Swedroe: Solving The Volatility Puzzle

If it’s a risk, why isn’t it rewarded?

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

One of the interesting puzzles in finance is that stocks with greater idiosyncratic volatility (IVOL) have produced lower returns. This is an anomaly, because idiosyncratic volatility is viewed as a risk factor—greater volatility should be rewarded with higher, not lower, returns.

Robert Stambaugh, Jianfeng Yu and Yu Yuan, authors of the study “Arbitrage Asymmetry and the Idiosyncratic Volatility Puzzle,” which appears in the October 2015 issue of The Journal of Finance, provide an explanation—and the evidence supporting it—for why the anomaly persists.

Explaining Volatility’s Anomaly
They begin with the hypothesis that IVOL represents risk that deters arbitrage and the resulting reduction of mispricings. The authors then combine this concept with what they term “arbitrage asymmetry”—the greater ability and/or willingness of investors to take a long position as opposed to a short position when they perceive mispricing in a security. This asymmetry occurs because there are greater risks and costs involved in shorting, including the potential for unlimited losses.

In addition to the greater risks and costs of shorting, for stocks with a low level of institutional ownership, there may not be sufficient shares available to borrow in order to sell short. Because institutions are the main lenders of securities, studies have found that when institutional ownership is low, the supply of stocks to loan tends to be sparse. Thus, short selling tends to be more expensive.

Furthermore, the charters of many institutions prevent, or severely limit, shorting. And finally, there is the risk that adverse moves can force capital-constrained investors to reduce their short positions before realizing profits that would ultimately result from corrections of mispricing. Importantly, when IVOL is higher, substantial adverse price moves are more likely. The authors write: “Combining the effects of arbitrage risk and arbitrage asymmetry implies the observed negative relation between IVOL and expected return.”

To see the effect of limits to arbitrage and arbitrage asymmetry, Stambaugh, Yu and Yuan note that stocks with greater IVOL—and thus greater arbitrage risk—should be more susceptible to mispricing that isn’t eliminated by arbitrageurs.

Among overpriced stocks, the IVOL effect in expected return should therefore be negative. Stocks with the highest IVOL should be the most overpriced. However, with arbitrage asymmetry, the reverse isn’t true, as the greater willingness to buy (versus short) allows arbitrageurs to eliminate more underpricing than overpricing.

The authors explain as follows: “As a result, the differences in the degree of underpricing associated with different levels of IVOL should be smaller than the IVOL-related differences in overpricing. That is, the negative IVOL effect among overpriced stocks should be stronger than a positive IVOL effect among underpriced stocks. When aggregating across all stocks, the negative IVOL effect should therefore dominate and create the observed IVOL puzzle.”

Testing The Hypothesis

To test their hypothesis, Stambaugh, Yu and Yuan constructed a proxy for mispricing. Specifically, a composite measure averaging each stock’s rankings associated with 11 return anomalies that are violations of the Fama-French three-factor (market beta, size and value) model:

  1. Net Stock Issues: Net stock issuance and stock returns are negatively correlated. It’s been shown that smart managers issue shares when sentiment-driven traders push prices to overvalued levels.
  2. Composite Equity Issues: Issuers underperform nonissuers, with “composite equity issuance” defined as the growth in the firm’s total market value of equity minus the stock’s rate of return. It’s computed by subtracting the 12-month cumulative stock return from the 12-month growth in equity market capitalization.
  3. Accruals: Firms with high accruals earn abnormally lower average returns than firms with low accruals. Investors overestimate the persistence of the accrual component of earnings when forming earnings expectations.
  4. Net Operating Assets: The difference on a firm’s balance sheet between all operating assets and all operating liabilities, scaled by total assets, is a strong negative predictor of long-run stock returns. Investors tend to focus on accounting profitability, neglecting information about cash profitability, in which case, net operating assets (equivalently measured as the cumulative difference between operating income and free cash flow) captures such a bias.
  5. Asset Growth: Companies that grow their total assets more earn lower subsequent returns. Investors overreact to changes in future business prospects implied by asset expansions.
  6. Investment-to-Assets: Higher past investment predicts abnormally lower future returns.
  7. Distress: Firms with high failure probability have lower, rather than higher, subsequent returns.
  8. O-Score: An accounting measure of the likelihood of bankruptcy. Firms with higher O-scores have lower returns.
  9. Momentum: High (low) recent (in the past year) past returns forecast high (low) future returns over the next several months.
  10. Gross Profitability Premium: More profitable firms have higher returns than less profitable ones.
  11. Return on Assets: More profitable firms have higher expected returns than less profitable firms.

