Interpreting Beta Regressions in Foreign Exchange Markets

Summary

The document considers whether a currency’s returns can be regressed on an average return across currencies to estimate beta, and whether that beta has a CAPM interpretation. One reply argues that this benchmark may be unsuitable because exchange-rate returns are relative and a broad currency average may have little or no aggregate appreciation. Another notes that regression can mechanically estimate beta as covariance divided by benchmark variance, while cautioning little about how the benchmark is formed.

The central lesson is that a regression coefficient can be calculated without necessarily being an economically meaningful measure of systematic risk. Currency returns depend on the choice of base currency and numeraire, and a market average must be defined carefully; those choices affect the interpretation of both beta and the benchmark return. The responses do not resolve CAPM’s assumptions or establish that a currency basket is a valid market portfolio. Consequently, the proposed beta should be treated as benchmark-dependent rather than as a universally meaningful FX risk measure.

Key ideas

• A regression coefficient can estimate covariance relative to benchmark variance.
• An FX beta depends on how the currency benchmark and return series are constructed.
• Currency returns are relative, so an average across currencies may not behave like an equity market return.
• A computable beta does not by itself validate a CAPM interpretation.
• The discussion does not establish a suitable universal market portfolio for foreign exchange.

Tags

# Beta in foreign exchange market


# Beta in foreign exchange market












Would it make sense to use a regression to calculate beta for returns on a foreign exchange currency (regressed on a market average of all currencies)?

Would the beta make sense? (why/why not)

Should I worry about CAPM assumptions?

Thanks for your assistance!

## Answer by Andrew (score 2)

https://quant.stackexchange.com/a/36842

I don't think it is making sense to choose the CAPM approach, since in the FX-Market there is no appreciation and the market average of the returns of every currency should be 0.

## Answer by BacktestMarket (score 1)

https://quant.stackexchange.com/a/36391

beta is a measurement of correlation and risk. Calculating beta with a regression can be a solution.

Beta = covariance / variance

Since Beta represents strength and level of correlation between two different symbols, it is correct to make a linear regression to calculate it.

CAPM is influenced by Beta, since the formula is:

CAPM = Rf + Beta * (Rm - Rf)

but I do not think you will affect negatively your CAPM if you compute Beta with a linear regression.

I do not see any problem related!

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