Leveraged and inverse exchange-traded funds seek daily returns equal to fixed multiples of indexes' returns. Trading costs implied by frequent adjustments of funds' portfolios create a tension between tracking error, reflecting short-term correlation with the index, and excess return, 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...

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...