There Is Nothing Certain But The Uncertain

Abstract: Risk and risk aversion are crucial concepts in finance. Models in finance typically assume a known probability distribution of returns, which does often not hold in reality. This papers aims to measure the uncertainty surrounding the probability distribution in equity markets and to evaluate if such uncertainty is priced. Our study defines uncertainty as the volatility of the option implied volatility (vol-of-vol). By employing a Factor Mimicking Portfolio approach, we observe a significant underperformance of the high vol-of-vol portfolio compared the low vol-of-vol portfolio. Over the sample period from January 2005 to March 2023, the average annualized return difference between the two portfolios is 11.9%. Interestingly, the vol-of-vol effect cannot be explained by the Carhart Four Factor Model, as the High-Minus-Low Portfolio exhibit a significant annual Carhart 4-Factor alpha of 13.9%.