As evidence that their mispricing measure is effective, they found that after assigning stocks each month to deciles based on their measure, the following month’s spread in benchmark-adjusted (for the three Fama-French factors) returns between the two extreme deciles averaged 1.48% over their sample period (August 1965 through January 2011) and was highly statistically significant.

Further Findings
Sorting stocks based on this composite anomaly ranking allowed the authors to investigate the IVOL effect within various degrees of cross-sectional relative mispricing. They found: “As predicted, the IVOL effect is significantly negative (positive) among the most overpriced (underpriced) stocks and the negative effect among the overpriced stocks is significantly stronger—the negative highest-versus-lowest difference among the most overpriced stocks is 3.7 times the magnitude of the corresponding positive difference among the most underpriced stocks.”

They also found that the vast majority of the differences in returns were explained by the short side (the most overpriced stocks). In addition, IVOL increased monotonically moving across deciles from the most underpriced to the most overpriced.

Moreover, consistent with their model, they found that the negative IVOL effect among overpriced stocks is stronger for stocks that are less easily shorted (as proxied by stocks with low institutional ownership). The authors also found that while the IVOL effect was strongest among overpriced small stocks—consistent with small stocks being more difficult/expensive to short than large stocks—the effect holds for large stocks as well, though it’s no longer statistically significant at conventional levels. Again, this supports their hypothesis regarding limits to arbitrage and arbitrage asymmetry.

Stambaugh, Yu and Yuan also hypothesized that “when aggregating across all stocks, the average negative relation between IVOL and expected return observed by previous studies should be stronger in periods when there is a market-wide tendency for overpricing.”

To test this hypothesis, they chose to use the sentiment index constructed by Malcolm Baker and Jeffrey Wurgler in the study “Investor Sentiment and the Cross-Section of Stock Returns,” which appeared in the August 2006 issue of The Journal of Finance.

Again, the evidence supports the theory: “The negative IVOL effect among overpriced stocks is significantly stronger following months when investor sentiment is high, and the positive IVOL effect among underpriced stocks is significantly stronger following months when investor sentiment is low.” In addition, there was “significantly stronger sentiment-related variation in the IVOL effect among the overpriced stocks.”


The study from Stambaugh, Yu and Yuan not only helps us to understand the role that idiosyncratic volatility plays in explaining returns, but it also helps us to understand why the anomaly persists. They show that “higher IVOL, which translates to higher arbitrage risk, allows for greater mispricing. As a result, expected return is negatively (positively) related to IVOL among overpriced (underpriced) securities.”

The authors also demonstrate that “the negative IVOL effect among overpriced stocks is stronger than the positive effect among underpriced stocks, and thus a negative IVOL effect emerges within the overall cross section. In addition, among the overpriced stocks, the negative IVOL effect is steeper for stocks less easily shorted.”

For investors, it’s important to note that the authors’ finding that there’s more uncorrected overpricing than uncorrected underpricing doesn’t mean a mutual fund has to short an overpriced stock to benefit. The fund can do so simply by avoiding the purchase of overpriced stocks with a filter that screens out stocks with the characteristic creating the mispricing.

Passively managed long-only mutual funds can put this knowledge to work by using screens to eliminate stocks that would otherwise be on their eligible buy list.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.