Title: Power properties of the out-of-sample portfolio performance measures tests
Authors: Ekaterina Kazak - University of Konstanz (Germany) [presenting]
Winfried Pohlmeier - University of Konstanz (Germany)
Abstract: While the literature on portfolio choice largely concentrated on stabilization strategies, little attention has been devoted to the quality of performance tests used to check, if a given strategy can significantly outperform an alternative in terms of some performance measure. We examine the quality of portfolio performance measures tests and conclude that the puzzling empirical results of inferior performance of the theoretically superior strategies based on the out-of-sample comparison are coming partly from the low power properties of the tests. We emphasize the importance of the underlying return distribution and show that the out-of-sample portfolio returns follow a mixture distribution depending on the return vector, but also the estimated portfolio weights. In the simulation study with the proposed mixture distribution design we show that in the realistic cases the test difference is overemphasized, the main issue here is the low testing power, which automatically leads to a conclusion, that the benchmark strategy cannot be outperformed significantly. More specifically, we show that in some circumstances it might be reasonable to select a low significance level (high Type One error) and to choose the alternative rather than sticking to the model that cannot be rejected under the null.