Choosing CAPM Beta Windows and Return Frequencies
Summary
The document explains that rolling CAPM beta can be calculated either by regression or from rolling correlation multiplied by the ratio of the asset’s standard deviation to the market’s. It argues that the estimation horizon should reflect the investor’s portfolio review or adjustment schedule, with the risk-free rate aligned to that horizon. It also cautions that daily observations can contain bid-ask bounce, which may bias beta estimates downward relative to estimates using less frequent observations.
Selecting how much history to include is more difficult: the answer depends on the estimation problem, and the response offers a common three-year lookback as a practical convention rather than an optimal rule. It further notes that beta may vary across business cycles and that a single-factor CAPM can produce unstable coefficients and apparent alpha. Adding economic and style factors may improve stability, though the note provides no comparative empirical results or definitive window selection method.
Key ideas
- Rolling beta can be computed from rolling correlation and relative standard deviations.
- The estimation horizon should match the investor’s portfolio decision schedule.
- Daily returns may include bid-ask bounce that affects beta estimates.
- A three-year lookback is presented as a convention, not a proven optimum.
- CAPM beta can vary over business cycles, motivating consideration of additional factors.
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# Time horizon of estimation period CAPM beta # Time horizon of estimation period CAPM beta When calculating CAPM beta, it is done by rolling regressions. If it is only the beta we want to obtain, am I correct to assume that we can estimate rolling correlations and stds, and use this to calcuate the betas as corr*stockSTD/mktSTD ? Next thing I wonder is what is the time horizon used in CAPM? More specifically, how long is the rolling windows? Is there any newer articles stating more optimal time horizons for the std and corr? Daily data as obviously best, but for 1 year, 3 years or 5 years? Thanks :) ## Answer by kurtosis (score 1) https://quant.stackexchange.com/a/63828 Yes, you may use rolling correlations and standard deviations to get rolling beta estimates. The time horizon used is your investment decision horizon: in other words, how often might you adjust your portfolio? If you revisit your portfolio's investments every year, then the time horizon should be a year. This also affects the risk-free rate you use when calculating excess returns for the stock and market index. Daily data is not necessarily the best for estimating betas. Daily data is slightly polluted by bid-ask bounce, so that added source of noise will tend to bias beta estimates to be lower than estimates produced using weekly, monthly, or longer-term data. The tougher question is how much data you should use for estimation: one year back? three years? more? The answer gets very complicated (see the statistical work of Allan Timmerman on optimal windows for mean vs variance estimation). Barring tackling that question with a complicated method, you can do as many people do and use three years prior. Finally, I would be remiss if I did not point out that the CAPM betas will vary across the business cycle and suggest the presence of alpha more often than we would expect from economic theory. This is because your model is too simple: you should use a multi-factor model. Typically, adding in other factors like small vs large firms (e.g. outperformance of Russell 2000 vs the S&P 500), changes in the level and slope of the yield curve, momentum, inflation, and a credit spread (e.g. IBoxx IG - UST 10Y) will yield coefficients that are more stable across the business cycle; and, the alpha will be much closer to 0.
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