One of the significant problems for the first formal asset pricing model developed by financial economists, the capital asset pricing model (CAPM), was that it predicts a positive relationship between risk and return. However, empirical studies have found the actual relationship to be flat, or even negative.
Over the past five decades, the most “defensive” stocks have delivered higher returns than the most “aggressive” stocks. In addition, defensive strategies (at least those based on volatility) have delivered significant Fama-French three-factor and four-factor alphas.
The superior performance of low-volatility stocks (as well as low-beta stocks, which are closely related) was initially documented in the academic literature in the 1970s, before even the size and value premiums were “discovered.” The low-volatility anomaly has been found to exist in equity markets across the globe, and not only for stocks but for bonds. In other words, it has been pervasive.
CAPM & Its Assumptions
One of the CAPM’s assumptions is that there are no constraints on either leverage or short-selling. In reality, though, many investors are constrained against employing leverage (by their charters) or have an aversion to its use.
The same is true of short-selling, and the borrowing costs for some hard-to-borrow stocks can be high. Such limits to arbitrage prevent arbitrageurs from correcting the pricing mistake.
Another assumption made by the CAPM is that markets have no frictions, meaning there are neither transaction costs nor taxes. Of course, in the real world, there are costs. The evidence shows that the most mispriced stocks are the ones with the highest costs of shorting.
The explanation for the low-volatility anomaly, then, is that, faced with constraints and frictions, investors seeking to increase their returns elect to tilt their portfolios toward high-beta securities to garner more of the equity risk premium.
High & Low Demand
This extra demand for high-beta securities and reduced demand for low-beta securities may explain the anomaly of a flat or even inverted relationship between risk and expected return relative to the CAPM’s predictions.
Some recent papers (Robert Novy-Marx’s 2016 study, “Understanding Defensive Equity,” and Eugene Fama and Kenneth French’s 2015 study, “Dissecting Anomalies with a Five-Factor Model”) argue that the low-volatility and low-beta anomalies are well-explained by asset pricing models that include the newer factors of profitability and investment (in addition to market beta, size and value).
For example, Fama and French write in their paper that when using their five-factor model, the “returns of low volatility stocks behave like those of firms that are profitable but conservative in terms of investment, whereas the returns of high volatility stocks behave like those of firms that are relatively unprofitable but nevertheless invest aggressively.”
They add that positive exposure to RMW (the profitability factor, or robust minus weak) and CMA (the investment factor, or conservative minus aggressive) also go a long way toward capturing the average returns of low-volatility stocks whether volatility is measured by total returns or residuals from the Fama-French three-factor model.
Dana D’Auria and John McDermott contribute to the literature with their recent study, “U.S. Low and Minimum Volatility Indexes: An Empirical Analysis of Factor Exposure,” which appears in the Fall 2017 issue of The Journal of Index Investing.
They investigated the major low-volatility and minimum-volatility indexes used as benchmarks for the largest ETFs in the space to determine whether findings in the academic literature on low and minimum volatility carry through to the indexes commonly used to implement these strategies.
They studied performance against both single-factor (market beta) and multifactor (market beta, size, value, momentum, investment and profitability) asset pricing models. Their examination covered the time periods of December 1990 through December 2016, and June 2001 through December 2016 (when data for small-cap strategies was available).
The four ETFs that the authors examined (two large-cap/midcap and two small-cap) were the iShares Edge MSCI Mini Vol USA ETF (USMV), the iShares Edge MSCI Mini Vol USA Small-Cap ETF (SMMV), the PowerShares S&P 500 Low Volatility ETF (SPLV) and the PowerShares S&P SmallCap Low Volatility ETF (XSLV).
Following is a summary of their findings:
- Consistent with the academic research on low and minimum volatility, low-volatility ETFs produce superior risk-adjusted performance for the indexes examined. In other words, they produce statistically significant single-factor alphas.
- Exposure to other common factors explains the significant one-factor alphas attributable to the strategies in large-cap/midcap stocks, but not in small-cap stocks.
- The r-squared ratios for the large-cap/midcap low-volatility strategies ranged from as high as 0.89 to 0.72. For the small-cap low-volatility strategies, the r-squared ratios ranged from as high as 0.90 to 0.86. The high r-squared ratios suggest that the models do a good job of explaining much of the variation of the returns of the low-volatility indexes.
- Over the full periods examined, for large-cap/midcap stocks, low-volatility strategies have significant exposure to both the profitability (RMW) and investment (CMA) factors, though statistically insignificant exposure to the value factor (HML, or high minus low).
- For small-cap stocks, low-volatility strategies have significant exposure to HML, RMW and the momentum factor (UMD, or up minus down), but insignificant exposure to CMA.
- There is evidence of time-varying exposure to UMD and HML in the large-cap/midcap low-volatility strategies. The exposure to UMD and HML were positive for only 57% and 47% of the rolling 36-month periods.
- For the S&P 600 Low Volatility index, UMD and HML loadings varied from highly positive to highly negative. The HML exposure varied from a high of 0.58 to a low of -0.29, while the UMD exposure ranged from 0.43 to -0.30.
The authors concluded: “The factor regressions suggest strong orientation (on average) toward profitable/quality firms that are conservative in their capital investment practices.” They also found the underlying indexes have different exposures to common factors.
For example, they write: “The MSCI index has a significantly higher market beta but significantly lower exposure to SmB, RmW, and CmA. Put another way, S&P 500 Low Vol has lower market exposure but greater exposure to size (smaller stocks), profitability (more profitable stocks), and investment (more conservative investment stocks).”
In other words, the authors are observing that fund construction rules matter, as do the time-varying exposures noted above.
They note: “This is an especially important consideration when combining low and minimum volatility strategies in a portfolio with other factor-based strategies. For example, a portfolio with dedicated factor tilts (e.g., momentum and/or value) may have its dedicated factors either diluted or strengthened over time with the addition of a strategy with significant time variation in its factor tilt.”
D’Auria and McDermott concluded: “Our examination of the indexes underpinning the major ETFs in this space reveals that they appear to have successfully captured the investment stratagems outlined in the significant academic works.”
However, they also write that “an inclusive set of factors can explain the high excess return of low and minimum volatility strategies in the large-cap space, at least over the timeframe considered.”
Finally, the authors add this caution: “Low and minimum volatility expose the user to significant deviation in other factor exposures. While the level of profitability and investment remained somewhat stable over time, these strategies had very different value and momentum loadings depending upon the time period. This suggests that managers must measure their overall factor exposures at the portfolio level on an ongoing basis to understand if they are inadvertently over- or underweighting factors.”
D’Auria and McDermott’s finding that once the asset pricing models are expanded to include the momentum, profitability and investment factors, the low-volatility anomaly is fully explained, at least in the large-cap/midcap space, providing support for Andrew Lo’s adaptive markets hypothesis.
Sophisticated investors learn about anomalies through published academic research and their actions serve to reduce/eliminate the mispricing. However, the persistence of alpha in the small-cap space, where arbitrageurs can incur significant costs related to illiquidity (that is, higher transaction costs), as well as higher costs of shorting, demonstrates that limits to arbitrage can prevent those same sophisticated investors from correcting mispricings, allowing anomalies to persist.
This commentary originally appeared October 13 on ETF.com
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