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.”