A word on "cross-currency basis"

A few weeks back, ESTER/SOFR cross-currency basis briefly crossed zero before retreating back into negative territory. This event flashed in news, but details were omitted. I will try to fill-in the gaps, using the latest market data: 

Have you ever wondered ?

1) What does cross-currency basis mean? 

2) Why it exists? 

3) Why it has been traditionally negative?

When I did my CFA more than 10 years ago, this basis was not mentioned anywhere in the curriculum. Instead, all three levels were grinding covered interest rate parity (IRP). According to this parity, the basis shouldn't exist:

FxFwd / FxSpot = 1 + (r1-r2) × n/360

Later, quants gave me the following explanation: 

🗣️ "Cross-currency discount curve (such as EUR) is used to discount EUR leg of an xccy swap, collateralized using USD rate. We fit this curve in order to correctly reprice both legs of xccy swap". 

Next, traders on desk told me: 

🗣️ "The basis is caused by supply and demand" 

I found none of these explanations helpful because they don't carry any economic meaning, nor do they reconcile with what I learned about IRP earlier. 

So, here is the main reason why this basis exists and IRP is seemingly broken: 

Funding preferences on credit markets

The covered interest rate parity (IRP) condition holds in simplified, risk-free settings (e.g., SOFR vs. ESTER). However, in real-world markets, most cross-currency transactions occur on the credit side beyond the reach of any parity/arbitrage rules. 

 If you are German AAA-rated corporation seeking 5-year funding as of 20/5/2025, you have two options: 

1) Borrow in EUR at the risk-free rate of 2.14% plus a 46 bp credit spread (all-in 2.60%). 

2) Borrow in USD at the risk-free rate of 4.06% plus a 29 bp credit spread (all-in 4.35%) + hedge USD exposure using 5Y FxSwap 

Without credit spreads, the risk-free rate differential (4.06% - 2.14% = 1.92%) would be offset by FX fwd premium (remember IRP), leaving the issuer indifferent between markets.

However, the USD AAA-rated market has historically offered a lower credit premium (here, 17 bp less than EUR), making it more attractive for international borrowers. This demand dislocated interest rate parity, requiring EUR/USD cross-currency market participants to give-up 8 bp on their ESTER rate to execute the trade. 

The attached graph shows that cross-currency basis on derivatives market has been traditionally correlated with the differential of credit risk premium in respective countries. Yet because credit markets are incomplete, this relationship holds only in a weaker form - no strict arbitrage forces these rates to converge perfectly. 

But how about the arbitrage ? 

Executing the IRP arbitrage effectively requires significant leverage. 

XCY swaps are essentially the only instruments which can be used to effectively arbitrage the long-end of the yield curve. However here is the catch: they are all collateralised in USD regardless of which counterparty is posting collateral. 

In fact, the asymmetric demand for USD collateral is therefore another reason why cross-currency basis exists. 

That closes the circle.