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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?

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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.

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  • $\begingroup$ Thank you very much. $\endgroup$
    – emot
    Jan 13 at 11:44
  • $\begingroup$ Keep in mind that Tuckman and Porfirio were writing in 2003, before the issues mentioned by dm63 were fully understood. The authors would probably write differently today. $\endgroup$
    – nbbo2
    Jan 13 at 13:30
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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

I hope this helps.

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  • $\begingroup$ If you have access to Bloomberg, look at the EUR/USD or USD/JPY basis before the GFC of 2008: was it zero? No, it wasn't. For the same exact reason that dm63 mentioned already: supply and demand. It has nothing (or very little) to do with credit risk or cpty failing. It has always been about the supply and demand for funding in a specific currency. $\endgroup$ Jan 14 at 7:57
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    $\begingroup$ The data from the BIS clearly shows a widening in the basis, although already a bit before the GFC. I think it is considered an early warning signal like the Libor-OIS spread. The data in Bloomberg of the ticker EUBSC BGN Curncy only goes back to 2008. I think the BIS convincingly argues the basis opens up due to hedging demand, although definitely funding also plays a role. $\endgroup$
    – thijs818
    Jan 14 at 10:28
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    $\begingroup$ quant.stackexchange.com/questions/53327/… this answer is in line with my previous remark $\endgroup$
    – thijs818
    Jan 14 at 13:10
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    $\begingroup$ Ok, thanks for the link and additional perspective. I still think the GFC might have played a (minor) role in the basis widening from a credit-risk perspective, but the main factor would have been supply-demand for funding. European institutions struggled to obtain USD funding during the GFC, but it wasn't so much about credit risk as it was about balance-sheet shrinkage for US-based banks and simply there not being enough liquidity in general. I used to trade Xccy basis swaps, in my experience the only factor is supply-demand, there's no credit risk component at all. $\endgroup$ Jan 14 at 13:41
  • $\begingroup$ Thank you, very interesting to get the perspective from someone who actually traded the swaps! Don't you think the lack of liquidity and the balance sheet shrinkage was related to more awareness of certain (liquidity) risks? The BIS writes about this in the Limits to arbitrage section on page 51 (it is just one page) $\endgroup$
    – thijs818
    Jan 14 at 14:40
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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.

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