Looking Under the Hood: What Does Quantile Regression Tell Us About the Low-Beta Anomaly?

54 Pages Posted: 15 Apr 2014 Last revised: 12 May 2014

See all articles by Stephen Bianchi

Stephen Bianchi

University of California, Berkeley

Date Written: May 8, 2014


In a CAPM world, the expected return of every portfolio is linearly related to its market beta. Further, the market portfolio attains the maximum Sharpe ratio among all portfolios of risky assets. Consequently, low-beta portfolios are predicted to earn a lower rate of return and to have Sharpe ratios no greater than the market portfolio. A low-beta portfolio of risky assets with beta B is predicted to earn the same rate of return as a portfolio that invests B in the market portfolio and 1 - B in the risk-free asset. Empirically, neither of these predictions has been realized. Low-beta (B < 1) portfolios have earned higher returns than their market portfolio plus risk-free asset counterparts, and they have achieved higher Sharpe ratios than the market portfolio. In the literature, this is referred to as the low-beta anomaly. This paper uses quantile regression to examine other dimensions of risk beyond beta and volatility, and finds that low-beta stocks and portfolios bear additional compensated risk in the form of excess kurtosis.

Suggested Citation

Bianchi, Stephen, Looking Under the Hood: What Does Quantile Regression Tell Us About the Low-Beta Anomaly? (May 8, 2014). Available at SSRN: https://ssrn.com/abstract=2424929 or http://dx.doi.org/10.2139/ssrn.2424929

Stephen Bianchi (Contact Author)

University of California, Berkeley ( email )

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