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Choosing a Currency Market Proxy for a Bitcoin CAPM

Article Quant Q&A · Author: o1ctav
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Summary

The document considers whether EUR/USD returns can serve as the market benchmark when applying CAPM to Bitcoin returns. Its response treats Bitcoin as a currency for this purpose and suggests constructing a broader currency-market proxy by averaging returns across traded currencies, rather than relying on one major pair.

The discussion cautions that even a broad currency average only approximates the market portfolio. It points to Roll’s critique of CAPM testing, which highlights the difficulty of identifying and testing against the true market portfolio. No empirical regression or performance results are provided, so the recommendation is conceptual and depends on how the currency basket is defined and weighted.

Key ideas

  • A single exchange rate such as EUR/USD may not represent the full currency market.
  • If Bitcoin is treated as a currency, a basket or average of traded currency returns could serve as a broader benchmark.
  • Any constructed currency benchmark remains an approximation of the theoretical market portfolio.
  • The choice of market proxy affects how CAPM results should be interpreted.

Tags

CryptoForexStatistics
Full text
# Apply CAPM using returns on a foreign currency as the market returns


# Apply CAPM using returns on a foreign currency as the market returns












I want to analize Bitcoin returns using the CAPM. I was thinking if it makes sense to compare returns of (BTC/USD) against (EUR/USD), taking the latter as the market returns.

However, since EUR is just a fraction of the foreign exchange market, I'm not sure if this makes much sense.

Is this analysis reasonable?

## Answer by Quantopik (score 1)

https://quant.stackexchange.com/a/18256

The CAPM model is based on the relationship existing between an asset and its benchmark market; assuming that the bitcoin could be thought as a currency, according to me, you should take the mean of returns over all the currencies traded and then regress the BTCUSD on the the average currency market returns.

Indeed, although the EURUSD is one of the most liquid and traded currencies, in my humble opinion, it should not be considered as a benchmark of the currency market. Anyway, in this case too you are only approximating the market portfolio, as Roll (1977) suggests.

Maybe you could find pretty interesting the Roll's critique about constructing a market portfolio and testing the CAPM model; here below you can find the paper citation:

> Roll, Richard (March 1977), "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory", Journal of Financial Economics 4 (2): 129–176

Hope this will help.

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