:blogger.com,1999:blog-19227640657020586022024-03-05T23:35:52.326+00:00Quantitative & FinancialBlog about Mathematics, Quantitative Analytics and Financial ModellingOndrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-1922764065702058602.post-60683901300866482542020-06-24T05:46:00.004+01:002020-06-24T08:34:18.191+01:00Factor Investing and Fama-French modelThis <a href="https://github.com/omartinsky/FamaFrench" target="_blank">notebook</a> illustrates factor investing and five-factor Fama-French model.<div><br /><a href="https://github.com/omartinsky/FamaFrench" rel="noopener" target="_blank"><img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /></a><br /><h3 style="text-align: left;"><span style="letter-spacing: 0.146667px;"><b><font face="inherit">Risk Factor</font></b></span></h3><p style="text-align: left;"><span style="letter-spacing: 0.146667px;"><font face="inherit">Certain characteristic of economy (Inflation/GDP) <b>or </b>stock market itself (S&P 500)</font></span></p><h4 style="text-align: left;"><span style="letter-spacing: 0.146667px;"><b><font face="inherit">Factor Model</font></b></span></h4><p style="text-align: left;"><span style="letter-spacing: 0.146667px;"><font face="inherit">Factor model uses movements in risk factors <b>to explains</b> portfolio returns</font></span></p><p style="text-align: left;"><font face="inherit"><img alt="" height="167" 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" width="364" /></font></p><p style="text-align: left;"></p><h3 style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: left; unicode-bidi: embed; word-break: normal;"><font face="inherit"><b>Questions which factor investing answers</b></font></h3><p></p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: left; unicode-bidi: embed; word-break: normal;"></p><p></p><ul style="text-align: left;"><li><span style="font-family: inherit;">Why different asset have systematically lower or higher average returns?</span></li><li><span style="font-family: inherit;">How to manage the asset portfolio with the underlying risks in mind?</span></li><li><font face="inherit">How to benefit of our ability to bear specific types of risks to generate returns?</font></li></ul><p></p><p></p><h3 style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: left; unicode-bidi: embed; word-break: normal;"><font face="Century Schoolbook">Fama-French Model</font></h3><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;">Assumes linear relationship between empirical factors and stock returns:</p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></p><ul style="text-align: left;"><li>Market Factor (MER)</li><li>Size Factor (SMB)</li><li>Value Factor (HML)</li><li>Profitability Factor (RMW)</li><li>Investment Factor (CMA)</li></ul><div><img alt="" height="98" 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" width="440" /></div><p></p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><b>Factors </b>are constructed daily from definitions, as illustrated previously</p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></p><ul style="text-align: left;"><li>They are global for the entire stock market</li></ul><p></p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><b>Factor sensitivities</b> are calibrated using regression</p><p style="margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></p><ul style="text-align: left;"><li>They represent “reward for taking a specific risk”, which is different for every stock</li><li>Risk/Reward relationship is expected to hold over time</li><li>Objective: maximize the model’s predictive power R2</li></ul><p></p></div><h3 style="text-align: left;">Market Excess Return (MER)</h3><div><ul style="text-align: left;"><li>Market excess return (over RF rate) alone explains around 80% of asset movements</li><li>Daily returns are ~normally distributed</li><li>Relationship between returns of the overall market and returns of selected portfolio</li></ul></div><div><img alt="" height="272" 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" width="578" /></div><h3 style="text-align: left;">Size (SMB) factor</h3><div><div><ul style="text-align: left;"><li>Small-cap companies typically bear additional risk premium - was it always the case?</li><li>Python can help you to see that this factor has a different prevalence in different economic regimes</li></ul></div><div><img alt="" height="295" 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" width="423" /></div></div><h3 style="text-align: left;">Value (HML) factor</h3><div><ul style="text-align: left;"><li>Value companies trade at higher yields to compensate for lack of growth potential</li><li>Python can help you to see that this factor has different explanatory power in different market situations and on different portfolios (very interesting)</li></ul></div><div><img alt="" height="200" src="data:image/png;base64,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" width="594" /></div><h3 style="text-align: left;">Profitability and investment factors</h3><div style="text-align: left;"><ul style="text-align: left;"><li><u>Profitability factor</u> (RMW) to attribute superior returns of companies with robust operating profit margins and strong competitive position among peers<br /><br /></li><li><u>Investment factor</u> (CMA) to segment companies based on their capital expenditures<br /><br /></li><li><b>Analysts opinion</b>: High capex structurally associated with growth companies, which puts usefulness of this factor in question</li></ul><div style="text-align: left;"><br /></div><img alt="" height="155" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAADyCAYAAAChxNetAAAgAElEQVR4Ae19C7RmRXXm4akoGECjOCxfiI/RJLbyMPGB4BN5NV7Tkpk4GsAgIkR5THQJ1yuXa4KMK2mypIGhWTdA3x6zEMTHyChOd8ujO0CCaBClGbqFBpqEZ4uNgMKetXfVrtq7Tp3zn///z733//+771p3/eecqtq197d37a+qzvnPX4D9GQKGgCFgCBgChsDIIVCMnEVmkCFgCBgChoAhYAiAEbwFgSFgCBgChoAhMIIIGMGPoFPNJEPAEDAEDAFDwAjeYsAQMAQMAUPAEBhBBIzgR9CpZpIhYAgYAoaAIWAEbzFgCBgChoAhYAiMIAJG8CPoVDPJEDAEDAFDwBAwgrcYMAQMAUPAEDAERhABI/gRdKqZZAgYAoaAIWAIGMFbDBgChoAhYAgYAiOIQCOC37xyDIqiyP5PrWsJlXVTUEyubUlYl2I2zcBYYl9rdnWpClZfO+mwbq7DZphZMgYzm1xn7K+xlZt76L1ZE9aR4kL5DXWJsdKrDXkt1sIU+WkK5ilS8mrZVUPAEDAEBhCBwSB4JHdM3Ioo5ggt7jsheNRnNgmyzjomz2bkyIQaCb5OdltlrCP5bckMhKlEMlkaZBvawsLkGAKGgCEwiAh0RfC1hFciynSVxasvv7pjMq9rl5Sp/plIlkzBlF8xuvKkn6KO+GJdSUS8Ai4KbYMitUQutxmbnPK7Adgvy5+CKb8q50kM1yeCTGRxP0GnBIeoF5N7XDEjBiw7ixdPZBh/isqo54zcrVF1dPiyjqn+3Le7XkDfNlTgSSv4gAv7ie2o87m2w84MAUPAEBhVBNoheCZbJg/+DATBiTcSEREAlockzWU+WZeuJxODUp+Y1MuE54iGCSBxI/cR9ORylKNJQhMa6xoJLCW2gla1ZbuR8Ep1Ca+oI/dF5FiyU+JQtjdL8FUywsq7rGeJoBka/xl0nHS7LzyZcNfjhKZfG1gPjWcZK+yfdWJdEpXt1BAwBAyBBYVAVwQfki0TeCCIBDMmFF8eCC0QKRNKQuahPBJXWAECt/HEy32o1S+3iwSQaKZOWa/YhyqOJ6EvIZcnB6mNChPWOU4EADI6ellMTExUWb1Yl9APy4sTErYrlcfnUQfWq6wn6xDbRDjwiMun1vm25Lt4HMt1OzrrwgZH7CyD9RR+CHHhJz4BF25jn4aAIWAILEwEWiZ4TsA62dYme8SdyZIJvkQAzjlMXGpVmCR0rhMmI0m5dDPXrSIxrpuvx8TqyCZfh/GoISSeLOGntz+PF8vS2EayriJ4bid1iJg72zN1kkkHY8GfUUeBg2gTy7kFfnI/3drAMri9toWxL9Rkj9vYpyFgCBgCCxOBrgi+kghTQk7O88leAJ4SPBNBQs6cyOsInqVyn47oI/lxOX2W+uVSR1phBS2Ii2tEYm2R4L29rHvWzgTbqEe0kXFy/hIEHJUPk6r+CT7echhbgt+2cHq0awMrnid47gt9XRmjLMI+DQFDwBBYIAi0QvCaUOLqkLdXuZzPS6RUIlomJd5CRm9wcvdEViK6vMe473ziZ5myn0hYTFbAfcmH7lhnT8r5fli+XHGybfKa1p0JCwm+JDfpt4QllNuwvIgB68B2Z/TMTmqiniyTJiGsk3iWQJa3YYPruVrPsGMjfRTVtSNDwBAwBBYcAq0SfEyy6RYsJ2Z/nbeleUteEYQncHVNtOM2TLpqlV/RT83WLZNPSfdkNciEldbjVT7LiSSKscT6aDLnulWyuC9J8Gnd8mTJYzS5tjwpYKwYd/4M2GX07Ibgg5352wxV9nZlAw3NVE89UQn9cIwsuOFsBhsChoAhEBFoheDjKtKRDBKTI6m4bRzJzhNRIBdUJibqsGrGywnJK/Jk0lJysBGTQJwUMAlHs5MjlsXEV/DKVtdj4nVkK20rr5pdS9ZFEzyWBTLyfUrbuB+nt8TG6VXCVuKUI3jsMLVRkWBGz64Inv0dcZsVG4JvHZ4Bw2AL2xH10B60M0PAEDAEFg4CjQh+4cBhlhoChoAhYAgYAqOBgBH8aPjRrDAEDAFDwBAwBBQCRvAKDjsxBAwBQ8AQMARGAwEj+NHwo1lhCBgChoAhYAgoBIzgFRx2YggYAoaAIWAIjAYCRvCj4UezwhAwBAwBQ8AQUAgYwSs47MQQMAQMAUPAEBgNBIzgR8OPZoUhYAgYAoaAIaAQMIJXcNiJIWAIGAKGgCEwGggYwY+GH80KQ8AQMAQMAUNAIWAEr+CwE0PAEDAEDAFDYDQQMIIfDT+aFYaAIWAIGAKGgELACF7BYSeGgCFgCBgChsBoIGAEPxp+NCsMAUPAEDAEDAGFgBG8gsNODAFDwBAwBAyB0UDACH40/GhWGAKGgCFgCBgCCgEjeAWHnRgChoAhYAgYAqOBgBH8aPjRrDAEDAFDwBAwBBQCRvAKDjsxBAwBQ8AQMARGAwEj+NHwo1lhCBgChoAhYAgoBIzgFRx2YggYAoaAIWAIjAYCRvCj4UezwhAwBAwBQ8AQUAgYwSs47MQQMAQMAUPAEBgNBIzgR8OPZoUhYAgYAoaAIaAQMIJXcNiJIWAIGAKGgCEwGggYwY+GH80KQ8AQMAQMAUNAIWAEr+CwE0PAEDAEDAFDYDQQMIIfDT+aFYaAIWAIGAKGgELACF7BYSeGgCFgCBgChsBoIGAEPxp+NCsMAUPAEDAEDAGFgBG8gsNODAFDwBAwBAyB0UDACH40/GhWGAKGgCFgCBgCCgEjeAWHnRgChoAhYAgYAqOBgBH8aPjRrDAEDAFDwBAwBBQCRvAKDjsxBAwBQ8AQMARGAwEj+NHwo1lhCBgChoAhYAgoBIzgFRztnGxeOQZFUdD/1Looc+2ku1YUYzCzCQA2zcCYr8f13ecUrMVmVeVLZmBzFDsURxKTYD8AyOs9YTVkWDh7vf+959S1dVMhdsZWRi+XcVoLUxg7kxQpQxgDPBYKCHY2sn0zzCwpoBB+D9iUrmmcBxmkYAPnA+FXWVY7RtjAkDeGx35WvZtPiYvMnyGewI8RxpQ/Bbbd9DeMdY3gZ8FrKvBCMPnEREGmCT4GZKKMH6iqPHctaTZwp15nl5z8oPPJuC+shhALZ69OvOqaIDlJYnFyWIDCMcTXwHm9pJCy05eqaw1td1j4STAARGwirmmdkjIDdMHpGnUHJqZux4jC1E2gVO4YIJvbUEXFjrKdsRy+SXAbuEgZRvASjZaOXeAVMLZkLK40mIzwWrKCrxyE3Eas5MLgH6LEDpy4Mzr3h9XwDeCOScljRbFTMIk5O9210SJ4jg2atDS0nWNGTXT86kxdy8RbS0O8PTHZMa7Fs70d8wk14x2OKZhKdjq01OE/y40lFU88URqGOJgldxjBzwKwPCCnJnG71c0m3bUpmKHtez/D7DS4c+W5a7NgQ6simeAxCYttVOyjL6yYENQEqFXNWxeWS0rqGts0OUW3byLxjcHMSrd9P3Qk5lFUduauNbVdjgHfZmqdmOzJ8tY92K7AHCZpD65OAR3zCTYUtjeRnfY1TOc5+/Q1ERPDZFiLuhrBtwgmiwoD0icdXKHTNtySGVibIXh5/4iOecbpB2taXrniZwUG8DNuo+pnE/rGKpkwDKDpSiW2N/UpTwR5BTK2cq271zy51k+CpmBtIDMUOXzJK287b6cC9GK7k4k7HbxynYHNCicF/8CdOP0FBhkNGTeexFTmkzBhbriAyPQ1TJcYFz2WJJZ+jPC9d3l7dJgM7UNXI/g+wKtqyoE3tc4nnckpeiAKB6Ya0GK2nZWlyuM9fLeCy7YY7Is+8boB6baf+8OKBzBvZQ+2+aid8r9XV13zGMUk7rdacdKniGtYCV6TTxFuQ0iC5wlxle1M5nobmnGcmsTbYMMRE6wzPXRbEb6uDt6a6ZBP5CSHZDFOw/dQbgUU6rLCLiyGpN+Hb4woA1s4MYJvAcRURByQnNDjqjUXlJUrckXwcfttWJJXigufy4eK+sXKyZKDmnsZzE/lf6+iuiYIngkdJ0QUI6NE8GGyI74J0Nh2Pa7C+PHtaQI5LDs76RjPhG3jMSLtV6tWfm4jI3yIL6lxk4unIdzlatsdRvBtIyoCLd4/RYJ3JKSCstPgzpTzVndIarOgf9siJaGjbEnKMnlFQmuKlZ+hD0syD7EhtxGZrPw1SXLe/+n2/ejcg+cdmG5tj6t9JPO4o8XyxKSh7WCeBXnp+Ai3X3xcNx0jZTliUcC3/WZB//kSqXIpKcH+5/Hlz0fQ9qaYG8E3RaqLempA8ixSDVYfgCGBuxW+27rGY12uyTwN4i4Um7eq8faCs5EHIJMbJ2lvW1dYDc/qHeEvJ6XkmiR43nLl7WZfpgg+WamlDzHOm8szHedsD5M69Hlj2wVxMTbUX4yzSPoZRQbwEueMkAP8GEBVuUz5vTRG9NiJJjImwzVOov7VRx3jiXOvEXw1iFZiCBgChoAhYAgYAsOHgK3gh89nprEhYAgYAoaAIdARASP4jhBZBUPAEDAEDAFDYPgQMIIfPp+ZxoaAIWAIGAKGQEcEjOA7QmQVDAFDwBAwBAyB4UPACH74fGYaGwKGgCFgCBgCHREwgu8IkVUwBAwBQ8AQMASGDwEj+OHzmWlsCBgChoAhYAh0RMAIviNEVsEQMAQMAUPAEBg+BDoSfHizUvrGLDsHwyZ9A5+dW0xYDFgMDG8MDB+F12vckeC3bt0K9m8YWAxYDFgMWAyMegzU0+XwlRrB2wTGJnAWAxYDFgMWA1u3Dh+Dd9DYCN4Gtg1siwGLAYsBiwEjeNuiGvUtKrPPYtxiwGJgocZAhwXx0BXbCt5m7jZztxiwGLAYsBiwFbzNbBfqzNbstti3GLAYGPUYGLolegeFbQVvM3ebuVsMWAxYDFgM2AreZrCjPoM1+yzGLQYsBhZqDHRYEA9dcWsr+A3Ti8OLXyZWxwGyapxferAYptdvha3rp2Fx9iU5E7AKZ9FV5WPTsGE2ZtnUn++7Qn7JhlBvFUywLal+0o7xVWp23La8NgZjtU7Rl9hPZb3VE8H/RYqFLKvEogAZN1u31mDL+BPGPq74WguflTbmZCfxI8dBfOGJ0LFRXNRgUQhZW7eC6i/Bdi7jgvpKsKBr0vdJXFTqLjEqClg8vSGMn8o20jfUXuM0Z1go3dO8ImI68WPQr1J3bKttUlhgHvL+j/HLuRc/U130uA79SxxrjmMfWqdUTqd6ZEMatzJmkrIoL46REg6Uk1mvDTA9JnBIYjDVd+gYvIPCs0LwHGhbt0pwPeB+AMhBq0DOleeu1QSfkldXz8utC34KHg4KCjweKM42toMCLwSjG8iOsHS9tuU1trUGh2qddBKorOdxZIJWWFCZHmyMmZJXU0/JC3ZwbLFsrWuvuCidlL8z8hvEj9a9YVzUYLEVdVLxyPbrOOvVftmubyw8Ptm4IGxzuqMdfJ0n/P4c5bHtPrdwLEW95zMutO4Kv1Rf6ceOMc0TA4GLn2yX7U/jdP7iQtmfGUtULiYm5MOa2FfyVD1tsxxz2CZi1BmLDnw5dMWtE/ziscUxAfkBTtd49snXxKw8Dk4e0HrWHlZzgUC1Q1X7MFg61OEEsxp3FJi0y20wWGKAyASNx2LAyQAmG6NMGZhty+vJ9gSjap00HpX10mQl7Ze48A6A9yPKi5PBhth63Wngjk/AYumDxK5esKm0MZXdJH4kDtg+OU/jIosFtgmkpv1B7eWYSP2Q6tzled9YpPoI+5vrXp2USzL8jsbi+YwLibGwl3xf4UeOU7SnpDvJwNVqkm/8hIEnTyyj9Jn6QOrX43HTuKirh2U4UV2FO79pDIt8TPU65gsxLiTmGfsoZmr8MHQM3kHh1gl+Yhy3ah3xEZjFBEzT9r2YhSfbbioofUBHUuXEKIlWODTjRCWvU3ltQLjkEgeRSDZpOzr3NqaDCs8paNuW1wYONTop7GrqpfZKLPxWu8NQ4IeyAy7sYxkjcYLkiNGXYTvGXvUzl1iIvlgXhZUr1wnO2yuTi7RfHku78Pr4tNhmjDiUCE7KyOjT1bgoEUjiu5z8FAvUR9or7Gquu5z4CdzTFfGgxQXfPmH7a/xIfmHsBEbaXynBO1zibSAxXoJv0jEr8ev1OJVZFRfN6pXioJd8Eex1txAVd4gyxFNOGDS+Do8OfDl0xe0TPM00HRmrWRqvtCiAxT0RvofNs7iK8jqn5RzV+BoPrCQQXPs0uYhgTpOpGJgUtDywUW6o27a8XgepbFejk8Kkpp73GU+EyH72N8lwbTEZcZ3gH8ImuUcY8PJ6CmyxHcYVyUmuB5lKb2lrp+MaG6tkkg6Z5Jq5Xh0XXq9KLCJuSgbVj4RP402sfvrDowUsCINEd46LhrpnE3IOp4GKi0y8e505/pUfG+mOMqOv00kv51r1nBL2KfNQVQx3db1pXDSrRzhw7g96ZPDjsgrfU6xnxpwaA9Q2M1ZZtj1FX50gyVGUwB0JFuMT9AAaErMr88HpB30lYatyLytHDMIpyondXq8NippZaNqOzr2N6cAKgdW2vGp/VGISBgiTao1OCsv6eux/JHG3zegHUrDd6SoTtjzm2zCRuMVATLHlhCCvK10b4tIzFkJ+Ggdej2ziwv5kwhXYVGKRtklspnZ+kky7Z1J+N5jMEhaVccGrqRrdybY6ewR+NIkepLgg7AXJ1fkRyzrqjrIEwae+TeICxz/iV5ln0/ZV5z3HRX2+4PxUGifSpxwjHpvKMeJ1L8mSNpHcGvx83aFbondQeBZW8PrJXkzYbpD3QvC8HctkJBKrdF4/xxUJmgNQDxIxYGkrSQSMDMxEJtnvE1Xb8ljPfj6rddJ4N60nHwTDNiF5oZ8CThJL10+smySz0MZvsfGuT/gUfugnFkpJsaxjCefE1648TW4ex6RujItyPwGLpE26cpP61Ca4HnBp7G+WnerK1/kT/VhB2Fp3h5+KG5YhP6k/53vCK8QD7xDOY1yQns4OItkUm651T8aExAGPU/lpfkrr93HeNC6a1NN+z2yhh7FfM0bIlooxx7dKGu5sdeDLoSueFYJ3STySMjmRZ58UiDUzy0w5D96+Z6O5oC4NDE1qpDsnpRBsWEcM3mSmqVajSb225ckE3+txtU4NsVAYalwioTtZ5Esx2YlJ3A1g52Mtg9rwCkf6kPptL4kjfk2xCFgr2xmvqmQsk1SdjWUseGtX4icnUjrmWI/+PvvGQmGj7a3TvdLfyQRB6TcQcZH4XcWnsz/rx0a6J7ITLEqYKez7i4MQ615PhbvKibqfJvWojhzbiTwZ79pGOUaw3wQfxjSRl9qSng8dg3dQeHYI3j8owbN1cmJC8PHhkGS2TYGZTgCcM/nhvdQpfZ2XBkI5UCiwaHWQkgnr5Z4IVfe/vB1kpwxgngy0KK8v+/1AyNvYHAvnY+/LxF5VpmbSLumFWFDtarDlwUsYpz7RSaYXbJpiQbJL8ZNbTQmdKuOiIRYKP72