Tail Mean-Variance Portfolio Selection with Estimation Risk

Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean and covariance of asset returns in the optimal portfolio weight with their sample counterparts. The plug-in method inevitably introduces estimation risk and usually has poor out-of-sample performance. We propose an optimal combination of the plug-in and 1/N rules to improve out-of-sample performance. Our proposed combined portfolio consistently outperforms both the plug-in and 1/N portfolios on both simulated and real-world datasets