Why Cross-Currency Basis Swaps Can Deviate from Zero
Article Quant Q&A · Author: emot
Summary
The document explains why cross-currency basis swaps exchanging overnight risk-free rates may trade away from zero, despite a theoretical flat-pricing argument based on covered interest parity. It describes a proposed arbitrage: borrow in one currency at its overnight rate, invest in the other, and use a basis swap to offset the currency exposures. The argument identifies a practical obstacle: market participants cannot generally borrow for long terms at those benchmark rates, and arbitrage also consumes balance sheet and carries counterparty risk.
The discussion attributes persistent basis levels to demand for dollar funding through swaps, alongside limited capacity to arbitrage the difference. It cites post-crisis concerns about counterparty default and the costs of carrying the trade, and notes that collateral and margin arrangements could change the arbitrage conditions. These are qualitative explanations drawn from the cited discussion, not a full pricing model or empirical analysis. The basis can also reflect differences in accounting currency and risk, so the simple risk-free-rate intuition does not settle how a traded swap should be priced.
Key ideas
- A theoretical flat basis result relies on assumptions that do not necessarily hold in actual funding markets.
- Borrowing at overnight benchmark rates for a long term is generally unavailable to arbitrageurs.
- Demand for dollar funding through currency swaps can push the basis away from zero.
- Balance-sheet costs and counterparty risk can limit arbitrage that would otherwise narrow the basis.
- Collateral and margin terms affect whether offsetting swap and rate positions can be arbitraged.
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# Should Cross-Currency Basis Swaps exchanging risk free rates trade flat? # Should Cross-Currency Basis Swaps exchanging risk free rates trade flat? In the paper "Interest Rate Parity, Money Market Basis Swaps, and Cross-Currency Basis Swaps" by Bruce Tuckman and Pedro Porfirio (2003) the authors claim that cross-currency basis swap exchanging default-free overnight rates should trade flat. To be more precise: > To understand why 3-month CDOR plus 10 is fair against 3-month USD LIBOR, it is best to begin by considering an imaginary cross-currency basis swap exchanging a default-free, overnight CAD rate for a default-free, overnight USD rate. Under relatively mild assumptions, Appendix 2 proves that this cross-currency basis swap should trade flat. Intuitively, paying 1 CAD today, receiving the default-free CAD rate on 1 CAD, and receiving 1 CAD at expiration is worth 1 CAD today. Similarly, receiving .677 USD, paying the default-free USD rate on .677 dollars, and paying .677 USD at expiration is worth .677 dollars today. Therefore, because the exchange rate is .677 USD per CAD, the exchange of these floating rate notes is fair today. But now post Libor reform actual risk free rates such as ESTR and SOFR exist and CBS exchanging the two is not traded flat. For example 5Y CBS ESTR vs SOFR currently trades at around -17.00 bps MID (Reuters ticker EUUSESSRBS=). Why is that? Are the authors or the market wrong? ## Answer by dm63 (score 7, accepted) https://quant.stackexchange.com/a/69463 You are correct, the currency basis swaps between risk free rates do not trade flat. To understand why , it’s instructive to imagine how to arbitrage it. Pretty easy, it might seem. One would borrow some USD for 5yrs at SOFR , invest some EUR for 5yrs at ESTR, and then enter the basis swap whereby you lend USD and borrow EUR , picking up 17bp. All the cash flows offset except the 17bp. So the answer is , there are not many people that can actually do that. Who can borrow for 5years at SOFR flat? No one, not even the US Treasury. Ok so that explains why it can persist at 17bp. But why did it go there in the first place ? The answer appears to be that there are a lot of people who need USD funding that cannot access it directly through the capital markets (eg a European investor who buys a USD asset backed security ). Those people can however execute a currency basis swap to obtain USD funding. Pressure from those people drives the basis swap away from zero towards the 17bp. ## Answer by thijs818 (score 1) https://quant.stackexchange.com/a/69465 You are right that the cross currency basis with risk free rates shouldn't be flat. I would like to add to dm63 that the Bank of International Settlements wrote a very interesting paper on the cross currency basis Covered interest parity lost The author of the article you are refering to assumes covered interest parity, which is an arbitrage relation, see Interest rate parity. So you could refrase your question as: why does the arbitrage relation doesn't hold? The BIS offers a two fold explanation. On the one hand there is the pressure to increase the basis due to a mismatch in supply and demand, mainly due to hedging needs by large banks, institutional investors and for non-financial firms debt issuance. Those institutions in Europe for example sell more dollars forward than vice versa, thereby putting pressure on the basis opening up. On the other hand a pressure to decrease the basis due to arbitrage is limited, because the balance sheet needed to carry out this arbitrage is not free. Before the GFC the risk awareness of this arbitrage position was considered very safe, and therefore the basis didn't exist. After the GFC, however, people realised the counter party in the FX swap/FX forwards could fail to pay, causing loses. The unwillingness to take position afterwards, caused to basis to open up. There is a lot of interesting literature around the cross currency basis, because it is related to some very important functions of the global financial system. See for example - Cross-currency basis, RIP? - Recent Trends in Cross-currency Basis I hope this helps. ## Answer by river_rat (score 0) https://quant.stackexchange.com/a/69454 Simple answer is that risk free in one currency does not mean risk free for all accounting currencies i.e estr in eur with eur as the accounting / pnl currency being approximately risk free does not mean that estr with usd as the accounting / pnl currency will be risk free. ## Answer by Pedro Porfirio (score 0) https://quant.stackexchange.com/a/79867 The whole issue here is that the deposits and the fx forward are not risk free as the counterparts can default, so the arbitrage using deposits is impossible. Why is it 17bps? Supply and demand. But you can arbitrage the 5Y fx fwd using ccs and rates if, and only if, there daily posting of collateral against the trades with inital margins that would cover a replacement trade if the cp defaults and the collateral is remunarated at the same rate for all the trades.
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