jMRsT4H6xUL5X/q3SXfhdrMjZNiUvwSL4ej7jQvq3dGtR2iZuQXE842el7uWxqLDgRQjLSiYAARsu7/OzaVzk68XxQDYkcaHsUj6uGSOEWxnT2D/zTCZXCyw68OXQFbdG8G0HkMmLg8CwMCwsBiwGLAZmPwaGjsE7KGwEL2ZvNoBmfwAZxoaxxYDFwKDGQAe+HLpiI3gj+PAa0EEddKaXEYLFgMXAXMTA0DF4B4WN4I3gjeAtBiwGLAYsBux78DaLnItZpPVhcWYxYDFgMTD3MdBhQTx0xbaCt5m7zdwtBiwGLAYsBmwFP/czKpvFGuYWAxYDFgMWA3MRA0O3RO+gsK3gbeZuM3eLAYsBiwGLAVvB2yxyLmaR1ofFmcWAxYDFwNzHQIcF8dAVd1zBD51FprAhYAgYAoaAIWAIgBG8BYEhYAgYAoaAITCCCBjBj6BTzSRDwBAwBAwBQ8AI3mLAEDAEDAFDwBAYQQSM4EfQqWaSIWAIGAKGgCFgBG8xYAgYAoaAIWAIjCACRvAj6FQzyRAwBAwBQ8AQMIK3GDAEDAFDwBAwBEYQgdYJfvPKMSiKwv+Pwcwmh5q8PrUuIrl2Mqm7aQbGQnsuK6BYMgObY7NWjkp9V0itrLduKtqa6ifLJtcqyVFeARILgLUwxban8lgC4RNx5cutfJLsKdDaaslR91SHGt2lTyuxaEee1ra3s2obtbzKetL3iR9jmwLGVvqIlviw/wtR7rulMSTwk7LimKv3n7ag81nsI/WPaCvtLZKYlrYpLDbDzJLO45tsFu1kHiGbPR5RTyGzmAcsACDqksesWz9WyYvX0ea8rVgnxJlwWRuHsf+8ndxHp3opHrKd0l3GUjo+ZJmIF5ZFn1SnXldVfwRO2iV4D7IjLZ/wPdhqYIYkJQe5B97LyDlWXesTfNKHA4ESVH6AVNZTtvpBzXapQHI2su5KXk09GhQsL9jKeM1CkHp7qhIFqqB0V5hpG7XuLg5cTOh6bcsLMPVxUK2TFlpZry4uELPgU4mLlg0KW1dG/SH5h/ZJG9DYpqW9nFfaqIShHWLsKN21jTIuUDaPCajSnWOSx6knz9hOKSJO5guLujHi1OvWj5U+ULGU5B+PBBNrZ7wEdA0PK/VK2neqV4VHWXf0qch7KndWx1lUx8VEUQgZsXBkj9oleBrc+STEjhxbMhZX434A0zUGnq/x6oagdw6sTm7d+wcDKAa+DhAprbIe2ioSD5DePtGpJKcHHwVuSNKyXzwWwZfIQJ0Qw7HJKRiT9aSyvR5TX2Mwsw53T0SyTuRVYkE7DxW6S1ySSULb8hJ1ezqt1kmLq6xXFxdaBK30YgxyoUtEcmcH+8JYW4u7YyF2uL7/TPtNins5rbSxVpiIafJ9jAuV7BMZ5TKX0KcmRb7wEwGJTSLGnc4jFnWY9eLHOnnKdhrDPHY9mU2urYgx1bKnk6Z61dXL49FUd1ePxk+DOJu13NkTenPXaHYIHlcakvw4seP23SRua7tBT4O6mIIZ2tb3iYCcJckXwK1okmt9YeSCIyYKESxKbk29NImoIBNJLl2dyIEo29AxD1AAN2GIyTFMIGQbpWsLJ6kOSmQNFmk7qWOKU7C/bXlK2R5PanRSEmvqpfZKLJQMGSOiIG0vimi8ZAk+1Uc06vkwlenOyxOSpANlr25DCT2rv54Eo0S2lT5DLnGY1d+OSPVO9OvpNJWp7Yoim9Vj22I7Psq375ynkp0DFtd4x0M0aHSY17McG83qVeGhJwepYnL8uH64/1KccX5SsZnKG83zdgle3X9y98I4OMmJdH/OOQadoWZwvColJ8j7aP44DPI2HCGDA+XpAIk91NTzemr7BCGL++lcJ8glkkvumwXi87WSYESsSE5yPchs44Bki0mGklmDRY3uOkHzZA37aFueUrbHkxqdlMSaeh3jwifjzCSY47AUL77vqkRIE+BWxwd2WGOjwkKe5MaRu4akzAlYtqDjNH6obxeHKn6S2Of8oZ7NQVnzhkUzzJr7sZm80mJAAIwYVeIu6nV32FCvhjFUhUed7uR7NVmsjjOsO+u5szsA56x26wRPmtOAZZIWA5UI3jticooeKMPgIwcnBK+D0gVU3f3hWsRK+jgdYiJ157pPlFhfz+nt7HRb554ck4Qlg1EeqySakqtMZiiPg1lerzW6h8JUByWiBou0ndQRdZcJN2DTtjylbI8nNTopifX1KuNCycisulIcc/U5DkQZxlQ5dkWFJofkFzlm620si3T1Q5xiBRkHvCqXsYB1qF85MXareR6bhGXahjtP5OPlVrBg+eGzKRbN6pFNjfzYQB5hkDzYGPRuCY+eY6OB/hwXjfBwhlEOlTGRxIGKGdSdZSf1BEwjezg7BO/hIkeo7XgXiDIB4kB25zVb9GFnwBNoC+7QiSCdkcYOmtaTqyiym4MKRdEAQd3L/cS6WCYSXWjjty/F09Vui1LUjer2d0QDoBrjaiyqdQ+3FrxmcvC1La8/413rap209Kb1ZFxoCTIuXAlhI+MmaZAvT7BP2vRz2thGH9fpJEP6mvRIEiyVl575cGMkbsP7SYdM6GxUKV7nH4smmHXjx1p5lCPq84Buz8D1/6nlOp/xpExKb1Ivj0ducuImDIGwfUd1cYb9l2JJ5lmp7Aget0rwDswYcO7cEYYbzH6mSYGJwMsy344Gbboi8YM+N8h7dIoKCkGmqbjKeiq5uMALCS6RRzh43ek4JHFnl2unZeh6QqskSYqS/g+VTWVxlVgktzi07nLwaxvbllfWuPsr1TppWZX1FIYZe4Pv/cQtOQ8xpLujM+pT1KeLqr9Moz4uVdqoZGobVVESqySPCT0ZI6qdOCnpIHKAjjPeMaieoAqxXR+W9GA7EklN6lGdhn6slJdgm6gRThGjupgKFbs8qNQrkdOkXhaPzG5Myd/cV4IFycv5J6nHzUf5s1WC5y3tOGOKZO9A560kTdiuTBN8lMEzsPYHLgUMrYyjnm7bXJ7LFbS+zjaRrsmAVWUq2FxCDPapdh6X7P1ZH4azGaQkW+KM+mib85ihbjW6k1zvR2VvNba9ymtjsOZtbI6F8n2lvemDqC4ucqsgtonkJvJqdwi4YR+fHbGQvhW7TMGOMJlH/8dYinJ5fKd4OKXJZkHqCltxnWpjX+m1PmxPm0adox3d5AuW160fc/0qHALucuy63rDtbBA8Ss/p1RoeJYIX+SXYK2yriDPGnD5nM3eqjgbnpGWCHxzDTBNDwBAwBAwBQ2AhI2AEv5C9b7YbAoaAIWAIjCwCRvAj61ozzBAwBAwBQ2AhI2AEv5C9b7YbAoaAIWAIjCwCRvAj61ozzBAwBAwBQ2AhI2AEv5C9b7YbAoaAIWAIjCwCRvAj61ozzBAwBAwBQ2AhI2AEv5C9b7YbAoaAIWAIjCwCRvAj61ozzBAwBAwBQ2AhI9CR4Ldu3Qr2bxhYDFgMWAxYDIx6DIzaZMAI3iYwNoGzGLAYsBiwGNi6ddT4HYzgbWDbwClQqCcAACAASURBVLYYsBiwGLAYMIK3LapR36Iy+yzGLQYsBhZqDIzaEt5W8DZzt5m7xYDFgMWAxYCt4G1mu1Bntma3xb7FgMXAqMeAreBtpmszXYsBiwGLAYuBEYwBI/gRdOqoz0rNPlt5WQxYDFgMdI4BI/gagt8wvRiKYjFMr49AqmurJ6AoCvpfPL0hzIBdHXd9YjW2XQUTWG98VagzG8G5atz1meqc7Wv9NCwuJmCVt1/qzDYpOVTfy0/siP0W4OxlvLzdhFEOx7y8rL41fsrVjzrpftO6lfWEb4uxadgg+o9tCgh+l/j4mEAcQ7nEWeAnZUXco19SfXs+T/ydkxN1STETfkyw2CrtFnah/Lbl5XTu9lq1Thyz7rNzPYeJincZMwkWTk9sk2LL/Wbk1WDbrd25+p1t3ArKvxTXudjM6O7jHfvQY2ADTI/V5ynKRVn8WJ8qDBnL7j8bYVET07E92pZgJP0oy6quI3YyltIxV4lt2W4jeA9WbgAoMvf11LUKJ0hnzxXBk14cCKRXEmTSzhBY1XXIhjDI5AB2A5QHreqX5PLg0/UoYJV+FfWknj0eK51qsKis5/Hh5K2wQHlZXJLBlemX+qud6CWY9Wh/KZYb+LsSi61aJ4WFn7g6nHS9tuWVbOoBm2qdtO+a1OMxzjHiiLAupt0YUpNmYUNJXg22c4mFGrdCX6lDWXeHJ1/nXIFt6BqPn67HiIuxKgylTt0cN/E3yqusp3JCYqPyo5dB9qMtHC+J7Lr8432QwzZnsxF8RdAGhyYzbnIyX6MALWDxGK70mSzdQHbXeEXrBzcHdk2fOSc1uYYOjwNJErJOXm5muBimV+sVvOqDAozt4VlzPJeBrgasDGaUwYSe2EvtJRaIY0VdpVcip6qsKRaV9VJ9UjyEHloGY+0SUUj+nNjGpmEV7gpJ24WsJsm0yubK6xSjHfzt9cvHD8ZSTEQufnwsJLikcdGmvEr7JH4djrWvqsdIx3qI6fgE7coFHxPOcYygjOBnwglzQYIl65uTV4PtXGJRGqusM3/mdPeTQrRfY6kngXpS5ImxZoygLovHJ2CxjEfWo49PrWMfccE6yFggfBrs3Ep/YxuZD2VZJbace/SnETw7JfNJwZ0Ek7pGjix80Hkyp2uLYXrabd+7BOCCJgz4TF/9DdqUUJKBlOtPBY0OCh3wfrtIBhzZ6JOZPCaZngzw+vh0djuulDSkjJyuXV1rikVNPdRH2ivtUrpUJIO0vWhTsj2Upfpon/QXH+VJmpaX9u3OiaDTOJFYpHYGP7Ytrw0sanQKPsB+OtVjkk59L88Ffko2t5X28DXZvsOYUzKlrKbHnWyMcmiiIm45hQkN6VChu9AvzSUU/zy2QrzE/jAus2OE41DGn+hHx7OWV1/WFIum9fRqHG1ZPD3tbtFW3uLQbUoT/QqbU2xzdhrB1wQJBZoI7niPVJAY3Wdd5YhsfJULTlzNU/DO1Qo+SQ7JtmrO8W72HFccoQ4PJIGLGpR4PR2Y3ta4i8F12P5MAIuJk0siGV2EDkG/jteaYlFTjzBIdBf6oi4hNjhZBb3SRKCTDbXLreARw5Is3bY5Bpl2Gb9GeTVYpL4WyaY6LtqWl7En4N20rEYnJau+HtrsdibSeqiHu4Z5QhMh64jlYjfEx1FOXjW2LKufz1R3F7Nxx4VlJ9cpFqL+9Vg4GTkSItswr1bEO5UnYwTlEKYi/mL8sr69fDbFomG9RD9na8SMcp2yzclVMUMyYgylMtjuHLZcxp9G8Gpw6wDJAauueWLDgUGOG5uACXyABB3oy2ZlBe9luwkHEmNKKsnAzNlIQVQmVbJPBWD9akIHrBgEqKMcwEngUzs/eZoYT+rm9G18rSkW9fWcn93DQG5bsIwVDiKqV7IzXzfUT/EtbZHrOOTB2tdnhb+dzBos0nbSj6mPKS47xGNP8nrAo+cx0gGL4GsR6xibwXanqx4XrD+2icmeJtl18kJZWX5fsdBLvqDx57ChiQD6MeiXYCHGKuIQJw6iPdaRsSTalHIQYstjpqJN73jU+Fvo1Hlnh+2JxIw6ZW0Jt3M5LvBTY9gk/2hspax4bASvnBiBCc6RA5Idxtd8EqEAFglFns8KwWd01s7WwZIN/jTRksw02D0eSd1IauV+QmJL2lQN5oAzD+CMbVn9a+o1xaJpvdKWmew7SeylAS3rcvyUbEUcReJP2nRrf7Z+6o+kj2osEt2kvYnMGBfufmpM7DJOepOXtSmxoVOdahv1uK+qJ5Nu3M1zCR3bBBJCvSROQU9te528dIdNYtvJziblVTbWt435oVb3YG8SBxQvMs4TwvftSLYYI4RtaSdVytH+q7ehXLcpFrX1yN8ZnfB6mAhVxQXqlMeCbElleJy0PmW7sO2o/bX6qloXxNpp6ho51c9QKXhxxefr+7K5InjSiwOJ+q5eRVLQJMnZDQqdgNw1DByZoHUg0uALg9HVc4k9JgOUQ/WkfnysZOeDNOrRrLwpFpX1FDbaXmoT7PV2JeeR2Mr6pu3JNtVfuU239mfrd+ijEosk8eT87WI8gxP7WMWjrtdUXtYmQSRNyqtt1Jg3qyfHRDlxq3gPelaNL+w/kafONWZNbO1Up7mNIv8pP0rMUt1jGeIQx0NiB8WkXvGi3qSbGFPKFmojdArYxj5V/QblzbBIduskFrU6SZ87+91EUF7n1b+3S43VBDNhj8Y2b78RvAAsDQxyPBO2r6eukZM5gL3zePvFlymCT2ehnABrdEh1qjunpEJ9yAGQBBL3pYLIB0fumqrvv7+qBh/bnStzAz/eSohBGHVl/GJZnY1Ny6L8eizy9fxgZn8pez2pc5nyocPC+TxvTzZ5YawoOfm2TW3P1iv5thwXVVgw+ZAfUz1Jbs73EifpA7RNxEUX8rJ2cXw2/Mzb2A0W7Btng/S1yw0eC84DSq9yP9Gmsjy3is9jG9uxPt1/NsJC+jfJhVGHjO7ebuwjEnzi+8x7IlBmdowwjqRPGk/d2x51d20bYcELlSTHar9n/C8xlPEuryfPbSiZSf5h3cvYlnEwgufAsc9ZfQkPB6V9lgehYWKYWAxYDMxGDBjBG7EbsVsMWAxYDFgMjGAMGMGPoFNnYyZoMm2FMUwx8Otf/xrw//HHHw//fA0/h8kW09XGXq8xYARvBG/JzmJgZGKASRyJfcuWLfDYY4/Bo48+Sp94/qtf/YoI30jeSLNX0hymdkbwltxHJrkP08AzXdsnGCRtJHYkcST1Bx98EP793/8dHnjgAfrE80ceeYSIH+sZybfvA4vrwcLUCN4I3gjeYmDoY4DJHVfpDz/8MJH63XffDXfeeSfccccd9InnSPhI8jgJMIIfLDKyyUH7/jCCt+Q+9MndEkP7iWGYMJXk/tBDD8F9990H69evh1tvvRXWrVsH119/Pdx4443w05/+FDZu3Egkjyt8XMUPk52m68KO8178bwRvBG9JzmJgaGMgJfd7770Xfv7znxOxX3311XD55ZfDP/3TP8G3v/1tuPbaa+G2224DrIOrfFvFG2H2QprD1MYI3pL70Cb3YRpopmv7ZJKS+6ZNm+BnP/sZXHfddXDFFVfAhRdeCF/96lfp/6KLLiKSv/nmm2kVj/fjcTvftunb94vF+uBguuAIftQMNnsMgYWIwLPPPgvPPPMM/Pa3v4UnnngCcGt+w4YNtBV/1VVXwXnnnQdf/OIX4ZRTToHPfe5zRPK4mkeCxxU8bs9jW5Rjf4aAITAcCHR8F/1wmGFaGgKGQBUCdeT+zW9+E84991w47bTT4OMf/zgcddRRcPTRR8P4+DhccsklcMMNNwA+bIfb808//bQRfBXIdt0QGEAEjOAH0CmmkiHQFgKdyH3p0qVw8sknw5IlS+C9730vvPvd74axsTE49dRTAbfp8T78L3/5S9qeN4JvyysmxxCYGwSM4OcGZ+vFEJhzBJqQ+2c+8xki9Le//e3wpje9CfbZZx/44Ac/CCeddBJccMEF8KMf/YjuweP9dyP4OXehdWgI9IWAEXxf8FljQ2AwEWhK7kceeSS89a1vhde+9rXwqle9Ct7whjfAe97zHvj0pz8N559/PqxZs8YIfjBdbFoZAh0RMILvCJFVMASGC4FuyH3//feHvfbaC/bYYw94yUteAq95zWvgoIMOghNOOAGWLVtmBD9crjdtDQGFgBG8gsNODIHhRqBbcsdV+4te9CJ4wQteALvvvjuR/bve9S741Kc+ZQQ/3KFg2hsCYARvQWAIjAgCvZD7C1/4Qnj+858PO+20E+y6667wyle+EpDgjz/+ePrq3OrVq+nrdHYPfkSCxMxYUAj0RfCbV45BURSl/7GVmx2I66ZCWbgGALLd1LrNMLOkgGLJDPhWsbx0bQxmNrXnn7WTrHsDuZtmYKyYgrWye2Gf1B+rSBuLSdGK5HC/BVThotrIPql9A31lmwbHjbCQ9hYFTK0TgqVdwm8A3r8cJ6ostie8RJnCD9t6DKOeEcMi9UsU29NR7KMe58711sJUipPEUMZF0BTbVPWbkSdxP/P67Pfc8atw+LQ8PlCH99xxWx5X7kjuSOw77LADPOc5z6FV/Cte8Qp45zvfCZ/85Cfha1/7GqxatQruuuHv4fDiDLi25mty1Vg4nSlPCP+SuVL3BIu25QV4+zio1kkLra4nsEh8HNvonAASo1KcV8tT4yfBVmvb21nUtypWndzqekJ3FRf1+SLKizgpWznPJPiSNoRlvb69oTG4rVogeA2YA9tfk8lMOFE6CUnCnUfyjOVRdlqnX0hJT9aJ9Iz9l2SHQSbq+GtMcqQfDySSx7q7gHVEjsd8HcANXn+O8lgfT4qS/J1OHPxCRknZ7i80wwIHpLBfYeYGaw4LlB3tkFgIPRnfYL+LidhO1FWHFfJUne5OmmHhJ3Csr8Ii9sdxzLgof2d9zEkv79+SPHD1z1qLL7G5Dy790wIW/+NG9RKbTuS+/fbbw3bbbUckv8suu8DLX/5ywCfqP/GJT9Ck4AcrPw/vp6R5BvzoqafoZTnRQndUjZn2jxojXneHja7XtrxU317Oq3XS0qrraRsBY0bGD+eOEi4xFpTsNH5SeYHgkn61uj2dKT0qYh8FV9fTOsm4wDZx3Ot6Sh7hFLGRhkh58bqTVQRcYskoH7VO8BS4vGoh5xcwtgRX+kwOLim5a24VSI7jNj7AeWfAJQCf+MIg6N8lGAQxkJz8kIileLJhDGbWJSt4OaCwPpGUs5HskbqmdYN8HcDhMg8OKcNfG5ucgrGWg7QxFlJBmYjI9jjY9EBUjfSgpyLEYAymJsdiwvPJK+sPKa4SV1mpu+OmWHSsh7pNTukVPF4L48BPbNnHfpIztQ5jMWIZtM/JozZnwfX+DXUb/3ExFIsvhBv9G+qakPvuL9gWttlmG0Ci33nnnWHPPfekp+o/9rGPwTknfgCK4m1wzv86Bw4rvgBrfvObLMFXY5HYIu0X4wVtlDHTtryAYR8H1TppoZX10F4mdN2kdKZliGKJWY285vlHyO7iUOtXnTur69XERaJHjAuXJzru4EqMhCyUMxu5U3QxkIetEzw5hBMUDejCA+u3dOnaGMysdNv3lMTJKZ5wfRuX6PzWrCxvBUZHrJFAqok2dJcGDuopByyVu8ScHWAisQeZkiTjRUx3dNsiTkDEBEL0o5r0fNIDFtiX0kPriwObt9RTtdIyxoo+A54uafAkT5JilJfqHUt6P0plarui3E71OIGlyU+eV8nmtrE3CKsV2R7g2bVnQfGnK2ATv372/3wBiuJUWH7jjdCU3H+8fBsieFzFP+95z6On6d/85jfDRz7yEfjSl75EPz5zy9VfhkOKz8H/ffzx8F14vN/v/u+HFUsKwF0EeT42cz88e88KGCvOghu4Lp2PwYp7nnW6L1kB93MZ2kJ125bHevXzWaMT60+fNfXQvjNXEFYurj0Oqj3qeAOcVUg8o973z+Ak2GNWI4/qnXmD94fHWvqh1GfsI/q16lqNjUpuTb26uFAynoUbziygIFsQl7NgBWLgt+EpxjL1S9e5Pxl/SbvOdlfhMb/XZZbIHbdA8PJeKB6L1QcT/Mq17j775Fp/b3oK1gYiR7Vc4kJScBMEXAm7BEgkqurmzOj2mk6UWUJNRaYET+fxPrTT29tO+kYciNQyBJ+SHXXpbU1JDevGyVCUnarZ/XkPWOQmIOyvQu6MJNqQbbyTg2XYt9j1YIJXkwe/0uUyFomy0mtc1vNnUyzq62EsuMlZWo9tdmMmTjClwthG+zcnDxPSfTMfguJPL4WN/G75K06Fojgezu5wzx1X67hyR3KHNU4XJPjnPve59EQ9fhf+0EMPpbfZXXzxxfCjb4zDB4pT4OqHHqIfm3nyySeJ6PHFN08/fS2cWRRw5nV4jP/3wKUfLuDIy+6Bp687E4riTLp3T2UbL4UjiyPh0o1Pwz2XHQnFhy+Fe6jN06Ju2/JYr34+a3Ri/RthEXEq2f+0xwTJS+Ii5CKxBZwJ23iu5FGZwxlxv3YCfSz8oHTuFpe2sBD6iLhwMeR1UvHj+i0mrnVxlmtD14RcbyfaT7jl2vSFRbfYtVMffxMC/3/3u9/Rjhr+xgTmg9xfCwTvk5EnPEVMnqww2RGZLZmCKXygDrclfZlLckzmvtwnbiZN2r7NEGTOoOw135eb+cXJQ0ywVaspIS0leN5W5NkkbZ1H8nKk7hP5ZJmMHB7xwULRkzsknb08PFZbuZoASm3rLvSNhfcV64N9JYRMfkvJl/rVeodJC2OZtmE7Evl4GduqHQ6u281nz1g4DLLxg7oGOxKCp/6SGJE4ku4JwWfkuXvuz8Bvr5+EYmwabucfjrn4eCiKP4fP1jxQl5I7E/y2224LO+64Iz1Jj9+LP+CAA+DYY4+Fc845B765/GQ4qPgUfOOuu+CBBx6ARx55BB577DF6fe2WLeth+ZEFjP9wizo//OL1sOXny+HwYhyu2eLL6PxwWP7zLbDlh+NQHLkc1nMZnlPdtuWxXv181ujE+tNnTb3UXomFkrEF1l98uMYmlF8D44XHuoO8a053uQdz3vjpCdZBXi+Y1Nio5NbUq4sLlkHx4GOFrqHt8tzJpzjzbQi306/xcehtQzl8rQZz/JbIMPzjb0LIn23myTaTfUr07RE8J2kkPE5aPoFSIhbJVJ5zknRk7oIyJG7Rpu3VmiaIJBHnSIJIJibnUhXUNSR2XUq2MSa80g3num44o/4cIdJkwE8keHtK7ZSERr0dNMfC4RT847srEbrQHas436bYOVnRHp+QchiWsE9IsDezs62aYlFVT8axtA3jnPwo/U7xncMlToSq5E1e/1t44s5pujf+DX/PffqUP4Zi0X+Dv6x4Wj5H7kzwfB8evzL30pe+FBYtWkRP3OM76c/78l/AnxQfhf+5di389Kc/hTvuuAPuuusu+voc/iLdFacUcPC5N9Eb7zZuvAJOLQo49cqN4I4PhqXr8HgjbLwSdxhOhSvweN1SOJiPN26Em849GIpDlsJNGze2Lo/6xj77+K+2UcutrJfY6+wX2EjdJE7y+sabYOkhHusu5BG2p1zRl/0Su0obla49+pFjQcSG69vZ7uIKMRdYUL9pufML6irHoTuuwD3RX9o8KMf4uxD440/4C4842X744YeJ8H/zm9/Qqj5dzbdK8GGrnbcYPUETIVCSRrB98vJlTPC8okcHhGu8dS8nDdm03P1FRUrZRJvITElGnSc7ACgvEJWePJSSPHej2uiHjrgKfVK/kQBUWY8nzbBIbJR9JTo5UvLE1QRbngQwZgkWJcwU9lKR/o+bYZH4p9JG7XsX45HQyS62OahePXnh+7NE7rQtfzWR6fEX4z33afhviwrY++C/zH4VrorcJcHzNv1uu+0Gr371q+lp+j/7sz+Dv/7UYfBHxaEwsWIFfOtb34If/OAH9PU5/I48vsr2yvEDoDjwDLhyzRpYs+xYKIpj4Tw8XnMlnHFgAQeMX0n1zjumgOKY8+h4zZrz4NiigGOXleu1LQ917Pe/Wictu7qew8LZuwYIC48ZtQm4+DI6R4wOgDMu931cfgYcEM6r5ZEP2B8KZ61rr5hU26jlV9eriQsVPxl5jBPVE9iQnfJctyVbFX6Z8hbipFdMm7TD34XAH3+6/vrr6Weef/KTn8D69euJ7HFXbevWrXT7QpJ8ywQPYeudCI4SH2+l+q1d3mr3ZYHMKWnjBCAmQL43rkk/ZMK+DyjB0spYEmZFgs2QiiMyP0OUKzO/hcwzx7jidQmfr/Mnlyt5CgdhakKmoqSvw45YBP/oGXHwn/ensyniGeWKdiVSSwiTCZ93LdL62Fd6rS/rdeOoc7QjPugW6+brxXKe8AaMUruyPs7HH269PfPM9TBZFDCxRvye+3cm4Y8Zpz/5SNfkzgSPfsNtevxOPK7iX/ziF8PrX/96+k78nx66P+xVvBX+4vTT4eyzz4alSz8LhxeL4Oi/WUZvu8NX2p52GPtXX1+27DQ4gvV7y9Fw9rLYZtnfHA2LuOyw04Ks2ZCHMvv9z9uI9mmb8/Wwf4FFcQScJnSKbQooJE4So6KAI/67tKOZvEXHnN237Sl2UV9pe49YCHujXI4njYcsV1gQThrTVGcXb1JfieVgH+PvQuD/hRdeCPhczIoVK+hBWnxPxa233kq/+Iir+SeeeIJW8rxV3xfBy1Rmx4aAITA7CDhyf6anl9jUrdyR3PH/uTu6ZIrb9HwvHr8Tz++m32+//eB973sf/ercRz/6Ubo3f9xxx9Hb7vCNd/haW/s3DCwGZj8G8EegPvvZz8IXvvAF+MpXvkJk/73vfQ9uueUW2LRpEz1H8JR4X4UR/OzkZJNqCLSCwGyTOxL8gYviaglJHrfq8YE7/F48vqf+ZS97Gbzuda+jn5PFt+Dhi3DwbXf4IB6+1tb+DQOLgdmPgQMPPBDe/e53wwc+8AGabONDsOPj47B8+XL44Q9/CL/4xS/gwQcfBLwfjw/dYe4wgm8lDZsQQ6B9BOaC3JHgP/9fI8HjVj2TPG7X46ts8Ydo8LW2uKLHF+Hg2+7wlbb43nr7NwwsBmY/BvDV0viPz8bgrbN99tmHdtWOOeYY+Nu//Vv4xje+Qav4+++/n77Kil+jM4JvPyebREOgFQTmityR4Dd+PW7T83MhvF2Pq3kkevyOPL4IB+/P4/Y9/iPx279hYDEwdzGAPwj1+7//+zTBxhdS4W9LfP7zn4dLLrkE1q1bR9v0jz/+eLgPbyv4VtKxCTEE2kNgLskdCR7///5EvYpPiR7vzSPZ4z19/EfSt3/DwGJgbmMAb53hJBtvneFts/e///30I1IXXXQRXHfddfQVOvyePL4wyFbw7eVkk2QItILAfJA7k/zV5xSwx+55ouete1zZ279hYDEwPzGAE2385UdcyeMLqQ466CDAB+8uuOACwK/R4ffk5U872wq+lbRsQgyB/hGYT3Jnkn/0uwUg0U/8hf0bBhYDgxYDOLHCXRO8LYLPPuDDjfjtBfxKIH6XHl/IYwTffy42CYZAqwgMArkzydunu21hOBgOgxYDRvCtpl0TZgjMPgJG7kYkg0Ykps9gxmTrBI+vv7N/w8BiYHZi4Ne//jXgU6+4rfbQQw