High-Dimensional Mean-Variance Spanning Tests

Abstract

We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio.