We report progress on our current research to account for data ambiguity in portfolio selection, and show that two well-known under-diversification puzzles are linked to ambiguity in the data. Specifically, we develop a novel robust optimization model under data ambiguity for skewed distributions of return and show that the optimal portfolios satisfy second-order stochastic dominance (SSD). We provide analytic solutions to a two-asset version of the model, and show that it can generate both home bias or foreign bias depending on the expected returns, variance, covariances, and relative ambiguity of the home and foreign markets. We then put the model to the data of 21 developed economies and 19 emerging markets, and find that it generates optimal international portfolios with allocations that match the observed home bias for reasonable ambiguity parameters. This speaks to the home-bias puzzle. We also apply the model to individual investors and find that portfolio ambiguity explains the household under-diversification puzzle. We specify ambiguity using different methods, either derived directly from observed data or proxied by some external factors such as economic policy uncertainty or differences among financial analysts’ projections. Our results are robust to the method of ambiguity estimation. Given that our portfolio selection model satisfies SSD, our empirical finding is also robust to investor risk-aversion. For all developed markets we find it is rational for investors to hold the portfolios they do given the empirically observed data ambiguity.

This is joint work with Somayyeh Lotfi of the University of Cyprus.