On robust portfolio and naïve diversification: mixing ambiguous and unambiguous assets

Effect of the availability of a riskless asset on the performance of naïve diversification strategies has been a controversial issue. Defining an investment environment containing both ambiguous and unambiguous assets, we investigate the performance of naïve diversification over ambiguous assets. For the ambiguous assets, returns follow a multivariate distribution involving distributional uncertainty. A nominal distribution estimate is assumed to exist, and the actual distribution is considered to be within a ball around this nominal distribution. Complete information is assumed for the return distribution of unambiguous assets. As the radius of uncertainty increases, the optimal choice on ambiguous assets is shown to converge to the uniform portfolio with equal weights on each asset. The tendency of the investor to avoid ambiguous assets in response to increasing uncertainty is proven, with a shift towards unambiguous assets. With an application on the CVaR risk measure, we derive rules for optimally combining uniform ambiguous portfolio with the unambiguous assets.