/RU7A/+9nP6H7a17/+dfqxF7zHdvjhh8O+++5L23K77747fX2tyUtsLFEPZqI2v5hfeokBI3ibkNiEbEhiwMjdknwvSd7aLNy4MYIfkuRuK+LZWREPC65G7gs3SRtBm+97jQEjeCN4W8EPeAwYuVuC7zXBW7uFHTtG8AOe3IdlhWl6zs4Og5H7wk7Qw0jQx/Ev/vnPt51oPpwvPxrBG8HbCn5AY8DI3RHD0jcWcNyJBXxvpoA7/Zv0MGHeOVPAcW8s4HviWm0i/UoBxRu1jFDfy+I38h33lQ6kNFPA26pkNdVnlOshnvNB8MKPS2c6+HCU8fe2GcEPaHK3FfHsrIiHBVcj95ickeCZeNPPjkQskjgRTgUpU9lhjvzvxIlAUUCdbNTJCCT6KEyUBN7stzldwRvB06uk2R9G8EbwtoIfsBhIyf3ee++FhfxVOF4JKnJHgu20yhZk873D/CQhR/Ce0CVhM+FzopSfd55YwJySlrBD6jHox7NB8Ih93cRr0DGZa/3mleA3TC/WM/PxVYFsZNnE6riaWzXOs/nFML0+Xt+6fhoW05ZQcr3F5F3Zt+wj6IF6TsAqWbZ1FUyE+1MVelL7XBm21dclRpT8PH5RT8Yqp4vATunY7HrsQ+uUrpA71SMbhN9j/bzusVz3G69X24p1Fk9vCDGW6trreexb66Tkqbio0tHFx8SqXwP+AMTDDz8M9913H9x+++1w/rEF7H/SBeJ77u+HvXZjjHaEHZ+7E/2oy+4v2BZ+vHwbNYuf66TSdn+4DS+35ruW7wmcxkhGFpO/JHgmp9L2v23NN44txrDNyRD6ygi+fudEjo95I3iXFGVC9OQ3Ng0btm4FRV6BADbA9BgnNdlW15+NJE76eN22rp7IkDcSI+oX9VJtqEwQDMpgeYFg2b4ow5EETwz09WaE5WS2iYmyqxIL7xO2MVMv+Dj4N51caN0r+0XZQgbFljhHDJmE28QB5VbqFHzqbcr6W9vLOn5x1ePw6KOPwubNm+GOO+6ACz/hYv4P/3wCTjzxRDjiiCPg9f+pgGLXlwK9xOY520NRbAu7jSC5Y7I67rDmCU0mNz7GCcJS/vW7GoKXZM7kJK+hPLwuJwLch32WfcQYtknwuLNiBF/Guir+5ofg/WqmLtly8l88tjgSIbfDa2o164lxbAImcALApJIm2T7ONZn6lZbYWVCrNe6H9PWreDzuoBfavHh8AhZL27zNE6uxT0nwzma5u5HVoQGxZNuxDZnPpljU1SMyG5uGVbiLk5Bx0CfRvU5eaIP6Yruwe+JjY3wVkXxdzCkZGbtz5U11oniuspN1Hp+gHZ7x/gwtnAAAGtVJREFUH26BBx98EH75y5vhy+8toPjz/wEnH1rA3h88jn7Peb/9FsHvP7+AHXfezb2hbrttYbedtxm5lTslLVwx90HwvOLDrd1+V/C2Nd+cWNB3bRM8yzOCb+6HeSF4R96SrPRKBhMpE/zEOCZrV9ddm4Bp2toX7Zn4pzf4dqKsYaLOJe94LSVTd96JLEhfJnUknfHpyh0Id4thAlaRLTn9U4LnVT3vaKS3AxDTVO8yztHGpmWpzCosmtUjjLLEl28fJzRV/SarauF/TcZN7a2rl9cxFxc0oQm3ZwqIdqB89u0q+GJRwPg1j8EDDzxAq3f8ScdLLrkEjj6wgJe97UPw9re/Hfbee2/YbecdodhuR9hu++1h9122gVsuaj7oq2b7A3kdH5rCJ+jxvrfAD59gx6fqa3X+Spwc1BE8NLkH3/bWvHgYjJ8twIlM7lYEPvSH9nI9/CZAjuTSZxV492HpYR478Y2DbuoyxqgH7oZ00oPrMyFXreBLdhXOX6lfg++E/4MOPPlD/yTljfutwJP1p778zk8Og0He0Rl8gqeVq9vapiTJqz6xmnXE70lRkH335FWVzB2ZxqRcTS6uz0i+oQ2tKmNiV+Tvt5CpblOCT+oxNnh7I9idrIDDdVmn6+OmWDSrV0nwJd2byXMTpdwEyW3T58i3d1wa6pS7PZPEr9PLEfwZ1zwK999/P9x2223w/e9/H84//3z4s7cV8NK3vB8WLVoEe+65J+yyyy6ww/bbwq47F3DLRaN1z50Jgj75ifYTI/nx1+Mw8eaIjtvLr9AFkshs0WN9fqgOCRaTeCobk31biZx1UYTOBJXox88HSDtZv+zOBssp3NcHsT0SJpOVIr0u6uZ0JoJGUmWSTR4GzPbp63CZfFAyyPO6sx/5k3WQWHBZ+MSJkyd6Zavvtx888TYPyuRJmNS3rdgIdiRY9np9CAjekWnhty8xESpC98kzbsv7+rxy7prAeIuXZ6q4Mm6+UtNkIQggJSxJ0FjGq1h5XemOsvLERX1m2rW/YsXJQ1MsmtWrIviy7g3kEQZxEqV9MRsE30An5UOefLl2ROqoc4jVpgS/B+y0QwHbbr8DvOW128Kj3x1dgkciyCZ0QU655IqJXLZjcujle/DYVpIFnTOJVKy6KxMyP/CXEDnvIsiJBess+2a5dWVMnkjsjAGTXkrGjeoy1jkiz0yGWEeWXdKfMSjKkya2i/VmWfhZVybrVfXL7Uv6CNm5MpaXYid1yrWTOs3X8bwQPD/xXreaciTukjUfY/DjKlcRPJJjsjXD52H1nE2ynGybfWrCEcRdKztJ5OG+8FaQK01afZdsSMm8CcHLbfoO9Wv1rsekKRZN6uUJPq97rTyKgxQzbYdur8vSyUDTcy2zu7iIscyTyfj5+f9ds0X/ypfAjsWOsONOz6Mn54nkv9Nhu7qlFcFcJyokphyBox68GislXiSkhIw4uVcSfBU+iSyWwzrxyr8pLkwWJQJjEhXb6FyX+1J9iPq8ouRybke3NpKVayqrSV3GuaSzl00YpBOWDvfgeas/1YfxzfVVV8a24yfblJIuX0/7pLYN8My248lKEm9Sn/k8nh+CD081y4TskiOvxJnUiaQDiTsCkwSPCZbv0Yek7FdyYVXcB5mxTOqTV1qkjyRTJouEmNSqWq/2SG+WJ/VTbVgufiayUQfRnuTxLgDKIzk5HaXM3o6bYZHcC6/AjGRJvWt0r+y3EjNtnyZjXcZ+7vazUifp05zv5GQv1HVjID5k90v413/9V/jOd77T8SG7N+9dwCMjvJLPJUlO+ClpYyLn+8/crqoul1d9ym1+rJMSOsvNJv/MpIHa10xagh5MOBXb1UGXjCwmstLEJ6NPk7pcJ2tjjZ7cLiXaYCNPPvC77W/U99BbJ/gaPVmfKt+wHWlMUTuWawRfTqiUHOXKVRAWl7lVeI78cXKgr8fk7Mg0Pkld7jvWbV7mJhPphCIhXiKbuBLTuwheX7K5gnwrySrpRzyISDsWAjuyLZkA9GJvXZtGWISJXIpZxJz8nBJ8je65fjlWeOfGfZbxnQ2CR4xyOpUmZCou5MQ2YuHaFJB+Te6GG26ALx9VgPya3L77vh52FWNnm223G/ntek7E/MnkKgker+UIJVeX5VR9ptv84JO5kl+zRV2Sy2RQQ9qhTYO6nQhJ6Zkhd+yLyauuLvejx1fMcXw9nQDUysbnAvzLh3C3Be/F47MV7Ccj+HZ25OZtBV9HHlYmk74dL7R4wDfZpS+6ufbaa+HrX/+6eNHN4bDvvvvCK1/5Svdd+J3ci25G7Z581VYukhOTgSR4JhUmnbrPHIkEghVP4IdrNQRfR5Bpe9QpJcNQh4m4BYKvtc/3w3jV1WWC76gz657ILmEjbUu+CcE+zelTVybxY5tUv7LPRE9uW2Uny7MVPEB8gjtsOxpBLTSCMnv7i/l+X1U7KiTPCR0JMZfw+d6wSuQVyTvIytwr5gQvP9OteSqrIficflIeHzNZVNVHPZlIuS6fswypi5zccDm3q+qD6+Fnk7qMc508lJMSIMtO/VMnr66Mfaj0wIlY8mt1Vf3y9V7xTO1TfrAt+v6SnpGG4beQYiAl+U2bNnX1PvqRIHm//V2bkJtsd1es9iXRyWMkGUUiYtJAqzyRzJl0sjqKdiyf61fdH8eJBT80x3VTAkNZdWVMZFU2sC742ahuhwfJUJecjiw7LePrJf3EKrtUJmyWZdi3PJc2pf3WYVZXxvoawdsK3nYwbOemtRgwkndPytP3xcVWLn7/uG7rXhIYH/PKEFe82UTNZJzbmucyQTJE6Pyda0H43F/dJ+ui7PIvvknJiuvK64GMKvrlrWZ8ir5ODyxrWlf2KV9EQy8gEpMS2R/7KCVatknuPrBPv+cnE2kbkssTDe4PJwR8LHxU1S/K4L4b48k+rritgnrTbaCMHhKL+Tq2e/BGSK0R0kJaYc+VrUby7sUz6k1u/o1nvNKtS56c0Ev34isSMpJD7QTAkzy/NY1IWpBLnS6yjF6SkrwVTr70pZe6TNYlWzO7HN3UZV3kC4a4j9wkolK2mJCgXxhDlCVxlD6TRIx64EQjtENf8cRPrP5Zt/CZ+Lop9rxyD3L8Q60UH1X9CRsZt/n8NII3gjeCH/AYMJLvvBKdzyRqfZt/BjUGjOAHPLnP1UrR+hnsZxyM5I1EBpVETK/BjU0jeCN4W8EPSQwYyQ9uIjWSM98MYgwYwQ9JcrcV9mCvsOfKP0byRiSDSCSm02DGZesED/ZnCBgCs4rAs88+C8888wz89re/hSeeeAIeeugh2LBhA9x4443wzW9+E5YuXQqf+cxn6Lfj999/f3jVq14FL3zhC91vx2+//YJ7452Rz2CSj/ll9v1iBD+rqdiEGwKzg4CR/OwnRyMgw3jYY8AIfnbyr0k1BGYdgUEh+d/8oIDVSwuY+Av9/6WjtwH7NwwsBuYvBrbddlvYcccd4fd+7/doJ+/AAw+EE044AZYtWwZr1qyBjRs3wpYtW+Dpp58GzCfFrGct68AQMAQaIzCfJL/5ygIO3l//6AiuGDCp4P92221HP2e7/fbbww477GD/hoHFwBzHAJL78573PLpFt/fee8N73vMeOPHEE+GCCy6AH/3oR/DLX/7SCL5xtrWKhsA8IDAfJH/1OQXsunMkdyZ2JHUk8+c+97mUWJ7//OfDLrvsQv8veMELwP4NA4uBuYsBXLnj8zd77rkn/MEf/AEccsghcPLJJ8Py5cvhuuuug7vvvpt+2MpW8POQuK1LQ6ApAnNJ8rgl/8o9NLkzse+0005E4phUXvKSl1BiefnLXw6veMUr6Jfv8Nfv7N8wsBiYmxjAB2xf85rXwB/+4R/CO97xDjjqqKPgjDPOgMsuuwz++Z//GfA3Lh5//HF6YNe26JtmW6tnCMwDAnNF8n97XJnccStw5513hhe96EXwspe9DF73utfBm970JsCn+N/+9rfDO9/5TjjggAPgXe96l/0bBhYDcxQDeM8dt+Vx5Y7k/ld/9Vfwd3/3d3DVVVfBrbfeCps3bwb86i1+I8cIfh6StnVpCHSDwFyQ/JHvcATP2/JI7rgNjyt2XC3st99+8L73vQ/Gxsbgox/9KBx77LFw3HHHwfHHH0//n/rUp8D+DQOLgbmJgU9/+tO0LX/66acTua9cuZLuv69fv56+Yvub3/wGfve7380fwW9eOeZ+sce/7J9f/j+2crPPfWthKimjOpNru8mNHeuuneSVyxjMbKqu3qke2ZPqtm4q2piURXkFTK1z/eYxYb02w8wS1rWAYskMMFLVWndfEvXifvMyOtXL4gEA2C76GAA2zcCY8HNlWZW91L5e17wF9Vc72cetq+rF6+izKVBRq2wWZVXXAeDZtWfFWBqbhtsz35P/yJ8U8J/2PZhW2N1+T57vveODdHi/He+zv/jFL4bXv/718KZXcNztBUeedDqcffbZ9L38r33ta/TkLj69i/+nHcb1FsHRf+OuubLT4Aj28VuOhrN9/WXLzoaj38JtCihUmZRXwKJjzqY+zj5mUcSBZRZpf8tg2d8cDYty10PfUr/mx9U2ahlV9eJ1tPsIOE3oI8vY3jK2EQuNeSqvHluW2/cn4aztSGVGu1I/VcUF+8/HxmGn9Rln9fJSfQf9/Pzzz4cLL7yQ7rmvWLGCVu7XXnst3HbbbXDffffR/fennnqK3quBeWpenqJ3ZKYTs77mCT4hRk6sbXxSf0wcRMYi2YoOOtVzehdQSF0V8ThyZvJS8lQ90aknQ5aJbbg9gJanW/V+pvRqGw+2p5AEj3aIGFBYOP/z5IcIU+JLZvKkR8jo3fzQsm8cEDuhq9Zd20V9UV2NhdKBcCngrLXuZTjXfamAYny1ehnO2f/FJcO9D/7Lnl6Gg5NnXL3jfXd8mG633XaDV7/61bDfa18Ixcv+BD79138NSz97KBTFEvjKt74FP/jBD2DVqlWwevVq+mrOleMHQHHgGXDlmjWwZtmxUBTHwnl4vOZKOOPAAg4Yv5LqnXdMAcUx54U2fD2tp+StOQ+OLQ6AMy5Hefpfyotlrs+iok2sp2V1uq50UjZqOZX1sI23HftSuqsytLeAY5c5uUqexEK10fKwTRW2nexsXH75GXAATbLY1xoHlKN0V5hVx8UaspHt1/XaltfY1iTu5rsdPi2PD9ThPXfclseVO5L7o48+CnL1jkltYAge/IrXJfXZJ3hMvJE0deIN2b606tT1KHkvmYG1uCMhkrqzJU4YZJKXxwBaXuiXknpsH677A0UAaWGP57OHhyfiybXlFbzS1dUjnyiyB8jZi9fGJqdgrGiX4NvAQZklJ0sJ+at68kT6H9v4iSht19+9Aj5UTMJqeuPd7bD0kAKK45YDkvwffWyypzfeMcHj199w9f7Sl74UFi1aBAf85wJec+jxcN5558G3v30O/db4SSt+CnfccQfcdddd9LY9fOPeFacUcPC5N9F3cDduvAJOLQo49cqN4I4PhqXr8HgjbLzyVCiKU+EKPE7+bzr3YCgOWQo3bbwJlh4i2iT1Qrt1S+HgjCyUc/App8LBRQMZVbIz16tt1LY0rVeHRZTREAvUtxG2WteAZcbe2jLq62BYemXeB9w22oH9NoyLxK8xLjb2Fmc18ljPYfzEr8PhA3V4zx3ffPmrX/2KyB3vveNbMTFX4N/AEDwl8ZCsZ5vgHZnwCrF6VdysHukuCV4RtyAuRFwm/ITIyCOlSQVfjZ96khCv937UzE7GqRNuZTycZpo8U23lZEdjVrKXCbACv1Ry8/N2ccB+CQtP0Hg8tnJG3H7KT+JkG4oX3mnC7fp7kOA/BJdu1K+1XX5cAX98ynRPr7VFgucXaOy6666w1157wQEH/DEc+KoCPnDiOfS63Jtv/j/w94cUcOj5P4VHHnkEHnvsMfq+7ZYt62H5kQWM/3CLOj/84vWw5efL4fBiHK7Z4svo/HBY/nOuGz+vOb2A4vRrYMuWa2C8GIflFx8etuNJFsvwn1i/dJ37q+kHXwLS/X+NjUpe03pbYD3ad+RyWK/ao25oP+PZDAu0p1reFojY9mJ7TRvGu2QDtqnBIm0n/fXDcY0LnlMMtS2vxq6sPYNVHwkdn5bH38zAVTtuy+N9d0numH/mkeD9PZZwL02uxDzBhzKsK8ubp+x8TUkmlIbpHndc0XOrZvXyhBZtiITo5RLJo02ZBM/kxSqkn3KCkJb1fN7MzvKOgyZi7j6PR+YePDfgLXw1SXKykXxSvyDhE6atE3y7OLhnDGLcEi4ijksTFz8xRJtDzJCN8ZxlrLhbv7v+GycXcNBZ3+vp3fXYH2/P41Pzb3jDG+DQQ98G7ygK+NDpF9MDPP/v/62DCxcXcMT0XfDkk0/Sm7Lwu7ZPP30tnFkUcOZ1eIz/98ClHy7gyMvugaevOxOK4ky4lq4/DU9vvBSOLI6ESzdyXf+p6jl5xcS1Tl6uDV0Tcr38aye8Hrk2rENPnzU2KnkN61Xod89lR7pJzYcvhXtIbgMssF6FPPKHwjbBXeneQ1mFH/qJC8Ig2P+0iKEabFMbBR7V8nqwt1+8Wm6Pq3X8l8TOK3dOrfNI8D7x+QSmyc6To0r4rHIPn4FQmVTbXamVCC0hYZnI5XGZMP2Kr8pukhsJowckXJO5xsMriranZI1FhIlYpWaJkctRd8andYJvMS4SYkY7O8WJhwkRoVU+k7wjdTchdrclpuCG5Adqrv58AR8498aefqCG77/jG7L22GMPePOb3wwf+cgR8OE3FvBfvnw53HLLLXD//bfCxR9yxM2rBEwmzz57P6xY4p4RkOdjM/fTbsNYcRbpSmX3rKBbKivuwXb+nx4gHIN47QY4q5DnTj7J823unxmD4swbogy8jnL4Wq4f7q+nzxoblbwG9Ug3iZfAwssi+5asgPuf7YwF7ujgg6r4jEbAlHUqYZupw3V7+aS+hX+VjBos0nZ07n2OOpPtMj6wj7bltYyFsn3uZcfcoY/mn+A58eFqnRM3r2TCuVa6jTNNNjqhSvlN6qWJmwhL6h4Iv9yPrpsSTNTEJfnMij9W6euoiZ3YQZN6KR6smG6LV/0qXWLF8cCEjtUEkRNeamen3d0drWPZX3lbknpVEzG8Lu0KccFS+dPhkpsMyS17TOj8K3Srxws47H/e3tOv0CHB4/13/N47viHrrW99K3zsYx+DT7+/gLf998vg9ttvh4ceuhq+hERywzOsZPisxgxxERPSxN58TKdjIMUiLXdqDHVcBCT9QcAptTXBguoJfIWcPLaiQhuHNC6rc1JPcZHIJDv8mGlbXhsQDLqMgSB4XrHEbXiXMCPhtw+jDBx1Xzzpqkk9qiNJKgxQJ4ySjwjSaJezMybyJCGyLok8vtzmZxM7sb8m9Up4eEX1APUrd4kbGyQIPfRZeTsjn+BYVLefTewLOjFZS/8kuuv+pX9dsnaxIK/rCY2b3HASTRI83pP3JI9P1y/+x43q6fqmPzWLBI9fj8PvvuNb6vBFNp/4xCdg8mN/BMUBn4e1d94Jj15zBm23X/9MmeCrMdP60jhgf0vMNEh6p4PqSR8nWCVt6bTWB7kGna9V26jbVtar0YnaMC68o+XPVZnEokZeXT7T2vZ5RjpwbJZlVWKRfBNIxYXavdLx07a8ssajd2VACJ4fPuPveOMgliv62QGeAotWg/UJJF8v6qQGob9M18JKUw4Cn9i5TAxsncyj/Ni/26bFe6ZqJRir9nUU+2kfD1QM5evJjLDH4xHKKZlxudRHmFiX5ES1bg/7wUH7nfUX/ied/XWeIKCC8rq8B8+Tqly8eMOQ5K8/s4APXbapp9+T59fS4jvF8RW0+Ja6T37yk4Dfdf/a0WzD4XTvHPtyE3LtkzxmqKAfy0nMxvosX8e0LOdbFWRuB1KJdbR+Hqq+PqJOUnZ5wpGr1ykuYhuNAyosyxiLOnmyPuWKBPu+QJCNS75ohoUTkY8LKpNjQeZHhYX0AbbqTZ40ZxSP54XgRxFIs8kQmE8EeCWPD908QV+he6jxdj2u3p/znOfQO+fxneL4Clp8Sx1+PQ6/645fhZM/QTmfdlrfhoAh0BwBI/jmWFlNQ2CgEeiV5PG77/ijMvgVOXwLHr5fHl87im/1wpd64PeEjeAH2vWmnCGQRcAIPguLXTQEhhOBXkgevxqH2/O77747fQcef9DCCH44/W9aGwISASN4iYYdGwIjgEC3JI8vtsGvx/GPyxx00EFwwgkn2Ap+BGLBTFjYCBjBL2z/m/UjikA3JI9fi3vta19L2/P4khv8OUr8xSr8YQvboh/RADGzFgQCRvALws1m5EJEoCnJ48/A4lfj8Pfe99lnH/jgBz8IJ510ElxwwQX0Fju7B78Qo8dsHgUEjOBHwYtmgyFQgUATkj/55JNhyZIl8N73vhfe/e530+++n3rqqXDRRRcB/hQl/rCFPWRXAbBdNgQGGAEj+AF2jqlmCLSBQCeSP/fcc+G0006Dj3/843DUUUfB0UcfDePj43DJJZfADTfcAHfffTf9WhW+Yxxl2Z8hYAgMBwJG8MPhJ9PSEOgLgTqSv+qqq+g771/84hfhlFNOgc997nPw1a9+FS6//HK4+eab4d5776VfrsLv2BvB9+UGa2wIzCkCRvBzCrd1ZgjMHwJVJI8k/t3vfhemp6fhH/7hH+gfV+/f//734d/+7d/ggQceoJ+lNIKfP99Zz4ZALwgYwfeCmrUxBIYUgZTkH374YbrH/uMf/xhWrVoF3/72twFX9EjuN910E9x1112AdfA3p/FnKW0FP6SON7UXJAJG8AvS7Wb0QkYgJflHHnkENm3aBL/4xS8Aif5f/uVf4Cc/+QnceeedtHp//PHH4amnnqJfrlvIuJnthsCwIWAEP2weM30NgRYQkCSPq3N8Sv4//uM/6H77PffcQ594/qtf/QqefPJJW723gLmJMATmGgEj+LlG3PozBAYEASZ53HrHFfrWrVuJ0JHskdjxHMkd773j787b9vyAOM7UMAQaImAE3xAoq2YIjCICSNpM9Ejk+FU4JHv8xHMkfyP3UfS82bQQEDCCXwheNhsNgQ4ISKJHQmdS5+sdmluxIWAIDCACRvAD6BRTyRAwBAwBQ8AQ6BcBI/h+EbT2hoAhYAgYAobAACJgBD+ATjGVDAFDwBAwBAyBfhH4/4s4/zQS85l6AAAAAElFTkSuQmCC" width="322" /></div><div style="text-align: left;"><br /></div><h3 style="text-align: left;">Evaluating 5-factor model</h3><div><div><ul style="text-align: left;"><li><b>Analyst opinion</b>: High correlations between risk factors puts usefulness of 5-factor model into question.</li><li>R2 10-20% for RMW, CMA</li><li>5 factor improvement only by 0.2%</li></ul></div></div><div><img alt="" height="206" 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" 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" width="475" /></div>Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-88648321748589018282019-01-10T22:51:00.005+00:002020-06-24T08:13:07.874+01:00Longstaff-Schwartz and American Monte CarloThis <a href="https://github.com/omartinsky/AmericanMonteCarlo/blob/master/main.ipynb">notebook </a>illustrates Longstaff-Schwartz (AMC) algorithm for pricing options and other derivatives with early-exercise features.<br />
<br />
This work is based on the paper<b> [1]</b>.<br />
<br />
The GitHub project also contains unit tests which are based on original numerical examples presented by Longstaff-Schwartz<br />
<a href="https://github.com/omartinsky/AmericanMonteCarlo/blob/master/main.ipynb" rel="noopener" target="_blank"><img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /> </a><br />
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<b>[1]</b> Valuing American Options by Simulation: A Simple Least-Squares Approach, Francis A. Longstaff, Eduardo S. SchwartzOndrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-65176256797484843232017-05-09T09:00:00.000+01:002019-01-03T21:22:11.670+00:00PYBOR - multi-curve interest rate framework in PythonI have been recently working on a project PYBOR, a multi-curve interest rate framework and risk engine based on multivariate optimization techniques, written in Python (hence the name twist of a libor rate).<br />
<br />
Please refer to the <a href="https://github.com/omartinsky/PYBOR/blob/master/main.ipynb">Jupyter notebook</a> for the overview of main features.<br />
<br />
<a href="https://github.com/omartinsky/PYBOR/blob/master/main.ipynb" rel="noopener" target="_blank">
<img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /> </a><br />
The entire project as well as the notebook above is available on <a href="https://github.com/omartinsky/pybor">GitHub</a>.<br />
<div>
<br /></div>
<div>
<h2>
Features</h2>
</div>
<div>
<br /></div>
<div>
<ul>
<li>Modular structure allows to define and plug-in new market instruments.</li>
<li>Based on multivariate optimization, no bootstrapping.</li>
