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

Last Updated on 10 February, 2024 by Rejaul Karim

Looking Under the Hood: What Does Quantile Regression Tell Us About the Low-Beta Anomaly?” by Stephen Bianchi delves into the intricate realities of the low-beta anomaly in the context of the CAPM framework.

Traditionally, the CAPM model implies a linear relationship between a portfolio’s market beta and its expected return, suggesting that low-beta portfolios should yield lower returns and possess Sharpe ratios no greater than that of the market portfolio.

However, empirical evidence has defied these predictions. Low-beta portfolios have demonstrated higher returns and superior Sharpe ratios, constituting what is termed the low-beta anomaly. Bianchi’s paper employs quantile regression to delve into the multifaceted dimensions of risk beyond beta and volatility.

The findings reveal that low-beta stocks and portfolios exhibit additional compensated risk in the form of excess kurtosis, enriching the understanding of the complex interplay of risk within the low-beta anomaly.

Abstract Of Paper

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.

Original paper – Download PDF

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Author

Stephen Bianchi
University of California, Berkeley

Conclusion

Stephen Bianchi’s research on “Looking Under the Hood: What Does Quantile Regression Tell Us About the Low-Beta Anomaly?” unravels significant insights into the enigmatic low-beta anomaly within the framework of the CAPM model.

While traditional expectations within the CAPM world anticipate a linear relationship between a portfolio’s market beta and its expected return, the empirical evidence profoundly contradicts these assumptions. Low-beta portfolios have exhibited higher returns and superior Sharpe ratios, defying the anticipated outcomes and giving rise to what is known as the low-beta anomaly.

Bianchi’s utilization of quantile regression has illuminated additional dimensions of risk beyond beta and volatility. The analysis underscores that low-beta stocks and portfolios carry extra compensated risk in the form of excess kurtosis, providing a deeper understanding of the intricate dynamics underlying the low-beta anomaly and contributing valuable dimensions to the discourse surrounding risk and portfolio performance.

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FAQ

What is the focus of the research on “Looking Under the Hood: What Does Quantile Regression Tell Us About the Low-Beta Anomaly?”

The research focuses on investigating the low-beta anomaly within the context of the Capital Asset Pricing Model (CAPM). Traditionally, CAPM implies a linear relationship between a portfolio’s market beta and its expected return. However, empirical evidence has shown that low-beta portfolios tend to exhibit higher returns and superior Sharpe ratios, leading to the low-beta anomaly. The study employs quantile regression to explore additional dimensions of risk beyond beta and volatility.

What is the traditional expectation within the CAPM framework regarding the relationship between beta and expected return?

In the CAPM framework, the traditional expectation is that the expected return of every portfolio is linearly related to its market beta. According to this expectation, low-beta portfolios should earn a lower rate of return compared to higher-beta portfolios, and the Sharpe ratios should not be greater than that of the market portfolio.

What are the implications of the research findings for the understanding of risk and portfolio performance?

The research findings contribute to a deeper understanding of risk and portfolio performance by highlighting that low-beta stocks and portfolios exhibit additional compensated risk in the form of excess kurtosis. This implies that factors beyond beta and volatility play a role in shaping the risk-return profile of low-beta portfolios. The study provides valuable insights that go beyond traditional CAPM assumptions, offering a more nuanced perspective on the multifaceted nature of risk within the low-beta anomaly.

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