## The Volatility Anomaly Uncovered

Recent academic papers have shown that low-volatility stocks have provided better returns than higher-volatility stocks. What’s more, this is a global phenomenon.

These findings, however, run counter to economic theory, which predicts that higher expected risk should be compensated with greater expected returns, resulting in the low-volatility anomaly. Of interest is that this finding holds true not only for stocks, but for bonds.

**Exploring The Volatility Anomaly**

Bradford Jordan and Timothy Riley—authors of the paper, “Volatility and Mutual Fund Manager Skill,” which was published in the November 2015 issue of the Journal of Financial Economics—contribute to the literature surrounding the low-volatility anomaly by attempting to answer three questions related to the anomaly through the use of mutual funds:

**1. **Can mutual fund investors actually obtain the large-volatility-anomaly returns found in previous studies?

**2. **How does the volatility anomaly affect the measurement of mutual fund manager skill?

**3. **Can pricing factors not directly formed on volatility account for the impact of the volatility anomaly?

Jordan and Riley began by forming two portfolios. Their low-volatility portfolio holds the 10% of mutual funds with the lowest standard deviation during the prior calendar year. Their high-volatility portfolio holds the 10% of mutual funds in the sample with the highest standard deviation. Each portfolio was equal-weighted. A fund remained in the same portfolio for the entire year.

Following is a summary of their findings, which cover the period 2000 through 2013:

- In a standard four-factor framework, mutual fund return volatility is a reliable, persistent and powerful predictor of future abnormal returns.
- There is a clear pattern of decreasing returns as volatility rises.
- A dollar invested in a portfolio of mutual funds with low past-return volatility at the beginning of 2000 is worth about $2.90 at the end of 2013, while a dollar invested over the same period in a portfolio of mutual funds with high past-return volatility has a final value of only $1.21. A zero-fee fund tracking the CRSP value-weighted index would be worth $1.79. The data was highly statistically significant.
- The difference in returns occurs despite the fact that the low-volatility portfolio has an annualized return standard deviation of 13.5%, compared with 24.4% for the high-volatility portfolio. The Sharpe ratio of the low-volatility portfolio was 0.49 versus 0.10 for the high-volatility portfolio.
- In the Fama-French three-factor framework, a portfolio of low-volatility funds has a four-factor alpha of about 1.8% per year, while a portfolio of high-volatility funds has an alpha of about -3.2% per year—a difference of 5 percentage points a year.
- Funds entering the low-volatility portfolio have an average four-factor alpha of 0.26%, compared with -1.62% for funds entering the high-volatility portfolio. The sorting process places funds with higher past risk-adjusted returns into the low-volatility portfolio.
- High-volatility mutual funds tend to be high beta, with significant small-cap and growth exposures, but those exposures do not explain the underperformance.
- The abnormal returns to low-volatility (high-volatility) portfolios are eliminated by the addition of a volatility anomaly factor contrasting the returns on portfolios of low- and high-volatility stocks. The volatility anomaly, rather than manager skill, appears to explain the performance of the low- and high-volatility funds.
- The profitability factor (RMW, or robust minus weak) and the investment factor (CMA, or conservative minus aggressive) are equally effective at eliminating the abnormal returns. Failure to account for the volatility anomaly, either directly or indirectly, can lead to substantial mismeasurement of fund manager skill. Accounting for exposure to the volatility factor prevents managers from generating apparent abnormal performance through simple exposure to a known pricing anomaly.
- The LVH (low volatility versus high volatility) factor is correlated with all the Fama-French factors. It has a correlation of -0.71 with the market factor, -0.60 with the size factor and 0.51 with the value factor. Given that low-volatility stocks are typically low beta, large market capitalization and high book-to-market compared with high-volatility stocks, these relationships are unsurprising.
- The LVH factor is also correlated with the profitability factor (0.83) and the investment factor (0.39). These loadings on RMW and CMA indicate that low-volatility funds hold stock in companies that are more profitable and invest more conservatively than companies whose stock is held by high-volatility funds. Given that the literature shows profitability explains a large portion of the volatility anomaly; the fact that RMW and LVH are related is also expected.
- The volatility anomaly is driven by small, low-profitability and, to a lesser degree, high-investment, growth stocks.

**LVH And Other Factors**

Jordan and Riley produced another finding of particular interest. They write: “The addition of LVH causes a substantial convergence of the other factor loadings on the low and high volatility portfolios. Beta for the low volatility portfolio increases from 0.80 to 0.91 while beta for the high volatility portfolio decreases from 1.24 to 1.00. The absolute difference in the HML loadings between the low and high volatility portfolios decreases from 0.52 to 0.20, and the absolute difference in the SMB loadings decreases from 0.48 to 0.17. These results suggest that mutual fund performance differences commonly attributed to market cap and value/growth exposure could actually be more related to differences in LVH exposure.”

The addition of the profitability and investment factors provide an even stronger explanation for the results. By adding CMA alone, alpha for the low-volatility portfolio decreases, and alpha for the high-volatility portfolio increases—although the changes are much smaller than those caused by adding RMW. Together, adding RMW and CMA to the model produces an alpha of just 0.02% for both the low- and high-volatility portfolios.

In other words, as the authors observe, “The difference in alpha between the two portfolios falls from about 5.0% per year with the four-factors alone to approximately zero after including RMW and CMA.”

In summary, the answers to the aforementioned three questions posed by Jordan and Riley are: First, yes, the volatility anomaly strongly impacts actual mutual fund returns. Second, failure to account for the volatility anomaly can lead to large errors in the assessment of fund manager skill. The underperformance of high-volatility mutual funds is fully explained by exposure to the volatility anomaly. And third, the skill mismeasurement created by the volatility anomaly can be corrected using factors (profitability and investment) not directly formed on volatility.

*This commentary originally appeared December 10 on ETF.com*

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