<li>Supports arbitrary tenor-basis and cross-currency-basis relationships between curves, as long as the problem is properly constrained.</li>
<li>Risk engine supports first-order (Jacobian) approximation to full curve rebuild when bumping market instruments.</li>
<li>Supports the following curve optimization methods:</li>
<ul>
<li>Linear interpolation of the logarithm of discount factors (aka piecewise-constant in forward-rate space)</li>
<li>Linear interpolation of the continuously-compounded zero-rates</li>
<li>Cubic interpolation of the logarithm of discount factors</li>
</ul>
</ul>
<br />
<ul><ul>
</ul>
</ul>
<h2>
Curve naming conventions</h2>
<br />
<a href="https://github.com/omartinsky/PYBOR#curve-naming-conventions"></a>For the purpose of this project, the curves are named in the following way:<br />
<ul>
<li><b>USD.LIBOR3M </b>refers to USD BBA LIBOR reference rate with 3 month tenor</li>
<li><b>GBP.SONIA </b>refers to overnight GBP SONIA compound reference rate</li>
<li><b>USD.OIS </b>refers to overnight USD Federals Fund compound reference rate</li>
</ul>
<br />
In a mono-currency context, the reference rates above can be used also for discounting (e.g. <b>USD.OIS </b>curve used for discounting of collateralised USD trades and <b>USD.LIBOR.3M </b>curve for discounting of unsecured USD trades).<br />
<br />
In a cross-currency context, the naming convention for discounting curves is as follows:
<br />
<pre class="sourcecode"><CurrencyOfCashFlow>/<RatePaidOnCollateral>
</pre>
Few examples:<br />
<ul>
<li><b>USD/USD.OIS</b> Discounting curve for USD cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USD.OIS. Names USD/USD.OIS and USD.OIS refers to the same curve.</li>
<li><b>GBP/GBP.SONIA</b> Discounting curve for GBP cash-flows of a trade which is collateralised in GBP, paying collateral rate linked to GBP.SONIA. Names GBP/GBP.SONIA and GBP.SONIA refers to the same curve.</li>
<li><b>GBP/USD.OIS</b> Cross-currency discounting curve for GBP cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USD.OIS.</li>
</ul>
<br />
<ul>
</ul>
</div>
<h2>
TODO</h2>
<div>
<ul>
<li>Solve stages for global optimizer (performance gain)</li>
<li>Proper market conventions (day count and calendar roll conventions)</li>
<li>Smoothing penalty functions</li>
<li>Risk transformation between different instrument ladders</li>
<li>Split-curve interpolators (different interpolation method for short-end and long-end of the curve)</li>
<li>Jacobian matrix calculation via AD (performance gain)</li>
</ul>
</div>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-53836477165443578152017-02-27T21:00:00.000+00:002018-02-21T00:57:12.395+00:00Automatic differentiation via C++ operators overloadingLink: <a href="https://github.com/omartinsky/AutomaticDifferentiation/tree/master/autodiff_operators_overloading">Implementation on GitHub</a><br />
<br />
Automatic differentiation is a powerful technique which allows calculation of sensitivities (derivatives) of a program output with respect to its input, owing to the fact that every computer program, no matter how complex, is essentially evaluation of a mathematical function.<br />
<br />
In banking, automatic differentiation has many applications including, but not limited to risk management of financial derivatives, solving optimization problems and calculation of various valuation adjustments.<br />
<br />
<h3>
Motivation for AD</h3>
<br />
Calculation of sensitivities has been done long time before introduction of the AD. Traditional approach is to approximate derivative \( \frac{\delta}{\delta x} f(x)\) of a function \(f(x)\) using central finite difference:<br />
<div>
<br />
$$ \frac{\delta}{\delta x}f(x) = \lim_{h \to 0}{\frac{f(x+h) - f(x-h)}{2 h}} $$<br />
<br />
The problem with this approach is the fact that too big differentiation step \(h\) ignores second-order risk (convexity).<br />
<br />
On the other hand, differentiation step which is too small brings to the light another complication related to the way how floating-point model of a CPU works. Operations on floating-point operands with disproportionate exponents lead to serious rounding errors. Example of such operation is \(x+h\) from the formula above, since \(x\) is considerably larger than \(h\).<br />
<br />
Furthermore, finite difference method is not only imprecise, but also extremely time-consuming for high-dimensional problems. In the context of banking, consider interest rate delta ladder calculation of a book of trades. In such situation, PV of every trade in a book needs to be calculated for every single interest rate risk factor (different currencies, indices and tenors), as illustrated by the following pseudo-code with <i><u>multiple function calls</u></i>:<br />
<br />
<pre class="sourcecode">pv_base = calc_pv(trade, {rate1, rate2, rate3, rate4, ...})
pv_rate1_bump = calc_pv(trade, {rate1<span style="color: red;">+bump</span>, rate2, rate3, rate4, ...})
pv_rate2_bump = calc_pv(trade, {rate1, rate2<span style="color: red;">+bump</span>, rate3, rate4, ...})
pv_rate3_bump = calc_pv(trade, {rate1, rate2, rate3<span style="color: red;">+bump</span>, rate4, ...})
pv_rate4_bump = calc_pv(trade, {rate1, rate2, rate3, rate4<span style="color: red;">+bump</span>, ...})
...
</pre>
<br />
The problem gets even more complicated for situations involving second-order risk. Moreover, due to increased regulatory requirements imposed on banks as part of the CCAR and FRTB frameworks, many banks are nowadays forced to reorganize their risk calculation and stress-testing infrastructures. In many of such situations, automatic differentiation can be the only plausible solution.
<br />
<br />
<h3>
Principle of automatic differentiation</h3>
<br />
The fundamental advantage of automatic differentiation is the ability to calculate function's result together with sensitivities to all its inputs in a <i><u>single function call</u></i>, as illustrated by the following pseudo-code:<br />
<br />
<pre class="sourcecode">{pv_base, delta_rate1, delta_rate2, ...} = calc_pv(trade, {rate1, rate2, ...})</pre>
</div>
<br />
There are few approaches to AD such as "<u>operators overloading-based</u>", "<u>handwritten</u>" and "<u>code-transformation</u>". This article address approach which utilizes C++ templates and overloading of C++ operators.
As each of the named approaches has its own advantages and disadvantages, the choice depends on a problem domain, maturity of the software project and constraints of the programming language.
<br />
<br />
<h3>
AD via operators overloading</h3>
<b><br /></b>
As mentioned, operators overloading-based AD utilizes two features of the C++ language, i.e. overloading of operators and function templates.<br />
<b><br /></b>
<b>Operators overloading</b> in the context of AD is used to alter behavior of elementary C++ operations such as "<complete id="goog_792219048">+", "-", "*" and "/"</complete> in order to record derivatives to its operands alongside the results as the calculation progress.<br />
<br />
We will also show how <b>function templates </b>are used in order to redefine existing C++ functions with AD-aware data types (e.g. <code>ADDouble</code>), on which the C++ operators are overloaded.<br />
<br />
For the illustration purposes, let's consider the following C++ program:<br />
<pre class="sourcecode">double f(double x0, double x1)
{
return log(x0) + x1 * x1 * x1;
}
double x0 = 3;
double x1 = 4;
double y = f(x0, x1);
</pre>
<br />
The sequence of mathematical operations together with temporary variables (denoted here as AD0 .. AD5) would look as follows:<br />
<pre class="sourcecode">AD0 = x0 = 3
AD1 = x1 = 4
AD2 = AD1 * AD1 = 4 * 4 = 16
AD3 = AD2 * AD1 = 16 * 4 = 64
AD4 = log(AD0) = log(3) = 1.09861
AD5 = AD4 + AD3 = 1.09861 + 64 = 65.09861
</pre>
<br />
The tree representation of this calculation would look as below:<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicRP-vSRoRIAfjDkyakat2ZriMoBTgzdtJgdChXQh9m3lboaPSPS41oHU6940_aIUJdBqCgOtajVHkYUwX9a7wx8dx7j_LcRGqGpIFeYESiHYkaVm1TA2hnaWtsAVORgdtk1JsfXFF4fao/s1600/ad_templated.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="519" data-original-width="534" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicRP-vSRoRIAfjDkyakat2ZriMoBTgzdtJgdChXQh9m3lboaPSPS41oHU6940_aIUJdBqCgOtajVHkYUwX9a7wx8dx7j_LcRGqGpIFeYESiHYkaVm1TA2hnaWtsAVORgdtk1JsfXFF4fao/s1600/ad_templated.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
Now, the only question remains how to overload C++ operators so the derivatives will be recorded for each operation automatically. Let's define a new data type <span class="sourcecode">ADDouble</span>. This variable behaves pretty much the same way as the standard <span class="sourcecode">double</span>, except the fact that it has unique identifier. This identifier is used to track the sequence of operations as illustrated on the figure above. The tree-representation of this calculatiion is stored in a global storage called <b>AD Engine</b>.<br />
<br />
<pre class="sourcecode">struct ADDouble
{
ADDouble(ADEngine& engine, double value) : _engine(engine), _value(value)
{
_id = engine._id_counter++;
}
double _value;
NodeId _id;
};
</pre>
The next step is to overload "+" and "*" operators and logarithm function for <span class="sourcecode">ADDouble</span> data type. Each time when the operator is executed, the function will instantiate a new <span class="sourcecode">ADDouble</span> data type and it will store direct derivatives of the result with respect to its input into the AD Engine tree.
<br />
<pre class="sourcecode">inline ADDouble operator+(const ADDouble& l, const ADDouble& r)
{
ADEngine& e = l._engine;
ADDouble out(e, l._value + r._value);
e.add_direct_derivative(out, l, 1.);
e.add_direct_derivative(out, r, 1.);
return out;
}</pre>
<pre class="sourcecode">inline ADDouble operator*(const ADDouble& l, const ADDouble& r)
{
ADDouble out(l._engine, l._value * r._value);
ADEngine& e = out._engine;
e.add_direct_derivative(out, l, r._value);
e.add_direct_derivative(out, r, l._value);
return out;
}</pre>
<pre class="sourcecode">inline ADDouble log(const ADDouble& x)
{
ADDouble out(x._engine, log(x._value));
ADEngine& e = out._engine;
e.add_direct_derivative(out, x, 1/x._value);
return out;
}</pre>
<pre class="sourcecode"></pre>
<h3>
Applying chain rule to the calculation tree</h3>
<br />
Calculation tree contains only derivatives of atomic operations with respect to their operands. In order to obtain sensitivity of the overall program output with respect to the initial program input, the chain rule for derivatives needs to be applied:<br />
<div>
<br /></div>
<div>
$$ \frac{\delta}{\delta x}f(g(x)) = \frac{\delta}{\delta g(x)}f(g(x)) \frac{\delta}{\delta x}f(x) $$</div>
<div>
<br /></div>
<div>
Referring to the example above, let's say we are interested in sensitivity of function \(y=f(x0,x1)\) to input variables \(x0\) and \(x1\). Variables \(y\), \(x0\), \(x1\) are represented in the derivatives tree by nodes AD5, AD0 and AD1.</div>
<div>
<br /></div>
<div>
Applying chain rule means multiplying and summing the following direct derivatives together in order to get \(\frac{\delta}{\delta x0}\):</div>
<div>
$$ \frac{\delta}{\delta x0}f(x0,x1) = dAD5/dAD4 \times dAD4/dAD0 $$</div>
<div>
$$ = 1 \times 0.33333 = 0.33333 $$ </div>
<div>
and \(\frac{\delta}{\delta x1}\):</div>
<div>
$$ \frac{\delta}{\delta x1}f(x0,x1) = dAD5/dAD3 \times dAD3/dAD2 + dAD3/dAD1 $$</div>
<div>
$$ = 1 \times (4 * (4 + 4) + 16) = 48 $$ </div>
<div>
<br /></div>
<div>
The chain rule is implemented in a function <span class="sourcecode">ADEngine::get_derivative()</span> (see source code on <a href="https://github.com/omartinsky/AutomaticDifferentiation/blob/master/autodiff_templated/ad_engine.cpp">GitHub</a>)
<br />
<br />
<h3>
Operators overloading-based AD from user's perspective</h3>
<br />
In order to implement operators overloading-based automatic differentiation, user needs to template all functions and methods through which the AD-aware calculation will flow. The previously mentioned function would be for example templatised as follows:
<br />
<pre class="sourcecode"><span style="background-color: yellow;">template <typename T></span>
<span style="background-color: yellow;">T</span> f(<span style="background-color: yellow;">T</span> x0, <span style="background-color: yellow;">T</span> x1)
{
return log(x0) + x1 * x1 * x1;
}
</pre>
The final steps involve invocation of the AD-aware calculation from the <a href="https://github.com/omartinsky/AutomaticDifferentiation/blob/master/autodiff_operators_overloading/example.cpp">main program</a> function:<br />
<br />
<b>Step 1: </b>Create AD engine which contains derivatives tree
<br />
<pre class="sourcecode">ADEngine e;
</pre>
<b>Step 2: </b>Create independent variables. Later, we will request derivative of the result with respect to these variables
<br />
<pre class="sourcecode">ADDouble x0(e, 3);
ADDouble x1(e, 4);
</pre>
<b>Step 3: </b>Perform the calculation by invoking the target function only once. All derivatives will be calculated automatically.
