Portfolio Selection under Ambiguity in Volatility

We study optimal portfolio choice when the variance of asset returns is ambiguous. Building on the smooth model of ambiguity aversion by Klibanoff et al. (2005), we introduce a one-period framework in which returns follow a Variance–Gamma specification, obtained by mixing a normal distribution with a gamma prior on the variance. This structure captures empirically observed excess kurtosis and allows us to derive closed-form solutions for optimal demand. Our main results show that ambiguity about volatility leads to bounded portfolio positions, in sharp contrast to the unbounded exposures predicted by the classical CAPM when expected excess returns are large or when the mean variance tends to zero. We characterize the comparative statics of the optimal allocation with respect to risk aversion, ambiguity aversion, and the parameters of the prior distribution. For small mean excess returns, portfolio demand converges to the CAPM benchmark, indicating that ambiguity aversion affects higher-order terms only. The model provides a tractable link between robust portfolio choice and realistic, heavy-tailed return dynamics.