Robust investment strategies with two risky assets

In reality, investors are uncertain about the dynamics of the risky asset returns (e.g., the expected returns and the correlation between the returns of two risky assets). Consequently, investors make robust investment decisions with special concerns on the expected returns and correlations. In this paper, we propose a hierarchical rule for robust investment between two risky assets: select the relatively safe asset first and then decide how much to invest in the relatively risky asset to hedge the ambiguity embedded in the relatively safe asset. After introducing criteria for relative riskiness and cross-hedging for investors with a constant relative risk averse (CRRA) utility, we find that a typical investor would equally invest in the two risky assets regardless of their correlation when they are indistinguishable from the riskiness perspective. Furthermore, the investor will take a long or short position on the relatively risky asset if it can work as the cross-hedging instrument due to their correlation; otherwise, it will not be traded at all. These results provide a unified explanation for the observed “under-diversification”, “home bias”, and “portfolioinertia” in financial markets from the cross-hedging point of view.