<br />
<pre class="sourcecode">ADDouble y = f(x0, x1);
cout << "y = " << y.get_value() << endl;
</pre>
<b>Step 4: </b>Retrieve derivatives with respect to the input variables x0 and x1
<br />
<pre class="sourcecode">cout << endl;
cout << "*** Automatic differentiation" << endl;
cout << "dy_dx0 = " << e.get_derivative(y, x0) << endl;
cout << "dy_dx1 = " << e.get_derivative(y, x1) << endl;
</pre>
<br />
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</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjis45I7pJEP1BYu1Jyjf5_TT_8Lt1ccjC8TTdG_yYdO8Z-oDkd1CgT4KaCn5NjQSLGQovPHQWU3Vp9IxkGTQGVLhiv-VrpK0gRMG4jomF7_rkY3YKszfLbeh6UXF5Aq6wNsZUHeJaYf7jS/s1600/autodiff_templated_screenshot.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="461" data-original-width="373" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjis45I7pJEP1BYu1Jyjf5_TT_8Lt1ccjC8TTdG_yYdO8Z-oDkd1CgT4KaCn5NjQSLGQovPHQWU3Vp9IxkGTQGVLhiv-VrpK0gRMG4jomF7_rkY3YKszfLbeh6UXF5Aq6wNsZUHeJaYf7jS/s320/autodiff_templated_screenshot.png" width="257" /></a></div>
<br />
<h3>
Final thoughts</h3>
The aim of this article is to illustrate the principle of operators overloading-based automatic differentiation. The implementation is provided just for the sake of illustration and is not meant to be used in production environment. For this purpose, I advice to use one of the existing high-performance AD libraries such as <a href="https://www.nag.co.uk/downloads/impl/dco-summary.html">NAG DCO/C++</a>.<br />
<br />
Operators overloading-based approach to automatic differentiation has the following advantages:<br />
<ul>
<li>Performed on the level of atomic C++ operations. Therefore, it is fully transparent to higher-level language constructs such as function calls, classes or inheritance hierarchies. </li>
<li>Suitable for legacy projects as adding AD support is just a matter of templatising the existing algorithms.</li>
<li>Easy to comprehend from the user's perspective.</li>
<li>Compared to the handwritten approach to AD, fairly resilient to bugs.</li>
<li>Readily-available commercial libraries.</li>
</ul>
<div>
Disadvantages:</div>
<div>
<ul>
<li>In some circumstances quite memory consuming due to the fact that every single arithmetical operation leaves memory footprint.</li>
<li>Due to memory concerns, not suitable for data-intensive algorithm which performs iterative calculations such as Monte Carlo.</li>
</ul>
</div>
</div>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-22247171683824144502016-11-13T23:25:00.001+00:002021-02-22T12:03:11.921+00:00Heath Jarrow Morton Multi Factor ModelThe <a href="https://github.com/omartinsky/HJM/blob/main/hjm.ipynb">IPython notebook</a> which is subject of this post contains working implementation of a multi factor Heath Jarrow Morton (HJM) model. As most of the details are already described in the notebook itself, this article provides just brief summary.<br />
<a href="https://github.com/omartinsky/HJM/blob/main/hjm.ipynb" rel="noopener" target="_blank">
<img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /> </a>
<br />
<b>Yield Curve Data</b><br />
<br />
The model is calibrated from historical daily yield curve <a href="https://github.com/omartinsky/HJM/blob/main/hjm_data.csv">data</a> over the last five years. The yield curve structure contains 51 tenors ranging from 1M to 25Y.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7xej2jWc8EBH0AHouD6EQQij_VGSgcYymor7UhnsPIulYX2-3n6UjDyYHlt2Y4nFjB5NmgjR1hSjznINIDfn0t7VKGsrhj8yLGgAGotRsi_6BDEJT9ljhhyphenhypheny4VVnYtlfbM8Nd7JWVWm71/s1600/historical_data_a.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7xej2jWc8EBH0AHouD6EQQij_VGSgcYymor7UhnsPIulYX2-3n6UjDyYHlt2Y4nFjB5NmgjR1hSjznINIDfn0t7VKGsrhj8yLGgAGotRsi_6BDEJT9ljhhyphenhypheny4VVnYtlfbM8Nd7JWVWm71/s640/historical_data_a.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Evolution of daily historical yield curve data with 51 tenors over 5 years. Each line represents a different tenor</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcIxu0Og31tlFI_NW8lLGtsPred3aMSyF6Ag6Hofkio7vNo7BM0AONvAjyFbRk5zsAFjhhmQWULSE5UCSz2DxuNI-_cx1O0TKZ4lEeKVSf4ew4baTuVZVIE_8yvAnSM-yWMz4UQLmDEBBI/s1600/historical_data_b.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="241" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcIxu0Og31tlFI_NW8lLGtsPred3aMSyF6Ag6Hofkio7vNo7BM0AONvAjyFbRk5zsAFjhhmQWULSE5UCSz2DxuNI-_cx1O0TKZ4lEeKVSf4ew4baTuVZVIE_8yvAnSM-yWMz4UQLmDEBBI/s640/historical_data_b.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Evolution of daily historical yield curve data with 51 tenors over 5 years. Each line represents different day in the past, while the horizontal axis represents tenor space.</td></tr>
</tbody></table>
<br />
<br />
<b>Principal Component Analysis</b><br />
<b><br /></b>
The principal component analysis is then used to identify common factors which are driving movements in these rates. Typically 3-5 factors are sufficient to explain dynamics of the yield curve.<br />
<br />
<b>Volatility Fitting</b><br />
<br />
Once the volatility factors are identified in historical data by PCA technique, cubic spline interpolator is used to fit these factors. These interpolators are then later used to generate discrete mesh of tenors for the purpose of Monte Carlo simulation.<br />
<br />
<b>Risk-neutral Drift Calculation</b><br />
<b><br /></b>
Drift function is calculated using numerical integration over fitted volatility functions <b><br /></b>
<b><br /></b><br />
<b>Monte Carlo Simulation</b><br />
<b><br /></b>
Monte Carlo Simulation with risk-neutral drift is used to generate evolution of yield curve for different simulation paths in order to price IR Caplet with strike 3%, expiring in one and maturing in two years.<br />
<b><br /></b>
<br />
<div style="text-align: right;">
More information in <a href="https://github.com/omartinsky/HJM/blob/main/hjm.ipynb">IPython notebook</a></div>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-31661822335047365422016-11-12T23:23:00.000+00:002017-02-18T22:57:32.839+00:00Principal Component AnalysisLink: <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/principal_component_analysis/PCA.ipynb">IPython notebook</a><br />
<br />
The referenced IPython notebook demonstrates use of SciPy library in order to perform Principal Component Analysis of a three dimensional data.<br />
<br />
<div style="text-align: right;">
More information in <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/principal_component_analysis/PCA.ipynb">IPython notebook</a></div>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-85138163953467343672013-08-31T12:09:00.005+01:002020-06-26T04:27:05.490+01:00Portfolio Optimization II : Black-Litterman model <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" rel="noopener" target="_blank">
<img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /> </a>
<br />
In the <a href="http://www.quantandfinancial.com/2013/07/mean-variance-portfolio-optimization.html" target="_blank">previous post</a>, we have been discussing conventional approach to the portfolio optimization, where assets' expected returns, variances and covariances were estimated from historical data. Since these parameters affect optimal portfolio allocation, it is important to get their estimates right. This article illustrates how to achieve this goal using Black-Litterman model and the technique of reverse optimization. All examples in this post are build around the <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" target="_blank">case study</a> implemented in Python.<br />
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<b>Instability of asset returns</b><br />
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Empirical studies show that expected asset returns explain vast majority of optimal portfolio weightings. However, extrapolation of past returns into the future doesn't work well due to a stochastic nature of financial markets. Nevertheless, our goal is to achieve optimal and stable asset allocation, rather than trying to predict future market returns.<br />
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<b>The world of efficient markets</b><br />
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To maximize investor's utility function, Modern Portfolio Theory suggests holding the combination of a risk-free asset and optimal risky portfolio (ORP) lying on a tangency of the efficient frontier and capital market line. Modern Portfolio Theory also suggests that optimal risky portfolio is a market portfolio (e.g. capitalization-weighted index).<br />
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If we assume markets are fully efficient and all assets are fairly priced, we don't have any reason to deviate from the market portfolio in our asset allocation. In such case, we don't even need to know equilibrium asset returns nor perform any kind of portfolio optimization, as outlined in the previous article. An optimization based on equilibrium asset returns would lead back to the same market portfolio anyway.<br />
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<b>An active investor's view</b><br />
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The different situation is when investor believes the market as a whole is efficient, but has concerns about the performance of specific assets or asset classes due to the possession of material non-public information, resulting for example from superior fundamental analysis.<br />
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If investor with distinct views on a performance of few specific securities doesn't want to completely abolish the idea of mean-variance optimization, he may still use quantitative approach to incorporate such view into the MVO framework, further referred to as the <b>Black-Litterman</b> model.<br />
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<b>Black-Litterman model</b><br />
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In the previous article, we have been discussing classic Mean-Variance optimization process. The process solves for <b>asset weights </b>which maximize risk-return trade-off of the <b>ORP portfolio</b>, given historical <b>asset returns </b>and <b>covariances</b>:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhltm0zRchWwdSb1LuVI9LcbfJukob_78ds1nfxPIQvPOYg5tDw5jMGnGvQh3ilnVdhLSnaho9nmZmfxuSS93HCtMZHsKvTyMmGEZioZu_5EhFigt7kwJkNOYPhwPz6CeMunBi-We7jpIC0/s1600/fig_a.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhltm0zRchWwdSb1LuVI9LcbfJukob_78ds1nfxPIQvPOYg5tDw5jMGnGvQh3ilnVdhLSnaho9nmZmfxuSS93HCtMZHsKvTyMmGEZioZu_5EhFigt7kwJkNOYPhwPz6CeMunBi-We7jpIC0/s1600/fig_a.png" /></a></div>
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On the other hand, the general workflow of the Black-Litterman optimization is illustrated on the diagram below.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvyXEec_Qgc39DpUDtuHDFaoGFBFT_8M_Kvg6KITPZxSNOX4gTRvjMpeZoMgpGeNG-HHmAu_s5t-SnoOZtckRqknMsdq-1kmkBbbkoli9AoByYVowayroDMm6ZpMqmFfLDsl8QtYX2eZQ5/s1600/fig_b.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvyXEec_Qgc39DpUDtuHDFaoGFBFT_8M_Kvg6KITPZxSNOX4gTRvjMpeZoMgpGeNG-HHmAu_s5t-SnoOZtckRqknMsdq-1kmkBbbkoli9AoByYVowayroDMm6ZpMqmFfLDsl8QtYX2eZQ5/s1600/fig_b.png" /></a></div>
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The forward-optimization part in this model is the same as in the classic MVO process (boxes <span style="color: red;">b</span>, <span style="color: red;">g</span>, <span style="color: red;">i</span>, <span style="color: red;">j</span>, <span style="color: red;">k</span>, <span style="color: red;">l</span>).<br />
However, the thing which differs is a way how we are observing <b>expected asset returns</b>, which is one of the inputs into the forward optimizer (<span style="color: red;">g</span>). Previously we have used <b>historical asset returns </b>as a proxy.<br />
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Now, as we can see in the diagram, <b>equilibrium asset returns </b>are used instead (<span style="color: red;">d</span> or <span style="color: red;">g</span>).<br />
Equilibrium asset returns (<span style="color: red;">d</span>) are returns implied from the market capitalization weights of individual assets or asset classes (<span style="color: red;">a</span>) and historical asset covariances (<span style="color: red;">b</span>) in a process known as <b>reverse optimization </b>(<span style="color: red;">c</span>).<br />
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Forward (<span style="color: red;">h</span>) and reverse (<span style="color: red;">c</span>) optimizations are mutually inverse functions. Therefore, forward-optimizing equilibrium asset returns (<span style="color: red;">d</span>) would yield to the optimal risky portfolio (<span style="color: red;">j</span>) with exactly the same weights as the weights observed from assets' capitalization (<span style="color: red;">a</span>).<br />
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However, the beauty of the Black-Litterman model comes with the ability to adjust equilibrium market returns (<span style="color: red;">f</span>) by incorporating views into it and therefore to get optimal risky portfolio (<span style="color: red;">j</span>) reflecting those views. This ORP portfolio may be therefore different to the initial market cap weights (<span style="color: red;">a</span>).<br />
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<b>Case Study</b><br />
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We will build upon the <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" rel="" target="_blank">case study</a> introduced in the previously published post <a href="http://www.quantandfinancial.com/2013/07/mean-variance-portfolio-optimization.html" target="_blank">Mean-Variance portfolio optimization</a>. In that post, we have used forward optimizer to calculate weights of an optimal risky portfolio \(\mathbf(W_{n \times 1})\) given historical returns \(\mathbf(R_{n \times 1})\) and covariances \(\mathbf(C_{n \times n})\) Now, we will use the same case study to illustrate the principle of the Black-Litterman model.<br />
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Before doing so, let us define some basic symbols:<br />
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<table>
<tbody>
<tr><td>\(\mathbf{R}\)</td><td>Vector of historical asset returns</td></tr>
<tr><td>\(\pi\)</td><td>Vector of implied equilibrium returns</td></tr>
<tr><td>\({\pi}'\)</td><td>Vector of view-adjusted implied equilibrium returns</td></tr>
<tr><td>\(\mathbf{C}\)</td><td>Matrix of historical return covariances</td></tr>
<tr><td>\(\mathbf{W}\)</td><td>Vector of market capitalization weights</td></tr>
<tr><td>\(\mathbf{W}'\)</td><td>Vector of optimal risky portfolio weights</td></tr>
<tr><td>\(\lambda\)</td><td>Risk-return trade-off</td></tr>
<tr><td>\(\mathbf{Q}\)</td><td>Vector of views about asset returns</td></tr>
<tr><td>\(\mathbf{P}\)</td><td>Matrix linking views to the portfolio assets</td></tr>
</tbody></table>
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<b>Reverse optimization of equilibrium returns</b><br />
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Equilibrium market returns are those implied by the capitalization weights of market constituents. They represent more reasonable estimates than those derived from historical performance. The another advantage is that equilibrium returns (whether or not adjusted) will yield into the portfolio weights similar than weights of the capitalization weighted index, thus representing more intuitive and investable portfolios.
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Equilibrium <i>excess </i>returns \(\pi\) are derived in Black-Litterman using this formula:<br />
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$$ \lambda = \frac{r_p - r_f}{\sigma_p^2} $$<br />
$$ \pi=\lambda \cdot \mathbf{C} \cdot \mathbf{W} $$<br />
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In our <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" target="_blank">example</a>, corresponding code is represented by the following snippet. Please note that excess returns don't include risk free rate.<br />
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<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Calculate portfolio historical return and variance</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_mean_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Black-litterman reverse optimization</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">lmb</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">-</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">/</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Calculate return/risk trade-off</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">Pi</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">dot</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">dot</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">lmb</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Calculate equilibrium excess returns</span><br />
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As we can see, equilibrium returns implied from capitalization weights represent more conservative estimates than those calculated from historical performance. For example, implied return on Google \(\pi_6\) is "only" <span style="background-color: yellow;">16.5%</span> given its capitalization weight of 11.6%, as opposed to unjustified historical performance \(\mathbf{R}_6\) of <span style="background-color: yellow;">33.2%</span>.<br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"><br /></span>
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<table style="width: 300px;">
<tbody>
<tr><td><b>Name</b></td><td>\(\mathbf{W}\) </td><td>\(\pi\) </td><td>\(\mathbf{R}\) </td></tr>
<tr><td>XOM </td><td>16.0% </td><td>15.6% </td><td>7.3% </td></tr>
<tr><td>AAPL</td><td>15.6% </td><td>17.9% </td><td>13.0% </td></tr>
<tr><td>MSFT</td><td>11.2% </td><td>15.2% </td><td>17.2% </td></tr>
<tr><td>JNJ </td><td>9.7% </td><td>9.9% </td><td>14.4% </td></tr>
<tr><td>GE </td><td>9.4% </td><td>17.9% </td><td>14.0% </td></tr>
<tr><td>GOOG</td><td>11.6% </td><td><span style="background-color: yellow;">16.5% </span></td><td><span style="background-color: yellow;">33.2% </span></td></tr>
<tr><td>CVX </td><td>9.2% </td><td>17.3% </td><td>9.2% </td></tr>
<tr><td>PG </td><td>8.5% </td><td>9.4% </td><td>11.2% </td></tr>
<tr><td>WFC </td><td>8.7% </td><td>21.8% </td><td>26.9% </td></tr>
</tbody></table>
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<span class="sc1" style="white-space: pre;"><span style="font-family: "courier new"; font-size: x-small;"><br /></span></span>
Efficient frontier based on historical returns is charted in <b><span style="color: red;"><u>red</u></span></b>, while implied returns are in <b><span style="color: #6aa84f;"><u>green</u></span></b>:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJquyGyv_35-oXGO280lkyKvO8z_VDjQQmw3ZcAqIh-Gly8pwwM71I4ktDuZScxE2_MX06itE_Hx7aQdAEqnRXx0SVCO-hW8Di0ztd9P6QGsdgrPW86e6-jCty_wbXxTMyIaC_xCAHEXlg/s1600/figure_hist_pi.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="481" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJquyGyv_35-oXGO280lkyKvO8z_VDjQQmw3ZcAqIh-Gly8pwwM71I4ktDuZScxE2_MX06itE_Hx7aQdAEqnRXx0SVCO-hW8Di0ztd9P6QGsdgrPW86e6-jCty_wbXxTMyIaC_xCAHEXlg/s640/figure_hist_pi.png" width="640" /></a></div>
<b>Incorporating custom views to equilibrium returns</b><br />
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As we have already mentioned, the whole idea behind the reverse and forward optimization in Black-Litterman model is a process of incorporating custom views to the returns. The good news is that the whole process can be expressed as mathematical formula, while the bad news is that the steps to derive this formula are beyond the scope of this article.<br />
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Given the views and links matrices \(\mathbf{Q}\) and \(\mathbf{P}\), we calculate view-adjusted excess returns \({\pi}'\) as follows:<br />
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$$ \tau = 0.025 $$
$$ \omega = \tau \cdot \mathbf{P} \cdot \mathbf{C} \cdot \mathbf{P}^T $$
$$ {\pi}' = [(\tau \mathbf{C})^{-1} + \mathbf{P}^T \omega^{-1} \mathbf{P}]^{-1} \cdot [(\tau \mathbf{C})^{-1} \pi + \mathbf{P}^T \omega^{-1} \mathbf{Q})] $$
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, where \(\tau\) is scaling factor, \(\omega\) is uncertainty matrix and \({\pi}'\) is vector of view-adjusted equilibrium excess returns.<br />
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Please note that rather than specifying uncertainty matrix of views \(\mathbf{P}\) explicitly by the investor, we derive it from the formula above. It's because we believe that volatility of assets represented by covariance matrix \(\mathbf{C}\) is affecting certainty of both returns and views in a similar way.<br />
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Going back to our example, we have the vector of <b>nine </b>excess returns \(\pi\), to which we want to apply our views. Let's our views to be as below:<br />
<ul>
<li>Microsoft (MSFT) will outperform General Electric (GE) by 2%</li>
<li>Apple (AAPL) will under-perform Johnson & Johnson (JNJ) by 2%</li>
</ul>
Of course these views are created randomly for the sake of our example, but in a real-world scenario they may be the result of some kind of observation based on statistical arbitrage. These <b>two</b> views will be mapped to a portfolio of <b>nine </b>assets. Therefore, the corresponding views and link matrices will have the following dimensions and content:<br />
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$$ \mathbf{Q}_{1 \times 2} = \begin{pmatrix}0.02 & 0.02\end{pmatrix} $$
$$ \mathbf{P}_{2 \times 9} = \begin{pmatrix}0 & 0 & 1 & 0 &-1 & 0 & 0 & 0 & 0\\ 0 &-1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix} $$
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, where the first row in a link matrix \(\mathbf{P}\) has a positive<span style="background-color: white;"> sign <b>+1 </b>for MSFT and negative <b>-1</b> for GE.</span><br />
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By applying these views to an original vector of excess equilibrium returns \(\pi\), we will get the view-adjusted vector \({\pi}'\), later used to forward-optimize optimal risky portfolio weights \(\mathbf{W}'\):<br />
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<table style="width: 375px;">
<tbody>
<tr><td><b>Name</b></td><td>\(\mathbf{W}\) </td><td>\({\pi}\) </td><td>\({\pi}'\) </td><td>\(\mathbf{W}'\) </td></tr>
<tr><td>XOM </td><td>16.0% </td><td>15.6% </td><td>14.9% </td><td>15.3% </td></tr>
<tr><td>AAPL</td><td>15.6% </td><td>17.9% </td><td>13.1% </td><td>3.3% </td></tr>
<tr><td>MSFT</td><td>11.2% </td><td><span style="background-color: white;">15.2% </span></td><td><span style="background-color: yellow;">15.7% </span></td><td>22.6% </td></tr>
<tr><td>JNJ </td><td>9.7% </td><td>9.9% </td><td>10.1% </td><td>21.9% </td></tr>
<tr><td>GE </td><td>9.4% </td><td>17.9% </td><td><span style="background-color: yellow;">16.1% </span></td><td>-0.0% </td></tr>
<tr><td>GOOG</td><td>11.6% </td><td>16.5% </td><td>15.2% </td><td>11.6% </td></tr>
<tr><td>CVX </td><td>9.2% </td><td>17.3% </td><td>16.4% </td><td>8.8% </td></tr>
<tr><td>PG </td><td>8.5% </td><td>9.4% </td><td>9.2% </td><td>8.4% </td></tr>
<tr><td>WFC </td><td>8.7% </td><td>21.8% </td><td>20.5% </td><td>8.2% </td></tr>
</tbody></table>
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These views are incorporated into equilibrium returns \(\pi\) also with respect to the uncertainty matrix \(\omega\). Therefore, for example, the stated view that MSFT will outperform GE by 2% is not fully incorporated into a difference in their implied returns, which is just <span style="background-color: yellow;">16.1%</span> - <span style="background-color: yellow;">15.7%</span> = 0.4%.<br />
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<b>Forward-optimization of view-adjusted returns</b><br />
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Once the view-adjusted equilibrium returns are ready, the final step is forward mean-variance optimization of the market weights \(\mathbf{W}'\) with respect to these returns \({\pi}'\) and historical covariances \(\mathbf{C}\), pretty much as described in the previous post: <a href="http://www.quantandfinancial.com/2013/07/mean-variance-portfolio-optimization.html" target="_blank">Mean-Variance Portfolio Optimization</a><br />
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Graphically, the efficient frontier constructed using equilibrium returns <b><span style="color: #6aa84f;"><u>before</u> </span></b>and <b><u><span style="color: blue;">after</span></u></b> incorporating views looks as follows.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY-rzflzgyenuL52UMpgyXM_M1Pr_iSiR3tehaByeilhFdF-ZYZTtk2Ecx5MgrJ4AgV7oVgnYwrb112R2lU7-gXfYTyEnzhAph8H3Sg3gQemaC7iGSecGab0nZKH2tXrsLEjjEA-WpShS0/s1600/fig_adj_pi.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="481" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY-rzflzgyenuL52UMpgyXM_M1Pr_iSiR3tehaByeilhFdF-ZYZTtk2Ecx5MgrJ4AgV7oVgnYwrb112R2lU7-gXfYTyEnzhAph8H3Sg3gQemaC7iGSecGab0nZKH2tXrsLEjjEA-WpShS0/s640/fig_adj_pi.png" width="640" /></a></div>
<b>Conclusion</b><br />
<b><br /></b>
Black-Litterman model is based on an assumption that asset returns have greatest impact to portfolio weightings in mean-variance optimization. It is therefore attempting to reverse-engineer these returns from index constituents rather than relying on historical data. This results into several advantages including but not limited to:<br />
<ul>
<li>Intuitive portfolios with weightings not too much different from benchmark indices.</li>
<li>Ability to incorporate custom views</li>
<li>Lower tracking error and reliance on historical data</li>
<li>Greater stability of efficient frontier and better diversification</li>
</ul>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com2tag:blogger.com,1999:blog-1922764065702058602.post-55767504664145673512013-07-20T22:00:00.001+01:002020-06-26T04:24:49.524+01:00Mean-Variance Portfolio Optimization<a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" rel="noopener" target="_blank">
<img src="https://raw.githubusercontent.com/omartinsky/QuantAndFinancial/master/img/open_jupyter_notebook.png" style="display: block; margin: auto; width: 110px;" /> </a>
<br />
This article introduces readers to the mean-variance optimization of asset portfolios. The underlying formulas are implemented in Python. Market data has been downloaded from Google Finance. The case study is available <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" target="_blank">here</a>.<br />
<b><br /></b>
<b>Calculation of assets' weights, returns and covariances</b><br />
<b><br /></b>
Our example starts with the calculation of vector of asset weights \(\mathbf{W}_{n \times 1}\), expected annual returns \(\mathbf{R}_{n \times 1}\) and covariances \(\mathbf{C}_{n \times n}\). Top nine S&P companies sorted by market capitalization are used as asset classes for the purpose of this article: <b>XOM</b>, <b>AAPL</b>, <b>MSFT</b>, <b>JNJ</b>, <b>GE</b>, <b>GOOG</b>, <b>CVX</b>, <b>PG</b> and <b>WFC</b>, as of 1 Jul 2013.<br />
<br />
The time frame of historical data should depend on planned investment horizon. For the purpose of our analysis, we will consider daily prices for recent two years. The function call from previously mentioned <u><a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" target="_blank">example</a></u> implementing the loader is as follows:<br />
<br />
<span style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Load names, prices, capitalizations from yahoo finance</span><br />
<span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">names</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">prices</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">caps</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">load_data</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">()</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><br />
<span style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Estimate assets's expected return and covariances</span><br />
<span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">names</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">assets_meanvar</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">names</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">prices</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">caps</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">.015</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Define Risk-free rate</span><br />
<br />
The data downloaded in this example will yield to the historical returns, deviations and capitalization-based weights as shown below. In the next section, we will use these figures to calculate portfolio risk/return characteristics and to optimize its asset weights.<br />
<br />
<span style="font-family: "courier new", courier, monospace;">Name Weight Return Dev</span><br />
<span style="font-family: "courier new", courier, monospace;">XOM 16.0% 7.3% 19.8%</span><br />
<span style="font-family: "courier new", courier, monospace;">AAPL 15.6% 13.0% 30.3%</span><br />
<span style="font-family: "courier new", courier, monospace;">MSFT 11.3% 17.2% 22.6%</span><br />
<span style="font-family: "courier new", courier, monospace;">JNJ 9.7% 14.4% 13.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">GE 9.4% 14.0% 24.3%</span><br />
<span style="font-family: "courier new", courier, monospace;">GOOG 11.6% 33.2% 25.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">CVX 9.2% 9.2% 22.6%</span><br />
<span style="font-family: "courier new", courier, monospace;">PG 8.5% 11.2% 15.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">WFC 8.7% 26.9% 30.0%</span><br />
<b><br /></b>
<b>Mean-variance trade-off and diversification benefit</b><br />
<br />
In the investment management process, almost every risky asset class exhibits some degree of trade-off between the returns and uncertainty of these returns. Mean returns are quantitatively measured by geometrically averaging series of daily or weekly returns over a certain period of time, while the uncertainty is expressed by the variance or standard deviation of such series.<br />
<br />
Naturally more volatile the asset is, higher is also the expected return. This relationship is determined by the supply and demand forces on a capital market and may be mathematically expressed by one of the capital pricing models, such as <b>APT</b>, <b>CAPM </b>or others.<br />
<br />
Most of these pricing models are based on an assumption that only systematic risk is reflected in capital prices and therefore investors shouldn't expect additional risk premium by holding poorly diversified or standalone investments.
