Measured as the standard deviation of log returns, volatility is widely regarded as a synonym for risk, and option implied volatility denotes the expected risk for an asset. However, following the economist Frank Knight‘s famous distinction between risk and uncertainty, we can ask about the events or outcomes that are not reflected in a given risk estimate. If our volatility estimate reflects the outcomes that we know might occur, what should we think about the outcomes we don’t know about, the “unknown unknowns”? More specifically, how do investor attitudes toward uncertainty affect subsequent stock returns? (Here is a quick video I put together clarifying the difference between risk and uncertainty.)
The authors of “Unknown Unknowns: Vol-of-Vol and the Cross-Section of Stock Returns” argue that we can estimate the effects of uncertainty – understood in this particular sense – by measuring the volatility of option-implied volatility (vol-of-vol). The results are striking:
Our results reveal that, compared to otherwise similar stocks in our sample from 1996 to 2009, stocks with a higher vol-of-vol earn signifcantly lower future returns. When we sorts stocks by vol-of-vol into value-weighted quintile portfolios, stocks in the highest vol-of-vol quintile underperform stocks in the lowest vol-of-vol quintile by 0.85% in the month following portfolio formation, equivalent to about 10% per year….Assuming that vol-of-vol captures uncertainty about expected stock returns, our results strongly suggest that uncertainty has a negative effect on future stock returns in the cross-section.
Portfolios consisting of stocks with low vol-of-vol have consistently outperformed their more uncertainty-laden peers.
Monthly Returns on Vol-of-Vol Portfolios
Source: Baltussen, Van Bekkum and Van Der Grient
The danger in a study like this is that the deviation in returns might be attributable to some other factor instead of, or in conjunction with, the effect studied. To exclude this possibility, the authors regress sample portfolios against more than twenty widely-studied drivers of portfolio returns including beta, momentum, skewness, liquidity, leverage, and short-sale constraints. They also claim that vol-of-vol is distinct from options-specific factors like volatility skew, the spread between implied and realized volatility, and option liquidity.
Another objection might be that some economically significant behavior other than uncertainty about expected returns might explain the data. Optimism bias would suggest that high vol-of-vol stocks will deviate further from their true values. The negative volatility risk premium might be present to lower degrees in low vol-of-vol stocks. Or vol-of-vol might be a priced factor reflecting a worsening market. The authors test for and exclude these explanations, too.
Finally, it might be plausible to object that since high-volatility stocks have larger absolute swings in implied volatility, the vol-of-vol estimate might just be tracking first-order volatility. To control for this, the authors scale each day’s IV estimate for a given stock by the trailing average IV for that stock. The vol-of-vol effect is not limited to U.S. stocks, either: the study covers ADRs of foreign companies, as well.
It has become common in the financial press to describe volatility estimates like CBOE Volatility Index (VIX) as a “fear gauge.” This is not necessarily a false metaphor, but it is too vague. Any given day’s VIX estimate reflects the information and expectations of market participants, but implied volatility also reflects the fact that we know our imaginations are finite. Our fears extend beyond the dangers we can perceive to the things that we know we can’t. The argument of this study is that the change in our collective uncertainty over time has been an effective indicator of future returns.