Matching the CAPM Risk-Free Rate to Return Frequency

Summary

The document addresses a choice of risk-free rate when calculating CAPM quantities or evaluating a portfolio strategy. The question contrasts a three-month Treasury rate with a ten-year rate for a strategy whose lookback window is one year and asks whether maturity should correspond to the investment horizon. The answer’s practical recommendation is to use a risk-free series that is observed at the same frequency as the portfolio returns, citing the Fama-French factor data as an example.

The central distinction is between the frequency of return observations and the maturity of the instrument underlying a quoted rate. The response specifically warns against pairing a rate based on one horizon with returns measured at another frequency, giving monthly equity returns and a three-month-based rate as an example. It does not work through annualization, rate conversion, maturity matching, or the strategy’s holding period, and offers no empirical test of how alternate choices affect results. Thus it gives a concise frequency-alignment rule, not a full treatment of risk-free-rate selection for every CAPM application.

Key ideas

• The answer recommends matching the risk-free series’ observation frequency to the portfolio return frequency.
• A risk-free rate series supplied with factors can provide a consistent choice for empirical work.
• The discussion does not fully resolve how instrument maturity should relate to a strategy’s holding horizon.
• If rates and returns use different frequencies, the comparison may not be on a consistent basis.

Tags

# Risk-Free Rate determinant in CAPM


# Risk-Free Rate determinant in CAPM












I have trouble understanding what type of maturity to use when calculating `CAPM`. My professor uses the `3-Month risk-free rate` to backtest a portfolio strategy that uses a lookback period of 1 year daily returns. Another professor uses the `10-year risk-free rate`? Shouldn't one use the maturity that corresponds to the holding period as it best describes the opportunity forfeited? Is the risk-free rate chosen out of preference? wouldn't this just under/overstate CAPM?

## Answer by James (score 1, accepted)

https://quant.stackexchange.com/a/14718

I think the best strategy is to follow Ken French who posted all of the Fama-French factors on his website a while ago, including the risk-free rate.

The latter is updated at the same frequency as the portolio returns, e.g. you can't use a 3-month - based rate if you work with monthly equity returns.

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