<br />
<br />
Assuming normal distribution of asset returns, we can quantitatively measure this diversification benefit by calculating correlation between two price series, which is equal or less than one.<br />
<br />
Let's consider a simple example of portfolio containing two assets, 50% of asset <b>A</b> and 50% of asset <b>B</b>, where asset returns are \(r_{A}=4\%\), \(r_{B} = 5\%\) and variances are \(\sigma_{A}^{2}=7\%^{2}\) and \(\sigma_{B}^{2}=8\%^{2}\).<br />
<br />
In case there is no diversification benefit, portfolio expected return and variance will be just linear combination of the asset weights, in this case \(r_{p}=4.5\%\), \(\sigma_{p}^{2}=7.5\%^{2}\).<br />
<br />
However, in case the correlation between these two assets is less than one and therefore diversification potential is available, portfolio variance will be less than linear combination of weights: \(\sigma_{p}^{2}<7.5\%^{2}\). The mean-variance trade-offs for different levels of diversification are shown on the Figure 1.<br />
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<b>Portfolio mean-variance calculation</b><br />
<br />
The generalized formula for calculating portfolio return \(r_{p}\) and variance \(\sigma_{p}\) consisting of \(n\) different assets is then defined as:<br />
$$ r_{p} = \mathbf{W} \cdot \mathbf{R} $$<br />
, where \(\mathbf{W}_{n\times 1}\) is the vector of asset weights and \(\mathbf{R}_{n\times 1}\) vector of corresponding asset returns.<br />
<br />
Portfolio variance is then defined as:<br />
$$ \sigma_{p}^{2} = \mathbf{W} \cdot \mathbf{C} \cdot \mathbf{W} $$<br />
, where \(\mathbf{C}_{n\times n}\) is the covariance matrix of asset returns.<br />
<br />
The corresponding code in our <a href="https://github.com/omartinsky/BlackLitterman/blob/master/black_litterman.ipynb" target="_blank">python example</a>:<br />
<br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Calculate portfolio historical return and variance</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_mean_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><br />
<br />
<b>Portfolio Optimization </b><br />
<br />
Considering the starting vector of weights \(\mathbf(W_{n \times 1})\), the optimization process is tailored towards maximizing some kind of mean-variance utility function, such as Sharpe ratio:<br />
$$ s=\frac{r_{p} - r_{f} }{\sigma_{p}} $$<br />
, because we know that optimal risky portfolio with highest sharpe ratio \(s\) lies on a tangency of efficient frontier with the capital market line (CML).<br />
<br />
Given the historical asset returns \(\mathbf{R}_{n \times 1}\) and covariances \(\mathbf{C}_{n \times n}\), the optimization code using SciPy's <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_slsqp.html">SLSQP method</a> may look for example as follows:<br />
<br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Given risk-free rate, assets returns and covariances, this function calculates</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># weights of tangency portfolio with respect to sharpe ratio maximization</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">def</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc9" style="color: magenta; font-family: "courier new"; font-size: 10pt; white-space: pre;">solve_weights</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">):</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">def</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc9" style="color: magenta; font-family: "courier new"; font-size: 10pt; white-space: pre;">fitness</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">):</span><br />
<span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"><span style="color: green;"> # calculate mean/variance of the portfolio</span>
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_mean_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">util</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">-</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">/</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">sqrt</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># utility = Sharpe ratio</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">return</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">/</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">util</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># maximize the utility</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">len</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">ones</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">([</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">])/</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># start with equal weights</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">b_</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">[(</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">0.</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1.</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">for</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">i</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">in</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">range</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)]</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># weights between 0%..100%. </span><br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"> # No leverage, no shorting</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">c_</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">({</span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'type'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'eq'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'fun'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">lambda</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">sum</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)-</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1.</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">})</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Sum of weights = 100%</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">scipy</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimize</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">minimize</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">fitness</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><br />
<span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> method</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">='SLSQP'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">constraints</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">c_</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">bounds</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">b_</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><br />
<span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">if</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">not</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">success</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">raise</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">BaseException</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">message</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">return</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">x</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span style="color: green; font-family: "courier new"; font-size: 13px; white-space: pre;"># Return optimized weights</span><br />
<span style="color: green; font-family: "courier new"; font-size: 13px; white-space: pre;"><br /></span>The function returns vector of optimized weights, which together with original vector of returns and deviations looks as follows:<br />
<br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># optimize</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">solve_weights</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_mean_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># calculate tangency portfolio</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">front_mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">front_var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">solve_frontier</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># calculate min-var frontier</span><br />
<br />
We can see that this optimization results in a concentrated portfolio consisting just of two constituents: Johnson&Johnson and Google:<br />
<br />
<span style="font-family: "courier new", courier, monospace;">Name Weight Return Dev</span><br />
<span style="font-family: "courier new", courier, monospace;">XOM 0.0% 7.3% 19.8%</span><br />
<span style="font-family: "courier new", courier, monospace;">AAPL -0.0% 13.0% 30.3%</span><br />
<span style="font-family: "courier new", courier, monospace;">MSFT -0.0% 17.2% 22.6%</span><br />
<span style="font-family: "courier new", courier, monospace;">JNJ 45.1% 14.4% 13.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">GE 0.0% 14.0% 24.3%</span><br />
<span style="font-family: "courier new", courier, monospace;">GOOG 52.8% 33.2% 25.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">CVX 0.0% 9.2% 22.6%</span><br />
<span style="font-family: "courier new", courier, monospace;">PG -0.0% 11.2% 15.9%</span><br />
<span style="font-family: "courier new", courier, monospace;">WFC 2.1% 26.9% 30.0%</span><br />
<span style="font-family: "courier new", courier, monospace; font-size: x-small;"><br /></span>
It is not surprising that these assets have one of the lowest correlations among all pairs (0.431). Companies Apple and Exxon were not selected despite the fact that they have even lower mutual correlation. This is because their stand-alone risk/return trade-off is not that great indeed.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmxP8qeVpMKZILEv12ZplNTYsDwPPcDERYJ1RUBZmm0-ejQna7ShTqEu9PctfS5CWqU0aM3R6a7u-xpBubfT0aTXSBTZzunbWlldh2UfOpRP6fHUodQ00fHDIc9D3iCSUliIXE2f6_jgS3/s1600/correl.png" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmxP8qeVpMKZILEv12ZplNTYsDwPPcDERYJ1RUBZmm0-ejQna7ShTqEu9PctfS5CWqU0aM3R6a7u-xpBubfT0aTXSBTZzunbWlldh2UfOpRP6fHUodQ00fHDIc9D3iCSUliIXE2f6_jgS3/s1600/correl.png" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Correlation between assets</td></tr>
</tbody></table>
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<b>Calculation of minimum variance frontier</b><br />
<b><br /></b>
In the previous section, we have used optimization technique to find the best combination of weights in order to maximize the risk/return profile (Sharpe ratio) of the portfolio. This resulted into a single optimal risky portfolio represented by a single point in the mean-variance graph. Although the utility function is clear, to maximize the Sharpe ratio, it has two degrees of freedom - the mean and the variance.<br />
<br />
In order to calculate the minimum variance frontier, we need to iterate through all levels of investor's risk aversity, represented by required return (y-axis) and use the optimization algorithm in order to minimize the portfolio variance. In each iteration, the required return is hold constant for the purpose of optimization, reducing the problem to one degree of freedom. The output of such optimization will be a vector of minimum variances, one value for each level of risk aversity, also called the minimum variance frontier.<br />
<br />
The corresponding Python function may look for example as follows:<br />
<br />
<span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Given risk-free rate, assets returns and covariances, this function calculates</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># min-var frontier and returns its [x,y] points in two arrays</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">def</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc9" style="color: magenta; font-family: "courier new"; font-size: 10pt; white-space: pre;">solve_frontier</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">rf</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">):</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">def</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc9" style="color: magenta; font-family: "courier new"; font-size: 10pt; white-space: pre;">fitness</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">r</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">):</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># For given level of return r, find weights which minimizes</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># portfolio variance.</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_mean_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><br />
<span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"><span style="color: green;"> # Big penalty for not meeting stated portfolio return </span></span><br />
<span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"><span style="color: green;"> # effectively serves as optimization constraint</span>
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">penalty</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">100</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">*</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">abs</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">-</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">r</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">return</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">+</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">penalty</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_var</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">[],</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">[]</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">len</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># Number of assets in the portfolio</span><br />
<span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"><span style="color: green;"> # Iterate through the range of returns on Y axis</span>
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">for</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">r</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">in</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">linspace</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">min</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">max</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">num</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">20</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">):</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">ones</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">([</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">])/</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># start optimization with equal weights</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">b_</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">[(</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">0</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">for</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">i</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">in</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">range</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">n</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)]</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">c_</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">({</span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'type'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'eq'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'fun'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">lambda</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">sum</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)-</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1.</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">})</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">scipy</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimize</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">minimize</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">fitness</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">R</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">r</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><br />
<span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> method</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc4" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">'SLSQP'</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">constraints</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">c_</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">bounds</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">=</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">b_</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">if</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">not</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">success</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">raise</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">BaseException</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">message</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc1" style="color: green; font-family: "courier new"; font-size: 10pt; white-space: pre;"># add point to the min-var frontier [x,y] = [optimized.x, r]</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">append</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">r</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">append</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">port_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">optimized</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">.</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">x</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">,</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">C</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">))</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">
</span><span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">return</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">array</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_mean</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">),</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">array</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">frontier_var</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)</span><br />
<br />
Again, we have chosen Sequential Least Square Programming method (SLSQP), which allows us to perform the constrained optimization based on the following constraints:<br />
<br />
<ul>
<li>Sum of weights must be 0</li>
<li>Weights must be in range (0,1) - no short-selling or leveraged holdings.</li>
<li>Portfolio required return is given</li>
</ul>
<div>
The first constraint is provided using the lambda function <span class="sc5" style="color: blue; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">lambda</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">:</span><span class="sc0" style="font-family: "courier new"; font-size: 10pt; white-space: pre;"> </span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">sum</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">(</span><span class="sc11" style="font-family: "courier new"; font-size: 10pt; white-space: pre;">W</span><span class="sc10" style="color: navy; font-family: "courier new"; font-size: 10pt; font-weight: bold; white-space: pre;">)-</span><span class="sc2" style="color: red; font-family: "courier new"; font-size: 10pt; white-space: pre;">1.</span>, which is equality constraint saying that the whole expression must be as close to zero as possible. The second constraint are effectively search bounds passed to the optimization function and third constraint is implemented in a fitness function itself. It imposes a big penalty for portfolio mean return not meeting the target return "r".</div>
<div class="separator" style="clear: both; text-align: center;">
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<div>
After solving minimum variance portfolios for all twenty levels of risk aversity, we will get the following minimum variance frontier with optimal risky portfolio represented by dot (o) and individual constituents represented by cross (x):</div>
<div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN8Q2ptjlmB8elKMi4asmseurjyb1A_9QSGKFG4UezFpqqkvJtYWoG3s1xIM9YmBxyv5zxu1VAjEV3D2SRPSEwK-mlyWd21CyI7kBI7VkMN-qskVSzXn1ps2aedrx8VtAweWtvxvBxzsaq/s1600/efffront.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN8Q2ptjlmB8elKMi4asmseurjyb1A_9QSGKFG4UezFpqqkvJtYWoG3s1xIM9YmBxyv5zxu1VAjEV3D2SRPSEwK-mlyWd21CyI7kBI7VkMN-qskVSzXn1ps2aedrx8VtAweWtvxvBxzsaq/s640/efffront.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Minimum Variance Frontier</td></tr>
</tbody></table>
</div>
<div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<b>Conclusion</b></div>
<br />
The major drawback of mean-variance optimization based on historical returns is that such optimization leads to undiversified portfolios, as seen in our example. The reason behind this observation is that market prices are often far from their equilibriums on a risk-adjusted basis, as modeled by the Capital Market Pricing Model.<br />
Moreover, extrapolated historical returns are notoriously bad proxies to be used instead of expected mean returns, which are direct inputs into the mean-variance optimization algorithm.<br />
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In the next post, we will illustrate how to use Black-Litterman model to overcome this problem by deriving returns from the market capitalization weights in the process known as reverse optimization.Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com7tag:blogger.com,1999:blog-1922764065702058602.post-69848530986133199312012-11-07T23:21:00.002+00:002017-02-26T11:56:03.033+00:00Binomial Option Pricing Model<div class="separator" style="clear: both; text-align: center;">
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Link: <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/binomial_option_pricing/binomial_option_pricing.ipynb">IPython notebook</a><br />
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So far we have been discussing mostly pricing and valuation of asset classes with certain and predictable cash flows, such as bonds, loans, bank deposits and others. The certainty of cash payments allowed us to price such instruments using time value of money framework.<br />
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However, the situation gets somewhat more complicated when the cash flows become uncertain or optional, as in case of stock options, pre-payable mortgages, interest-rate collars or other contingent claims. In fact, many complex financial instruments have embedded optionality to some extent.<br />
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When we consider optionality of cash flows, we usually think in terms of probabilities of such cash flow occurring. In most of the cases we can simplify that whether the cash flow does or doesn't occur is determined by the underlying embedded option. The options valuation is therefore quite fundamental topic of quantitative finance.<br />
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In this article, we will discuss Cox-Ross-Rubinstein Option Pricing Model. The model is using binomial tree to value american and European-style call and put options. The aim of this article is to analyze and explain this model on a numerical example and to compare calculated results with the real market prices.<br />
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For the purposes of this post, I have also prepared a <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/binomial_option_pricing/binomial_option_pricing.ipynb" target="_blank">case study</a> implementation in Python.<br />
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<b>Input Data and Case Study</b><br />
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Through this article, we will consider a simple plain-vanilla American-style call option giving the right to buy the underlying instrument at predetermined time and strike price. The important factors to consider would be how the current market value of instrument is far from the strike price, how volatile the market is, how much time is there left till the option expires and what is the risk-free rate and dividend yield.<br />
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All these factors constitute inputs to the option pricing model. Let's assume the underlying instrument to be <b>iShares S&P 500 Index ETF</b>, as of 5th of November 2012. The price series in attached <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/binomial_option_pricing/ivv_2012_11_05.csv" target="_blank">data file</a> looks as follows (Source: Google Finance):<br />
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<span style="font-family: "courier new" , "courier" , monospace;">date, open, high, low, close, volume</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2012-11-01 00:00:00,142.23,143.58,142.13,143.46,628236</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2012-11-02 00:00:00,144.28,144.28,142.0,142.1,569903</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2012-11-05 00:00:00,141.94,142.73,141.53,142.41,345956</span><br />
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To retrieve the price history from Google Finance in Python, we can use the code already present in the datasources.google module:<br />
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<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">import</span><span style="color: #000066; font-family: monospace;"> datasources.</span><span class="me1" style="font-family: monospace;">google</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">as</span><span style="color: #000066; font-family: monospace;"> google</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">prices = google.</span><span class="me1" style="font-family: monospace;">getquotesfromweb</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'IVV'</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">getprices</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">prices = prices</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">-</span><span class="nu0" style="color: orangered; font-family: monospace;">250</span><span style="color: #000066; font-family: monospace;">:</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># We will use last 250 trading days</span></span><br />
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For the valuation, we will need additional information, such as Dividend Yield and Risk Free Rate. The latest price and dividend yield on iShares S&P 500 Index ETF can be retrieved also from Google Finance:<br />
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The risk-free rate is derived from US treasury yields with maturity date similar to the option's expiry date, as of 5th of November 2012. In this case, 1 month yield seems to be the most appropriate. We can safely assume that there is virtually no credit risk for both US Treasuries and option contracts, since their performance is guaranteed by US government and clearing houses, respectively:<br />
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As we have already mentioned, the option being valued is an American Call on iShares S&P 500 Index ETF. We will choose the option with strike price 140, expiring on 2012/12/22. Given the valuation date of 2012/11/05, the time to expiration is precisely 46 calendar days.<br />
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<b>Instrument Volatility Calculation</b><br />
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Calculation of instrument's volatility may be a bit tricky because of several reasons. The most important one is question how long history of data we should consider. If the data window is too short, we may end up with insufficient number of samples with very little statistical significance. On the other hand, looking to far to the past includes a risk of underlying structural changes which make the outcome irrelevant as well. Choosing a time-frame of 1 year (250 trading days) sounds like a reasonable solution.<br />
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First what we need to do is to calculate daily returns from the above price history. Bearing in mind the fact that daily returns are continuously compounded, we need to apply a logarithm function to get the nominal rates:<br />
$$ e^{r} = \frac{p_i}{p_{i-1}} \; ; \; r = log \frac{p_i}{p_{i-1}} $$<br />
Daily volatility is then defined as a standard deviation of these returns. Annualized figure will be calculated as follows:<br />
$$ stdev\left ( R \right ) \times \sqrt{250} $$<br />
The Python code performing the whole calculation just reflects this principle:<br />
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<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">returns = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">range</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span style="color: #000066; font-family: monospace;">, </span><span class="kw2" style="color: green; font-family: monospace;">len</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">prices</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">-</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> r = log</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">prices</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">i</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> / prices</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">i-</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">]</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> returns.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">r</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">volat_d = numpy.</span><span class="me1" style="font-family: monospace;">std</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">returns</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Daily volatility</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">volat = volat_d </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> </span><span class="nu0" style="color: orangered; font-family: monospace;">250</span><span class="sy0" style="color: #66cc66; font-family: monospace;">**</span><span style="color: #000066; font-family: monospace;">.5 </span><span class="co1" style="font-family: monospace; font-style: italic;"># Annualized volatility</span></span><br />
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the output of this calculation is an annualized volatility of 18.2%, which will be used later as an input to the pricing model:<br />
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<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'Volatility %0.3f'</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> volat</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">Volatility : </span><span class="nu0" style="color: orangered; font-family: monospace;">0.182</span></span><br />
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><br /></span></span>Another solution would be to imply the volatility from other options' market prices using the reverse valuation process, instead of trying to calculate it directly from price data. The advantage of implied volatility approach is reduced model risk of choosing inappropriate parameters.<br />
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<b>Generating a Binomial Tree</b><br />
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To generate the binomial tree, we first need to summarize all relevant inputs for the pricing model which we have mentioned previously. The inputs are as follows:<br />
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<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> Price : </span><span class="nu0" style="color: orangered; font-family: monospace;">142.410</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> Strike : </span><span class="nu0" style="color: orangered; font-family: monospace;">140.000</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> Risk-free : </span><span class="nu0" style="color: orangered; font-family: monospace;">0.001</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> Div Yield : </span><span class="nu0" style="color: orangered; font-family: monospace;">0.020</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> TTE Days : </span><span class="nu0" style="color: orangered; font-family: monospace;">46.000</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">Volatility : </span><span class="nu0" style="color: orangered; font-family: monospace;">0.182</span></span><br />
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From the given risk-free rate, dividend yield and annual volatility, we will calculate the up and down movements for each node of the tree. Assuming the binomial tree with 8 levels and 46 days to expiration, it turns out that each level represents step of 5.75 days, or 0.015753 years. This is denoted as \(t_\bigtriangleup=0.015753\).<br />
Up and down price movements per step (u, d) are then calculated by de-annualizing instrument's volatility \(\nu\) from previous section and converting it back to an (expected) continuous daily return:<br />
$$ u = e^{\nu \cdot \sqrt{t_{\bigtriangleup}}} \; ; \; d = \frac{1}{u} $$<br />
