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Interpreting the Sign Convention of Cross-Currency Dollar Basis

Article Quant Q&A · Author: Tamás F
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Summary

The document addresses a sign mismatch in a calculation of the cross-currency dollar basis. The questioner derives an implied dollar interest rate from spot and three-month forward exchange rates, then compares the implied rate with three-month USD LIBOR. The resulting plot appears to have the opposite sign from reports of a more negative basis during dollar funding stress, prompting a question about whether it represents the premium for offshore dollar financing.

The answer identifies the likely source of the discrepancy: cross-currency basis is generally quoted as an adjustment on the non-dollar currency leg. A calculation that instead assigns the basis to the dollar leg can therefore reverse the displayed sign. This brief exchange offers a convention check, not a full derivation or verification of the underlying data. Interpreting any chart still requires confirming which leg carries the spread and how the exchange-rate and interest-rate inputs are defined.

Key ideas

  • Cross-currency basis is generally quoted on the non-dollar leg.
  • Applying the spread to the dollar leg can reverse the sign in a calculation.
  • Comparisons with reported basis moves require checking the quote convention and the leg receiving the adjustment.
  • The excerpt identifies a likely sign-convention issue but does not validate the dataset or provide a full calculation.

Tags

ForexFixed incomeCarry
Full text
# Dollar basis calculation. Where do I miss the point?


# Dollar basis calculation. Where do I miss the point?












I read that recently, due to the covid-19, the pressure on the dollar market has risen significantly on the demand side. That is why the dollar basis became largly negativ.

https://www.bloomberg.com/news/articles/2020-03-17/how-cross-currency-basis-swaps-show-funding-stress-quicktake https://www.bis.org/publ/bisbull01.pdf

I tried to replicate this calculation for a university Essay. From the spot and 3M fwd rate I calculated the implied dollar interest rate. Then for the basis from this I extracted the 3M USD LIBOR. However my graph is looking like this: It seems to me pretty the same, but on the positive side. Do I misinterpret it, if I say, it shows the premium which I have to pay, due I don't have access to direct us market, so I finance through the off-shore dollar market? Could someone explain me, whether I misunderstood something or am I using the wrong dataset. Thank you!

## Answer by river_rat (score 1, accepted)

https://quant.stackexchange.com/a/53999

Basis is almost always calculated on the non-usd leg - which explains why your signs are the wrong way around.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.