LO 64.8: Compare the volatility anomaly and beta anomaly, and analyze evidence

LO 64.8: Compare the volatility anomaly and beta anomaly, and analyze evidence of each anomaly.
Using data from 19261971, Haugen and Heins (1975)3 found that over the long run, stock portfolios with lesser variance in monthly returns have experienced greater average returns than riskier counterparts. Ang, Hodrick, Xing, and Zhang (2006)4 tested whether increased volatility, as measured by standard deviation, has a positive relationship with returns and Sharpe ratios. They organized their data, which comprised monthly return data from September 1963December 2011, into quintiles and controlled for numerous variables including leverage, volume, bid-ask spreads, dispersion in analysts forecasts, and momentum. They observed a volatility anomaly which shows that as standard deviation increased, both the average returns and the Sharpe ratios decreased. For the lowest three quintiles, the average return was above 10%, but declined to 6.8% for quintile 4 and to 0.1% for the quintile with the highest volatility. Likewise, Sharpe ratios declined from 0.8 for the lowest volatility quintile to 0.0 for the highest volatility quintile. It was found that the most volatile stocks produce the lower returns, while the least volatile stocks performed the best.
When the capital asset pricing model (CAPM) was first tested in the 1970s, a positive relationship was found between beta and expected returns. Numerous academics have since retested this relationship with interesting results. Ang et al. (2006) found that stocks with high betas tend to have lower-risk-adjusted returns. Organizing monthly return data from September 1963December 2011 into quintiles, they found that the Sharpe ratio fell from 0.9 for stocks with the lowest betas to 0.4 for stocks with the highest betas. This beta anomaly does not suggest that stocks with higher betas have low return because they do not. It means they have lower Sharpe ratios (risk-adjusted performance) because higher betas are paired with higher volatility as measured by standard deviation, which is the denominator in the Sharpe ratio.
Interestingly, CAPM does not predict that lagged betas (measured over previous periods) should produce higher returns. It does predict that investors should find a contemporaneous relationship between beta and expected returns. This means that stocks with higher betas should also have higher returns during the same time period when the beta was measured. This is a confirming, not a predictive, metric. Following this logic, if investors could reliably predict future betas, then they could more accurately predict future expected returns. The trouble is that historical betas are not good predictors of future betas. Buss and Vilkov (2012)5 estimated future betas using implied volatility measures in option pricing models and found some improvement over using historical betas. The beta anomaly is less a mystery as it is a challenge to find a reliable way of predicting future betas to improve the risk perspective of beta.
3. Robert A. Haugen and A. Janies Heins, Risk and the Rate of Return on Financial Assets: Some
Old Wine in New Bottles, Journal of Financial and Quantitative Analysis 10, no. 5 (1975): 775-84.
4. Andrew Ang, Robert J. Hodrick, Yuhang Xing, and Xiaoyan Zhang, High Idiosyncratic
Volatility and Low Returns: International and Further U.S. Evidence, Journal o f Financial Economics 91 (2009): 1-23.
5. Adrian Buss and Grigory Vilkov, Measuring Equity Risk With Option-Implied Correlations,
The Review of Financial Studies 25, no. 10 (2012): 3113-40.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Potential Explanations for the Risk Anomaly