These price movements must be balanced in terms of the probability in such a way that expected outcome will yield into the arbitrage-free future price determined by the risk-free rate and dividend yield:<br />
$$ u \cdot \pi_u + d \cdot \pi_d = e^{(r_f - dy) \cdot t_{\bigtriangleup}} $$<br />
where \(\pi_u\) is the probability of up movement, \(\pi_d = 1-\pi_u\) is the probability of down movement, \(r_f\) is the risk-free rate and \(dy\) is dividend yield.<br />
Given the inputs above, generated binomial three with 8 levels would graphically look as follows:<br />
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<b>Backward Reduction of the Tree</b><br />
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As soon as the binomial tree is generated using the up and down turns, we will use it to value options. It is quite apparent that options just before the expiration have no uncertainty or time value associated, so their whole appraisal consists only from the intrinsic value given as a difference between the strike price (140) and underlying instrument's price (black figures in the terminal nodes of tree). If the option is out-of-money, it's price is naturally zero, as portrayed by the bottom half of the terminal nodes.<br />
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In fact, we are not interested in options' value at their expiration, but at the present time. Hence, we will use non-terminal nodes of the tree to bring the terminal option value back to the present. This is done by a reduction of the binomial tree as depicted by red arrows.<br />
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Value of European-style option at any node is again determined by the probabilistic outcome of up and down movements, discounted to the present using a risk-free rate. For American-style options, we need to bear in mind also an early exercise scenario, where the node is prematurely terminated, similarly as other terminal nodes in the 8th level. The option value for any such node is then calculated as follows:<br />
$$ v = max \left( \frac{v_u \cdot \pi_u + v_d \cdot \pi_d}{e^{r_f \cdot t_{\bigtriangleup}}} \; ; \; p - s\right) $$<br />
where \(v\) and \(p\) are the option value and instrument price at given node, \(s\) is the strike price, \(u\) and \(d\) are up and down movements, \(\pi_u\) and \(\pi_d\) are probabilities of these movements, and \(e^{r_f \cdot t_{\bigtriangleup}}\) is a risk-free discount factor.<br />
If we speak in terms of concrete figures, option value in the starting node is calculated as an expected value in the successive nodes \((0.488 \times 6.924 + 0.512 \times 2.791=4.899\)), which is almost the same as after application of the discount factor \(e^{r_f \cdot t_{\bigtriangleup}}\) (0.07% treasury yield is negligible on a daily basis for the purpose of this example).<br />
In case of the option being exercised prematurely, it's intrinsic value would be \(p-s = 2.41\), which is less than the expected value. The option value at starting node is therefore 4.899.<br />
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The corresponding Python implementation of tree reduction algorithm would look similarly to this:<br />
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<span style="background-color: white;"><span class="co1" style="font-family: monospace; font-style: italic;"># Generate terminal nodes of binomial tree</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">level = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'Tree level %i'</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">range</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span style="color: #000066; font-family: monospace;">, n+</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span class="co1" style="font-family: monospace; font-style: italic;"># Iterate through nodes</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Instrument's price at the node</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pr = price </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> d</span><span class="sy0" style="color: #66cc66; font-family: monospace;">**</span><span style="color: #000066; font-family: monospace;">i </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> u</span><span class="sy0" style="color: #66cc66; font-family: monospace;">**</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n-i</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Option value at the node (depending on side)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> ov = </span><span class="kw2" style="color: green; font-family: monospace;">max</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, pr-strike</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> side==call </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">else</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">max</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, strike-pr</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> level.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pr, ov</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'Node Price %.3f, Option Value %.3f'</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pr, ov</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;">levels = </span><span class="br0" style="font-family: monospace;">[</span><span class="kw2" style="color: green; font-family: monospace;">None</span><span style="color: #000066; font-family: monospace;">,</span><span class="kw2" style="color: green; font-family: monospace;">None</span><span style="color: #000066; font-family: monospace;">,</span><span class="kw2" style="color: green; font-family: monospace;">None</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Remember levels 0,1,2 for the greeks</span><br style="color: #000066; font-family: monospace;" /><br style="color: #000066; font-family: monospace;" /><span class="co1" style="font-family: monospace; font-style: italic;"># reduce binomial tree</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">range</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n-</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">, -</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">, -</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span class="co1" style="font-family: monospace; font-style: italic;"># [n-1 to 0]</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> levelNext = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'Tree level %i'</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> i</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> j </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">range</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span style="color: #000066; font-family: monospace;">, i+</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span class="co1" style="font-family: monospace; font-style: italic;"># Iterate through nodes</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> node_u, node_d = level</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">j</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;">, level</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">j+</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">]</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Instrument's price at the node</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pr = node_d</span><span class="br0" style="font-family: monospace;">[</span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> / d</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># Option value at the node (depending on side)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> ov = </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">node_d</span><span class="br0" style="font-family: monospace;">[</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> pd + node_u</span><span class="br0" style="font-family: monospace;">[</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> pu</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;"> + rf</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> style==american: </span><span class="co1" style="font-family: monospace; font-style: italic;"># American options can be exercised anytime</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> ov = </span><span class="kw2" style="color: green; font-family: monospace;">max</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">ov, pr-strike </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> side==call </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">else</span><span style="color: #000066; font-family: monospace;"> strike-pr</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> levelNext.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pr, ov</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">'Node Price %.3f, Option Value %.3f'</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pr, ov</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> level = levelNext</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> j</span><span class="sy0" style="color: #66cc66; font-family: monospace;"><</span><span style="color: #000066; font-family: monospace;">=</span><span class="nu0" style="color: orangered; font-family: monospace;">2</span><span style="color: #000066; font-family: monospace;">: levels</span><span class="br0" style="font-family: monospace;">[</span><span style="color: #000066; font-family: monospace;">j</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;">=level </span><span class="co1" style="font-family: monospace; font-style: italic;"># save level 0,1,2 of the tree</span></span><br />
<br />
<b>The Real Market</b><br />
<b><br /></b>
We originally based our case study on the real market conditions as of 2012/11/05, taking into the consideration underlying instrument's market data from Google Finance and Financial Times. Google also provides market data for options traded on NYSE Arca.<br />
<br />
As we can see from the following screenshot, the option being discussed and valued in this article is currently trading at <b>4.500 - 4.900</b>, which is fairly close to the theoretical option price of <b>4.899</b>.<br />
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The difference between theoretical value and real market price could have several possible causes, such as the model risk or inefficiency of a market itself. As we have seen, there have been done lots of assumptions regarding model parameters and it would be also reasonable to expect that not all analysts are using the same estimates.<br />
<br />
It is also worth noting that there may be significant fluctuations in model's output depending on the length of volatility look-back window, mostly due to volatility clustering and conditional heteroskedasticity. For instance, a time-frame of 100, 200 and 250 days would lead to valuations of 4.714, 4.339 and 4.899. As we have mentioned previously, this problem could be partially solved by implying volatility from option market prices.<br />
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<br />
<b>The Greeks</b><br />
<b><br /></b>
Apart of the option value at the head node, we can extract few other figures from the tree, such as option's delta, gamma and theta. For this purpose, we need to process first three levels of the tree:<br />
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<b>Delta </b>is the rate of change of option's value with respect to changes in underlying instrument's price. Looking to the figure above, this rate is derived from nodes <b>10</b> and <b>11 </b>as follows:<br />
$$ \delta =\frac{v_{10} - v_{11}}{p_{10} - p_{11}} = \frac{6.924 - 2.971}{145.701 - 139.194} = 0.607 $$<br />
<b>Gamma</b> is a rate of change of option's delta with respect to changes in underlying instrument's price. Again, we first need to calculate deltas in nodes <b>10 </b>and <b>11:</b><br />
$$ \delta_{10} =\frac{v_{20} - v_{21}}{p_{20} - p_{21}} \; ; \; \delta_{11} =\frac{v_{21} - v_{22}}{p_{21} - p_{22}} $$<br />
Gamma is then calculated as:<br />
$$ \gamma = \frac{\delta_{10}-\delta_{11}}{p_{10} - p_{11}} = 0.022 $$<br />
<b>Theta</b> is sensitivity of option's value with respect to the passage of time. Please note that nodes <b>00</b> and <b>21 </b>have the same instrument's price, only the option's value differs. It is therefore possible to derive option's theta as follows:<br />
$$ \theta = \frac{v_{21} - v_{00}}{2 \times t_{\bigtriangleup}} = -13.157 $$Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-21514224858851178552012-10-20T18:18:00.000+01:002017-02-26T10:45:29.989+00:00Treasury Yield Curve BootstrappingLink: <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/yield_curve_bootstrapping/bootstrapping.ipynb">IPython notebook</a><br />
<br />
In the previous post, we have introduced readers to basic principles of time value of money and presented Python implementation of the calculator. The time value of money is an essential principle applied in almost all areas of the financial mathematics. Today, we will discuss one of them - the basics of yield curve construction and bootstrapping. Please note that full implementation of this example can be found <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/yield_curve_bootstrapping/bootstrapping.ipynb" target="_blank">here</a>.<br />
<b><br /></b>
<b>Calculation of Yield Curve from Market Prices</b>
<br />
<br />
<span style="font-family: inherit;">When calculating yield curves from market prices, the big question is which securities we should consider in the calculation. If we ge</span>neralize the problem to a set of credit risk-free government securities, our choices will be as follows:<br />
<ul>
<li>All on-the-run securities</li>
<li>All on-the-run and some off-the-run securities (to fill the gaps)</li>
<li>All securities (both on and off-the run, with aggregated YTMs)</li>
</ul>
On-the-run securities are those which have been issued recently, thus the most liquid ones. Unfortunately, there are often wide maturity gaps between them. Because of this, analysts often fill these gaps with additional off-the-run issues. For example, a 50-year bond issued 2 years ago effectively serves as a security filling the maturity gap of 48 years.<br />
<br />
It is even possible to combine all on and off-the run securities in such a way they will expire on the same date. This will naturally lead to collisions in yields and maturities, which can be then aggregated and interpolated for even better results.<br />
<br />
Another solution is to use treasury coupon strips. The coupon strip with a single payment is priced in a way which yields directly to the spot rate for given maturity. With this approach, the bootstrapping process discussed later will not be necessary. However, the drawback using coupon strips is different tax treatment skewing the whole calculation.<br />
<br />
With respect to the facts above and for the purpose of this simple example, we will be using on-the-run market prices of UK Gilts, as of 19th of September 2012. The quoted gilts span maturities from 6 months to 48 years, sufficient enough for the sake of this analysis. The relevant prices were obtained from<a href="http://www.bondscape.net/"> www.bondscape.net</a> and look as follows:<br />
<br />
<span style="font-family: "courier new" , "courier" , monospace;">epic, description, coupon, maturity, bid, ask</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">TR13, Uk Gilt Treasury Stk, 4.5, 07-Mar-13, 101.92, 102.07</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">T813, Uk Gilt Treasury Stk, 8, 27-Sep-13, 107.86, 107.98</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">TR14, Uk Gilt Treasury Stk, 2.25, 07-Mar-14, 102.90, 103.05</span><br />
<br />
Calculated yields to maturity don't necessarily correspond to those quoted in data file due to accrued interest and a fact that coupon payments are bound to specific calendar date, which is not necessarily one semi-annual period from now.<br />
<br />
The code performing the calculation in Python would look as follows. The input is a set of bonds, each with given maturity, price and coupon rate. These values are passed into the <a href="http://www.quantandfinancial.com/2012/08/time-value-of-money-calculator.html" target="_blank">TVM calculator</a> introduced in one of the previous articles to calculate the bond's yield to maturity:<br />
<b><br /></b>
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">tr = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># list of raw (not interpolated) times to maturity</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">yr = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># list of raw (not interpolated) yields</span></span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> b </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> bonds:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> ttm = </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">b.</span><span class="me1" style="font-family: monospace;">maturity</span><span style="color: #000066; font-family: monospace;"> - localtime</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">days</span><span style="color: #000066; font-family: monospace;"> / </span><span class="nu0" style="color: orangered; font-family: monospace;">360</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> price = </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">b.</span><span class="me1" style="font-family: monospace;">bid</span><span style="color: #000066; font-family: monospace;">+b.</span><span class="me1" style="font-family: monospace;">ask</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">/</span><span class="nu0" style="color: orangered; font-family: monospace;">2</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> ytm = TVM</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n=ttm</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">b.</span><span class="me1" style="font-family: monospace;">freq</span><span style="color: #000066; font-family: monospace;">, pv=-price, pmt=b.</span><span class="me1" style="font-family: monospace;">couponRate</span><span style="color: #000066; font-family: monospace;">/b.</span><span class="me1" style="font-family: monospace;">freq</span><span style="color: #000066; font-family: monospace;">, fv=</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">calc_r</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> b.</span><span class="me1" style="font-family: monospace;">freq</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> tr.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">ttm</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> yr.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">ytm</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<b><br /></b>
These yields, together with maturities are then aggregated in lists <span style="font-family: "courier new" , "courier" , monospace;">tr</span> (time to maturity) and <span style="font-family: "courier new" , "courier" , monospace;">yr</span> (yield to maturity)<br />
<b><br /></b>
<span style="font-family: "courier new" , "courier" , monospace;"><b>TTM YTM</b></span><br />
<span style="font-family: "courier new" , "courier" , monospace;">0.47 0.23%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.04 0.34%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.48 0.24%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.99 0.30%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">... ... </span><br />
<br />
<b><span style="font-family: inherit;">Interpolation</span></b><br />
<br />
As the time passes, the maturities of all issues are shortened by one day each day. However, if we want to compare the same yield curve across different dates, the maturities must match. Hence, we need to interpolate and normalize all yield curves into a common set of maturities, e.g. <b>1m</b>, <b>3m</b>, <b>6m</b>, <b>1y</b>, <b>2y</b>,<b> 5y</b> and etc.<br />
<br />
On the other hand, for the purpose of bootstrapping, it would be convenient to interpolate all maturities into a scale with annual intervals, such as from 1 year to 40 years. Therefore, we will go this way.<br />
<br />
The interpolation is performed in Python automatically using SciPy's interp1d command. Apart of the linear interpolation, it provides few others, such as nearest, cubic or quadratic. Unfortunately this algorithm is not able to interpolate outside the initial range - this could be problematic especially for short-term maturities, such as 1 month:<br />
<br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">t = </span><span class="kw2" style="color: green; font-family: monospace;">list</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">range</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">,</span><span class="nu0" style="color: orangered; font-family: monospace;">41</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="co1" style="font-family: monospace; font-style: italic;"># interpolating in range 1..40 years</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">y = </span><span class="br0" style="font-family: monospace;">[</span><span class="br0" style="font-family: monospace;">]</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">interp = scipy.</span><span class="me1" style="font-family: monospace;">interpolate</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">interp1d</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">tr, yr, bounds_error=</span><span class="kw2" style="color: green; font-family: monospace;">False</span><span style="color: #000066; font-family: monospace;">, fill_value=scipy.</span><span class="me1" style="font-family: monospace;">nan</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">for</span><span style="color: #000066; font-family: monospace;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">in</span><span style="color: #000066; font-family: monospace;"> t:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> value = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">interp</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">i</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">not</span><span style="color: #000066; font-family: monospace;"> scipy.</span><span class="me1" style="font-family: monospace;">isnan</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">value</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span style="font-family: monospace; font-style: italic;"># Don't include out-of-range values</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> y.</span><span class="me1" style="font-family: monospace;">append</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">value</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<br />
The output of this step would be interpolated yield curve <span style="font-family: "courier new" , "courier" , monospace;">y</span><span style="font-family: inherit;"> with maturities </span><span style="font-family: "courier new" , "courier" , monospace;">t=1..40</span><span style="font-family: inherit;">. </span><br />
<br />
<span style="font-family: "courier new" , "courier" , monospace;"><b>TTM YTM </b>(Interpolated)</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.00 0.33%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2.00 0.30%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">3.00 0.40%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">4.00 0.60%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">... ...</span><br />
<b><span style="font-family: inherit;"><br /></span></b>
<b><span style="font-family: inherit;">Bootstrapping of spot rates</span></b><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">Before going into details regarding the bootstrapping algorithm, we should explain the difference between yield curve and spot rat</span>e curve.<br />
<br />
By definition, the yield curve shows several bond yields to maturity (ytm) across different bond contract lengths, or times to maturity (ttm). Yield to maturity is an overall discount rate which equalizes principal and coupon payments to the initial investment value, assuming reinvestability of all cash flows.<br />
<br />
In contrast to the yield curve, a spot rate curve represents spot rates used to discount individual cash flows of the bond. Hence, a whole range of different spot rates is typically used when equalizing bond's future cash flows to its present value.<br />
<br />
To bootstrap the yield curve, we will be building upon a fact that all bonds priced at par have coupon rate equal to the yield-to-maturity, as denoted in the following equation:<br />
<br />
$$ \frac{C}{\left ( 1+r \right )^1} + \frac{C}{\left ( 1+r \right )^2}+...+\frac{1+C}{\left ( 1+r \right )^n} = $100 $$<br />
Given the par value is $100, coupon rate \(C\) is equal to \($100*r\)<br />
<br />
Starting from the annual coupon bond which matures in one year, we will gradually derive all spot rates by forward substitution of the previously calculated ones. This can be best illustrated on a numerical example. To make the example more obvious, we will use exaggerated yields as opposed to the real yield curve calculated in previous step:<br />
<br />
<br />
<b style="font-family: 'Courier New', Courier, monospace;">TTM YTM </b><span style="font-family: "times" , "times new roman" , serif;">(Interpolated)</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.00 3.00%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2.00 5.00%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">3.00 7.00%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">... ...</span><br />
<br />
Starting from the bond which pays both annual coupon and principal in one year, the yield-to-maturity is apparently the same as the first and single spot rate \(y_1 = s_1 = 3\%\). Hence, the following equation holds:<br />
$$ \frac{$100+$3}{\left ( 1+0.03 \right )^1} = $100 $$<br />
In the next step, we will put into the equation a bond maturing in two years. In this case, yield to maturity will be y_2 = 5\%. We will also employ the spot rate \(s_1=3\%\) "calculated" in the previous step. Please bear in mind that since this bond is also priced at par, the coupon rate will be this time 5%, or $5:<br />
<div>
$$ \frac{$5}{\left ( 1+0.03 \right )^1} + \frac{$100+$5}{\left ( 1+s_2 \right )^1} = $100 $$</div>
<div>
Solving this equation for the second spot rate will lead to the root \(s_2 = 5.0510\%\).</div>
<div>
<br /></div>
<div>
Similarly, solving all other rates iteratively in the same manner will lead to the following spot rate curve:</div>
<div>
<br /></div>
<div>
<b style="font-family: 'Courier New', Courier, monospace;">TTM Spot Rate </b><br />
<span style="font-family: "courier new" , "courier" , monospace;">1.00 3.0000%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">2.00 5.0510%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">3.00 7.1979%</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">... ...</span>
<br />
<br />
The Python code implementing the calculation described above would look as follows. The spot rates will be populated in output list <span style="background-color: white; font-family: monospace;">s</span><span style="background-color: white;"><span style="font-family: inherit;">, based on the same time scale </span></span><span style="background-color: white; color: #000066; font-family: monospace;">t</span><span style="background-color: white;"><span style="font-family: inherit;"> as the original YTM rates </span><span style="font-family: "courier new" , "courier" , monospace;">y</span></span><br />
<h2>
<span style="background-color: white;"><span style="font-size: small;"><span style="color: #000066; font-family: monospace; font-weight: normal;">s = </span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="co1" style="font-family: monospace; font-style: italic; font-weight: normal;"># output array for spot rates</span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span class="kw1" style="color: #ff7700; font-family: monospace;">for</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> i </span><span class="kw1" style="color: #ff7700; font-family: monospace;">in</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">range</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">0</span><span style="color: #000066; font-family: monospace; font-weight: normal;">, </span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">len</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span style="color: #000066; font-family: monospace; font-weight: normal;">t</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span style="color: #000066; font-family: monospace; font-weight: normal;">: </span><span class="co1" style="font-family: monospace; font-style: italic; font-weight: normal;">#calculate i-th spot rate </span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">sum</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> = </span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">0</span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace;">for</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> j </span><span class="kw1" style="color: #ff7700; font-family: monospace;">in</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">range</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">0</span><span style="color: #000066; font-family: monospace; font-weight: normal;">, i</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span style="color: #000066; font-family: monospace; font-weight: normal;">: </span><span class="co1" style="font-family: monospace; font-style: italic; font-weight: normal;">#by iterating through 0..i</span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span style="color: #000066; font-family: monospace; font-weight: normal;"> </span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">sum</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> += y</span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span style="color: #000066; font-family: monospace; font-weight: normal;">i</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> / </span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">1</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> + s</span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span style="color: #000066; font-family: monospace; font-weight: normal;">j</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span class="sy0" style="color: #66cc66; font-family: monospace; font-weight: normal;">**</span><span style="color: #000066; font-family: monospace; font-weight: normal;">t</span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span style="color: #000066; font-family: monospace; font-weight: normal;">j</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span style="color: #000066; font-family: monospace; font-weight: normal;"> value = </span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">1</span><span style="color: #000066; font-family: monospace; font-weight: normal;">+y</span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span style="color: #000066; font-family: monospace; font-weight: normal;">i</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> / </span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">1</span><span style="color: #000066; font-family: monospace; font-weight: normal;">-</span><span class="kw2" style="color: green; font-family: monospace; font-weight: normal;">sum</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span class="sy0" style="color: #66cc66; font-family: monospace; font-weight: normal;">**</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">1</span><span style="color: #000066; font-family: monospace; font-weight: normal;">/t</span><span class="br0" style="font-family: monospace; font-weight: normal;">[</span><span style="color: #000066; font-family: monospace; font-weight: normal;">i</span><span class="br0" style="font-family: monospace; font-weight: normal;">]</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span><span style="color: #000066; font-family: monospace; font-weight: normal;"> - </span><span class="nu0" style="color: orangered; font-family: monospace; font-weight: normal;">1</span><br style="color: #000066; font-family: monospace; font-weight: normal;" /><span style="color: #000066; font-family: monospace; font-weight: normal;"> s.</span><span class="me1" style="font-family: monospace; font-weight: normal;">append</span><span class="br0" style="font-family: monospace; font-weight: normal;">(</span><span style="color: #000066; font-family: monospace; font-weight: normal;">value</span><span class="br0" style="font-family: monospace; font-weight: normal;">)</span></span></span></h2>
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;"><b>Final result</b></span><br />
<div>
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">We are of course interested mostly in final results based on the real market data. Previously in this article, we gathered and interpolated on-the-run market prices of UK Gilts, as of 19th of September 2012. Based on these prices, the original and interpolated yield curves and spot rates curve would look as follows:</span><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuCwpRSyUjXIOmfvXEEuoPbA-BoBrWTqHTSZMs2ro7IrwqDhgHA6IjBLGJF54EeR6JZfXnLjMqJyM3KBP1UqHnNkgJPx8-8xYzUQHPBicDix7oqHpKFyqa00OKK3y7afqes57_WMEvhyphenhyphen-_/s1600/yield_curve.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="481" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuCwpRSyUjXIOmfvXEEuoPbA-BoBrWTqHTSZMs2ro7IrwqDhgHA6IjBLGJF54EeR6JZfXnLjMqJyM3KBP1UqHnNkgJPx8-8xYzUQHPBicDix7oqHpKFyqa00OKK3y7afqes57_WMEvhyphenhyphen-_/s640/yield_curve.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<span style="font-family: inherit;">Please note that in this partic</span>ular example, there is not a big difference between yield curve and spot rate curve, especially for short term maturities. This is due to low-yield nature of government bonds. If the coupon rates were bigger, the difference between spot and YTM rates would be more evident as well.</div>
