Is there a distinct systematic asset risk, as measured by its market beta, associated with each return measurement interval (frequency, such as daily, monthly or annually)? In other words, is return measurement frequency a risk factor? In their October 2018 paper entitled “Measuring Horizon-Specific Systematic Risk via Spectral Betas”, Federico Bandi, Shomesh Chaudhuri, Andrew Lo and Andrea Tamoni introduce spectral beta, an asset’s market beta for a given return measurement frequency, as a way to assess this frequency as a source of systematic investment risk. They specify how to combine spectral betas into an overall beta and explore ways to interpret and exploit spectral betas. Using mathematical derivations and samples of monthly and daily returns for broad samples of U.S. stocks and stock portfolios, they find that:
- A linear combination of an asset’s spectral betas, weighted according to their respective stabilities over time, is a reasonable way to estimate overall asset beta.
- For 25 stock portfolios formed by first sorting into fifths (quintiles) based on market capitalization and then based on book-to-market ratio:
- Spectral market betas generally increase (decrease) for small value (large growth) stocks when going from high to low return measurement frequencies. These results suggest a frequency-based explanation for the value premium.
- A Capital Asset Pricing (1-factor) Model with beta constructed from low-frequency spectral betas explains differences in returns across the 25 portfolios better than the Fama-French 3-Factor Model.
- Constructing market betas using spectral betas generates optimal portfolios with lower out-of-sample variability than comparable portfolios constructed under the assumption that risk is constant across frequencies.
In summary, evidence suggests that recognizing market beta measurement frequency as an investment risk may improve conventional models of stock returns and associated optimal portfolio formation.
Investors may want to:
- Adjust/optimize the beta measurement frequency for their individual investing styles.
- Match the frequency at which they check portfolio performance to the selected beta measurement interval.
Cautions regarding findings include:
- Reported return analyses are gross, not net. Accounting for trading frictions, shorting costs and shorting constraints would reduce returns and may affect findings.
- The method described is beyond the reach of most investors, who would bear fees for delegating to an investment/fund manager. It may also be beyond the reach of many managers.
- The proposed spectral approach introduces a new variable into beta estimation that invites data snooping. Moreover, spectral betas may be meaningful for factors other than the market factor, introducing further complexities.
See also “Sensitivity of Stock Market Return Predictability to Predictor Measurement Interval” and “Sensitivity of Risk Adjustment to Measurement Interval”.
