An intersection–union test for supporting the hypothesis that a given investment strategy is optimal among a set of alternatives is presented. It compares the Sharpe ratio of the benchmark with that of each other strategy. The intersection–union test takes serial dependence into account and...

Pearson's correlation coefficient is typically used for measuring the dependence structure of stock returns. Nevertheless, it has many shortcomings often documented in the literature. We suggest to use a conditional version of Spearman's rho as an alternative dependence measure. Our approach is...

In the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the...

In the present work I derive the risk functions of 5 standard estimators for expected asset returns which are frequently advocated in the literature, viz the sample mean vector, the James-Stein and Bayes-Stein estimator, the minimum-variance estimator, and the CAPM estimator. I resolve the...

In the present work, I derive the risk functions of 5 standard estimators for expected asset returns which are frequently advocated in the literature, viz the sample mean vector, the James-Stein and Bayes-Stein estimator, the minimum-variance estimator, and the CAPM estimator. I resolve the...

We propose the outperformance probability as a new performance measure, which can be used in order to compare a strategy with a specified benchmark, and develop the basic statistical properties of its maximum-likelihood estimator in a Brownian-motion framework. The given results are used to...