Implied Ambiguity: Mean-Variance Inefficiency and Pricing Errors

We investigate the optimal portfolio choice problem for an investor who has a utility function of the smooth ambiguity model. We identify necessary and sufficient conditions for a given portfolio to be optimal for such an investor. We define the implied ambiguity of a portfolio as the smallest ambiguity aversion coefficient with which the portfolio is optimal, and the measure of ambiguity perception as the part of the variability in asset returns that can be attributed to the ambiguity. We show that there are one-to-one relations between the implied ambiguity, the Sharpe ratio, and the pricing errors when the portfolio is taken as the pricing portfolio, and that the measure of ambiguity perception is determined by the Sharpe ratio and the alpha. Based on the U.S. stock market data, we assess how ambiguity averse the representative investor is and what types of stocks the investor perceives as having more ambiguous returns than others. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.