Abstract: The term Knightian uncertainty is well known in economics literature, and it has come to be known today as ambiguity. I conduct a study to measure the investor-perceived ambiguity of the stock market. More specifically, I construct a forward looking ambiguity index based on option-implied volatilities extracted from European index options. As the option-implied volatilities across strike prices each represent a different estimate of future realized volatility, we can take the standard deviation across these values to represent the ambiguity over stock market returns. Using options data on the EURO STOXX 50, I show that my constructed ambiguity index is valid through comparison with other famous ambiguity indices. I also utilize the ambiguity index to decompose the equity premium into risk and ambiguity components, showing that the ambiguity attitude of aggregate investors is contingent on the average daily probability of favorable returns.

Abstract: By timing exposure to option implied information based on ambiguity (Knightian uncertainty) and risk, one can earn superior risk-adjusted returns, larger utility gains for mean variance investors, and an alpha even above that of volatility managed portfolios in Moreira & Muir (2017). These results are attributed to the contribution of timing ambiguity, conditional on a high (low) probability of favorable returns that is proxied with low (high) volatility levels, which allows investors to benefit from a positive (negative) ambiguity premium that stems from probability-varying ambiguity preferences shown in Brenner & Izhakian (2018). Even after robustness tests that simulate real-world conditions, controlling for returns that stem from the low risk anomaly or volatility timing strategies, my option implied timing approach still produces superior outperformance when compared to a set of timing approaches.