</div>
Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-25407300385945365812012-08-29T19:16:00.001+01:002017-02-26T10:44:38.315+00:00Time Value of Money Calculator<span style="background-color: white; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px;">Link: <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/time_value_of_money/tvm.ipynb">IPython notebook</a></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">This article shows how to use the principle of offsetting annuities to solve basic TVM problems, such as yields on bonds, mortgage payments or arbitrage-free bond pricings. The underlying implementation is done in Python and illustrates practical use of these principles on simple <a href="https://github.com/omartinsky/QuantAndFinancial/blob/master/time_value_of_money/tvm.ipynb">time value of money examples</a>.</span><br />
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<b style="background-color: white;">Theoretical background</b><br />
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<span style="background-color: white;">Time Value of Money is a central concept of finance theory that gives different value to the same nominal cash flow, depending on a pay-off date. In another words, one dollar has bigger value if received now as opposed to some future point of time. Hence, the difference in these valuations is a function of time passed between some present and future date. Another parameter of this function is the rate defining interest earned during one period of time. Mathematically, this relation could be written as:</span><br />
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<span style="background-color: white;">$$ FV = PV\times (1+r)^{n} $$</span><br />
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<span style="font-family: inherit;">, where </span><span style="color: #333333; font-family: inherit; line-height: 18px;"> </span><span style="color: #333333; font-family: inherit; line-height: 18px;">\(PV\) is the present value of cash flow, \(FV\) is the value at some future date, \(r\) is an interest accrued during one period and \(n\) is number of periods between the today's and future date.</span></span><br />
<span style="background-color: white;"><span style="color: #333333; font-family: inherit; line-height: 18px;"><br /></span>
<span style="color: #333333;"><span style="line-height: 18px;">The relation above always holds no matter of how complex the timing of cash flow is. Thanks to this, it can be used to value virtually any cash-flow scenario.</span></span></span><br />
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<span style="color: #333333;"><span style="line-height: 18px;"><b style="background-color: white;">Annuity</b></span></span><br />
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<span style="background-color: white;">Annuity can be understood as a bank deposit or other cash investment generating constant periodic interest payments (coupons). Since all earned interest is paid-out at the end of each period, the outstanding balance is never changed and payments last constant forever. Initial deposit \(PV\), periodic interest rate \(r\) and periodic payments \(PMT\) are in the following relation:</span><br />
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<span style="background-color: white;">$$ PV = \frac{PMT}{r} $$</span><br />
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<span style="background-color: white;">If we depict all cash inflows and outflows as arrows above and below the time line, respectively; the annuity would look for example as follows:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjspM0pTBCtv0qBmvZwT6DgDrzWVLVS69YNzvi7az93xP2VZVF3ceqxV5hm0Fu_8ApUW1uzGKY5iWP9-yHIucOg_61bdPfgCEx1a1_d6VgAXxypHOjWQwpJkpoTQu5-PT7XA7bepdirXBZZ/s1600/drawing_annuity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjspM0pTBCtv0qBmvZwT6DgDrzWVLVS69YNzvi7az93xP2VZVF3ceqxV5hm0Fu_8ApUW1uzGKY5iWP9-yHIucOg_61bdPfgCEx1a1_d6VgAXxypHOjWQwpJkpoTQu5-PT7XA7bepdirXBZZ/s1600/drawing_annuity.png" /></a></div>
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<span style="background-color: white;"><b style="color: #333333; line-height: 18px;">Plain Vanilla bond model</b></span><br />
<span style="background-color: white;"><span style="color: #333333;"><span style="line-height: 18px;"><br /></span></span>
<span style="color: #333333;"><span style="line-height: 18px;">One of the common scenarios used in finance is Plain Vanilla bond model, where initial outflow is typically followed by a series of periodic cash inflows, enclosed by a final principal inflow paid at maturity. </span></span><span style="color: #333333; line-height: 18px;">This model can be applied to a wide-range of fixed-rate contracts, such as bonds, mortgages, non-amortizing loans, etc.</span></span><br />
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<span style="color: #333333; line-height: 18px;">In case of a Plain Vanilla bond, the initial outflow is considered to be the price of a bond, periodic cash inflows are coupons are final cash inflow at maturity is the face value of bond.</span>
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<span style="color: #333333; line-height: 18px;">The following picture illustrates the structure of cash aflows in a Vanilla bond model:</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz4pFDTf6emAMiitmCwCuN1NRKYDGTVL3BmUHiAFmjUKOwXS6lrADTSQe7g4ksQr3OjFDESTl3-w6pU1pg5rIihkGMjV1jjRG1S44bXTeSkXC43Ja46HNwqtrdXHQrIDXUCvHlIY4Qhh_-/s1600/drawing_toothbrush.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz4pFDTf6emAMiitmCwCuN1NRKYDGTVL3BmUHiAFmjUKOwXS6lrADTSQe7g4ksQr3OjFDESTl3-w6pU1pg5rIihkGMjV1jjRG1S44bXTeSkXC43Ja46HNwqtrdXHQrIDXUCvHlIY4Qhh_-/s1600/drawing_toothbrush.png" /></a></div>
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<b style="background-color: white; color: #333333; line-height: 18px;">General Principle of Calculation</b><br />
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<span style="background-color: white;">The mathematical equation for a generalized model looks as follows:</span><br />
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<span style="background-color: white;">$$ FV = PV \times (1+r)^{n} + \sum_{i=1}^{n}\left ( PMT_{i} \times (1+r)^{n-i} \right ) $$</span><br />
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<span style="background-color: white;">, where \(PV\) is initial inflow, \(PMT_{i}\) are periodic cash outflows, \(FV\) final inflow and \(r\) is the interest rate, as defined previously.</span><br />
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<span style="background-color: white;">In case all periodic payments are the same, as in a plain-vanilla bond model, the formula above may be reduced into two mutually offsetting annuities, starting each at different point of time:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghTIAdK05vpGoNV3cGxYbHdW9QNM1jUpXXqzcruyUltQCqb2DU4LaMjFICSM0PlW13NYwMqXzlY1a5MdFsp3UtqgD0hYe-P7UgO2KN9TgFNepAbJNIGISCa2nBdkpuNQaHnVHqC_0voV8L/s1600/drawing_annuity_offset.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghTIAdK05vpGoNV3cGxYbHdW9QNM1jUpXXqzcruyUltQCqb2DU4LaMjFICSM0PlW13NYwMqXzlY1a5MdFsp3UtqgD0hYe-P7UgO2KN9TgFNepAbJNIGISCa2nBdkpuNQaHnVHqC_0voV8L/s1600/drawing_annuity_offset.png" /></a></div>
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<span style="color: #333333;"><span style="line-height: 18px;"><b>The formula</b></span></span></span><br />
<span style="background-color: white;"><b style="color: #333333; line-height: 18px;"><br /></b><span style="color: #333333; line-height: 18px;">To derive the formula, assume the composition of two annuities mentioned above is priced to be arbitrage-free.</span></span><br />
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<span style="color: #333333;"><span style="line-height: 18px;">The value of Annuity A in today's money is:</span></span></span><br />
<span style="background-color: white;"><span style="color: #333333; line-height: 18px;"><br /></span>
<span style="color: #333333; line-height: 18px;">$$Value_{A}=\frac{PMT}{r}-PV$$</span></span><br />
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<span style="color: #333333; line-height: 18px;">The value of Annuity B in the future money is:</span></span><br />
<span style="background-color: white;"><span style="color: #333333; line-height: 18px;"><br /></span>
<span style="color: #333333; line-height: 18px;">$$Value_{B}=\frac{-PMT}{r}+FV$$</span>
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<span style="color: #333333; line-height: 18px;">, which gives us the today's valuation of </span></span><br />
<span style="background-color: white;"><span style="color: #333333; line-height: 18px;"><br /></span>
<span style="color: #333333;"><span style="line-height: 18px;">$$Value_{B}^{now}=\left(1+r\right)^{-n}\left(\frac{-PMT}{r}+FV\right)$$</span></span></span><br />
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<span style="background-color: white;">Using the substitution \(z=(1+r)^{-n}\) for discount factor, we can construct the arbitrage-free equation as follows:</span><br />
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<span style="background-color: white; color: #333333; line-height: 18px;">$$Value_{A}+Value_{B}^{now}=0$$</span><br />
<span style="color: #333333;"><span style="background-color: white; line-height: 18px;">$$\left(\frac{PMT}{r}-PV\right)+z\times\left(\frac{-PMT}{r}+FV\right)=0$$</span></span><br />
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<span style="background-color: white;">After isolation of \(FV\), the final equation is:</span><br />
<span style="background-color: white;"><span style="color: #333333; line-height: 18px;"><br /></span>
<span style="color: #333333;"><span style="line-height: 18px;">$$FV=\frac{1}{z}\left(\left(z-1\right)\times\frac{PMT}{r}-PV\right)$$</span></span></span><br />
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<span style="color: #333333;"><span style="line-height: 18px;">Other variables, such as \(PV\), \(PMT\), \(n=-log(z)\)</span></span><span style="color: #333333; line-height: 18px;"> can be isolated in a similar manner. The only difficulty is the calculation of discount rate \(r\), which must be done through a root-finding methods, such as Newton-Raphson or other.</span></span><br />
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<b style="color: #333333; line-height: 18px;">Python Implementation</b></span><br />
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<span style="color: #333333;"><span style="line-height: 18px;">Algebraic</span></span><span style="color: #333333; line-height: 18px;"> equations are implemented in the TVM class:</span></span><br />
<span class="kw1" style="background-color: white; color: #ff7700; font-family: monospace; font-weight: bold;"><br /></span><span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">from</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw3" style="color: crimson; font-family: monospace;">math</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">import</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">pow</span><span style="color: #000066; font-family: monospace;">, floor, ceil, log</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">from</span><span style="color: #000066; font-family: monospace;"> quant.</span><span class="me1" style="font-family: monospace;">optimization</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">import</span><span style="color: #000066; font-family: monospace;"> newton</span><br style="color: #000066; font-family: monospace;" /><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">class</span><span style="color: #000066; font-family: monospace;"> TVM:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> bgn, end = </span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span style="color: #000066; font-family: monospace;">, </span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw4" style="color: mediumblue; font-family: monospace;">__str__</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> </span><span class="st0" style="color: darkslateblue; font-family: monospace;">"n=%f, r=%f, pv=%f, pmt=%f, fv=%f"</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span style="color: #000066; font-family: monospace;">, </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;">, </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;">, </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;">, </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw4" style="color: mediumblue; font-family: monospace;">__init__</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">, n=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, r=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, pv=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, pmt=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, fv=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0</span><span style="color: #000066; font-family: monospace;">, mode=end</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span style="color: #000066; font-family: monospace;"> = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;"> = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">r</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;"> = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pv</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;"> = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">pmt</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span style="color: #000066; font-family: monospace;"> = </span><span class="kw2" style="color: green; font-family: monospace;">float</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">fv</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;"> = mode</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> calc_pv</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> z = </span><span class="kw2" style="color: green; font-family: monospace;">pow</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;">, -</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pva = </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;"> / </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;">==TVM.</span><span class="me1" style="font-family: monospace;">bgn</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: pva += </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> -</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">z + </span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">-z</span><span class="br0" style="font-family: monospace;">)</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">pva</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> calc_fv</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> z = </span><span class="kw2" style="color: green; font-family: monospace;">pow</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;">, -</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pva = </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;"> / </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;">==TVM.</span><span class="me1" style="font-family: monospace;">bgn</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: pva += </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> -</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;"> + </span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">-z</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> pva</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">/z</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> calc_pmt</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> z = </span><span class="kw2" style="color: green; font-family: monospace;">pow</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;">, -</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;">==TVM.</span><span class="me1" style="font-family: monospace;">bgn</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;"> + </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">z</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">z-</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">else</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;"> + </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">z</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">z-</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> calc_n</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pva = </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;"> / </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;">==TVM.</span><span class="me1" style="font-family: monospace;">bgn</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: pva += </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> z = </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">-pva-</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span style="color: #000066; font-family: monospace;">-pva</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> -log</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">z</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / log</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">r</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> calc_r</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> function_fv</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">r, </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> z = </span><span class="kw2" style="color: green; font-family: monospace;">pow</span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">+r, -</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">n</span><span class="br0" style="font-family: monospace;">)</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> pva = </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><span style="color: #000066; font-family: monospace;"> / r</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">mode</span><span style="color: #000066; font-family: monospace;">==TVM.</span><span class="me1" style="font-family: monospace;">bgn</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: pva += </span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pmt</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> -</span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">pv</span><span style="color: #000066; font-family: monospace;"> + </span><span class="br0" style="font-family: monospace;">(</span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">-z</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> pva</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">/z</span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> newton</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f=function_fv, fArg=</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">, x0=.05, </span><br style="color: #000066; font-family: monospace;" /><span style="color: #000066; font-family: monospace;"> y=</span><span class="kw2" style="color: green; font-family: monospace;">self</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">fv</span><span style="color: #000066; font-family: monospace;">, maxIter=</span><span class="nu0" style="color: orangered; font-family: monospace;">1000</span><span style="color: #000066; font-family: monospace;">, minError=</span><span class="nu0" style="color: orangered; font-family: monospace;">0.0001</span><span class="br0" style="font-family: monospace;">)</span>
</span><br />
<pre class="prettyprint lang-py" style="font-family: Monaco, 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Lucida Console', monospace; overflow: auto; padding: 0px;"><span class="br0" style="background-color: white; font-family: monospace; white-space: normal;">
</span></pre>
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">The generic code for Newton-Raphson method:</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">from</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw3" style="color: crimson; font-family: monospace;">math</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">import</span><span style="color: #000066; font-family: monospace;"> fabs</span></span><br />
<span class="co1" style="background-color: white; font-family: monospace; font-style: italic;"># f - function with 1 float returning float</span><br />
<span class="co1" style="background-color: white; font-family: monospace; font-style: italic;"># x0 - initial value</span><br />
<span class="co1" style="background-color: white; font-family: monospace; font-style: italic;"># y - desired value</span><br />
<span class="co1" style="background-color: white; font-family: monospace; font-style: italic;"># maxIter - max iterations</span><br />
<span class="co1" style="background-color: white; font-family: monospace; font-style: italic;"># minError - minimum error abs(f(x)-y)</span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> newton</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x0, y, maxIter, minError</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> func</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x, y</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> f</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">x, fArg</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> - y</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">def</span><span style="color: #000066; font-family: monospace;"> slope</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x, y</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> xp = x </span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;"> </span><span class="nu0" style="color: orangered; font-family: monospace;">1.05</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">func</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, xp, y</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">-func</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x, y</span><span class="br0" style="font-family: monospace;">)</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">xp-x</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> counter = </span><span class="nu0" style="color: orangered; font-family: monospace;">0</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">while</span><span style="color: #000066; font-family: monospace;"> </span><span class="nu0" style="color: orangered; font-family: monospace;">1</span><span style="color: #000066; font-family: monospace;">:</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> sl = slope</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x0, y</span><span class="br0" style="font-family: monospace;">)</span><span class="sy0" style="color: #66cc66; font-family: monospace;">;</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> x0 = x0 - func</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f, fArg, x0, y</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> / sl</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">counter </span><span class="sy0" style="color: #66cc66; font-family: monospace;">></span><span style="color: #000066; font-family: monospace;"> maxIter</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">break</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">if</span><span style="color: #000066; font-family: monospace;"> </span><span class="br0" style="font-family: monospace;">(</span><span class="kw2" style="color: green; font-family: monospace;">abs</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">f</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">x0, fArg</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">-y</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;"><</span><span style="color: #000066; font-family: monospace;"> minError</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">: </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">break</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> counter += </span><span class="nu0" style="color: orangered; font-family: monospace;">1</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">return</span><span style="color: #000066; font-family: monospace;"> x0</span>
</span><br />
<span style="background-color: white;"><br /></span>
<b style="background-color: white;">Example 1 - Mortgage Payments</b><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Consider a regular mortgage for $500'000, fully amortized over 25 years, with monthly installments, bearing annual interest rate 4%. Regular monthly payments will be then calculated as follows:</span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">from</span><span style="color: #000066; font-family: monospace;"> quant.</span><span class="me1" style="font-family: monospace;">tvm</span><span style="color: #000066; font-family: monospace;"> </span><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">import</span><span style="color: #000066; font-family: monospace;"> TVM</span></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;">pmt = TVM</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n=</span><span class="nu0" style="color: orangered; font-family: monospace;">25</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span class="nu0" style="color: orangered; font-family: monospace;">12</span><span style="color: #000066; font-family: monospace;">, r=.04/</span><span class="nu0" style="color: orangered; font-family: monospace;">12</span><span style="color: #000066; font-family: monospace;">, pv=</span><span class="nu0" style="color: orangered; font-family: monospace;">500000</span><span style="color: #000066; font-family: monospace;">, fv=</span><span class="nu0" style="color: orangered; font-family: monospace;">0</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">calc_pmt</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">"Payment = %f"</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> pmt</span><span class="br0" style="font-family: monospace;">)</span>
</span><br />
<span style="background-color: white;"><span class="br0" style="font-family: monospace;"><br /></span>
</span><br />
<pre class="prettyprint lang-py" style="font-family: Monaco, 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Lucida Console', monospace; overflow: auto; padding: 0px;"></pre>
<pre style="font-family: Monaco, 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Lucida Console', monospace; padding: 0px;"></pre>
<pre style="padding: 0px;"><span style="background-color: white; font-family: "times" , "times new roman" , serif;">The output of calculation:</span></pre>
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span>
<span style="color: #000066; font-family: monospace;">Payment = -</span><span class="nu0" style="color: orangered; font-family: monospace;">2639.184201</span></span><br />
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><br /></span>
<b>Example 2 - Yield to Maturity</b></span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span>
Consider a semi-annual bond with the par value of $100, coupon rate 6% and 10 years to maturity, currently selling at $80. What is the yield-to-maturity ?</span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span>
<span style="color: #000066; font-family: monospace;">r = </span><span class="nu0" style="color: orangered; font-family: monospace;">2</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span style="color: #000066; font-family: monospace;">TVM</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">n=</span><span class="nu0" style="color: orangered; font-family: monospace;">10</span><span class="sy0" style="color: #66cc66; font-family: monospace;">*</span><span class="nu0" style="color: orangered; font-family: monospace;">2</span><span style="color: #000066; font-family: monospace;">, pmt=</span><span class="nu0" style="color: orangered; font-family: monospace;">6</span><span style="color: #000066; font-family: monospace;">/</span><span class="nu0" style="color: orangered; font-family: monospace;">2</span><span style="color: #000066; font-family: monospace;">, pv=-</span><span class="nu0" style="color: orangered; font-family: monospace;">80</span><span style="color: #000066; font-family: monospace;">, fv=</span><span class="nu0" style="color: orangered; font-family: monospace;">100</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">calc_r</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">"Interest Rate = %f"</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> r</span><span class="br0" style="font-family: monospace;">)</span>
</span><br />
<span style="background-color: white;"><span class="br0" style="font-family: monospace;"><br /></span>
The output of calculation:</span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span>
<span style="color: #000066; font-family: monospace;">Interest Rate = </span><span class="nu0" style="color: orangered; font-family: monospace;">0.090866</span>
</span><br />
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><br /></span>
<b>Example 3 - Arbitrage-free pricing of a bond</b></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Consider an annual bond with par value of $100, coupon rate 5% with 8 years to maturity. Calculate an arbitrage-free price of such bond assuming that market interest rate is 6%.</span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span><span style="color: #000066; font-family: monospace;">pv = TVM</span><span class="br0" style="font-family: monospace;">(</span><span style="color: #000066; font-family: monospace;">r=.06, n=</span><span class="nu0" style="color: orangered; font-family: monospace;">8</span><span style="color: #000066; font-family: monospace;">, pmt=</span><span class="nu0" style="color: orangered; font-family: monospace;">5</span><span style="color: #000066; font-family: monospace;">, fv=</span><span class="nu0" style="color: orangered; font-family: monospace;">100</span><span class="br0" style="font-family: monospace;">)</span><span style="color: #000066; font-family: monospace;">.</span><span class="me1" style="font-family: monospace;">calc_pv</span><span class="br0" style="font-family: monospace;">(</span><span class="br0" style="font-family: monospace;">)</span></span><br />
<span style="background-color: white;"><span class="kw1" style="color: #ff7700; font-family: monospace; font-weight: bold;">print</span><span class="br0" style="font-family: monospace;">(</span><span class="st0" style="color: darkslateblue; font-family: monospace;">"Present Value = %f"</span><span style="color: #000066; font-family: monospace;"> </span><span class="sy0" style="color: #66cc66; font-family: monospace;">%</span><span style="color: #000066; font-family: monospace;"> pv</span><span class="br0" style="font-family: monospace;">)</span>
</span><br />
<span style="background-color: white;"><span class="br0" style="font-family: monospace;"><br /></span>
Output of the calculation:</span><br />
<span style="background-color: white;"><span style="color: #000066; font-family: monospace;"><br /></span><span style="color: #000066; font-family: monospace;">Present Value = -</span><span class="nu0" style="color: orangered; font-family: monospace;">93.790206</span></span>
<br />
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><br /></span></span>
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><span style="color: black; font-family: "times new roman";"><i>Note: For simplicity, we have discussed TVM calculations only in "END" mode. However, the implementation supports also "BGN" mode.</i></span></span></span><br />
<span style="background-color: white;"><span class="nu0" style="color: orangered; font-family: monospace;"><br /></span></span>
<span style="background-color: white;"><b>Next Time: Spot rates, forward rates and bootstrapping of yield curves</b></span><br />
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Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com0tag:blogger.com,1999:blog-1922764065702058602.post-34990951163232719462012-08-28T22:03:00.000+01:002016-11-08T21:26:29.090+00:00WelcomeWelcome to the Quantitative & Financial Blog<br />
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As the title suggests, Quantitative & Financial blog is dedicated to Mathematics, Quantitative Analysis and Financial Modeling. Moreover, you can find here technical articles regarding underlying tools, such as C++, Python, Excel/VBA and others.<br />
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For the purposes of this blog, I will be using Python programming language as a basic framework to demonstrate all discussed principles. Python is an object-oriented, dynamically-typed scripting language suitable for rapid application development and prototyping far beyond the borders of financial engineering industry.<br />
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This blog doesn't provide nor expect in-depth knowledge of the used tools, just the ability to passively understand scripts. Since the topics are partly or fully related to each other, the comprehensive source codes and full model implementations are typically not included in articles. Instead of this, you can find the self-contained "library" regularly updated at <a href="https://github.com/ondrej1234/QuantAndFinancial">https://github.com/ondrej1234/QuantAndFinancial</a>.<br />
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<br />Ondrej Martinskyhttp://www.blogger.com/profile/06849416026045098367noreply@blogger.com