Uncertainty aversion, robust control and asset holdings

Optimal portfolio rules are derived under uncertainty aversion by formulating the portfolio choice problem as a robust control problem, with ambiguity aversion with respect to the joint distribution of assets and the distribution of each risky asset. Robust portfolio rules indicate that the total holdings of risky assets as a proportion of the investor’s wealth may increase as compared with the holdings under the Merton rule, which is the standard risk-aversion case. This result departs from the general belief that ambiguity aversion induces conservative behavior. We also show that an investor following optimal robust portfolio rules increases the holdings of the asset for which there is less ambiguity, and reduces the holdings of the asset for which there is more ambiguity, a result that might provide an additional explanation for the home bias puzzle.