Portfolio concentration, portfolio inertia, and ambiguous correlation

Abstract

When an investor is ambiguous about the asset returns' correlation and evaluates the portfolio in a multi-prior framework, we show that the optimal portfolio may contain only a fraction of risky assets. In particular, if the level of ambiguity is high enough, the optimal portfolio contains only the one with the highest Sharpe ratio. Moreover, we demonstrate that the optimal portfolio may be independent of feasible correlation matrices and may not change when the Sharpe ratios of some assets change. Ambiguity-aversion on correlation uncertainty explains portfolio concentration and portfolio inertia in household portfolios and retirement accounts, and the model can explain the growth of indexing and ETFs from an optimal portfolio choice perspective. We further show that these properties do not hold in an alternative smooth ambiguity model, suggesting that the smooth ambiguity model does not depart from the standard model sufficiently to explain portfolio concentration and portfolio inertia.