Abstract
AbstractThe sample squared Sharpe ratio (SSR) is a critical statistic of the risk-return tradeoff. We show that sensitive upper-tail probabilities arise when the sample SSR is employed to test the mean-variance efficiency under different test statistics. Assuming the error's normality with a nonzero mean, we integrate the sample SSR and the arbitrage regression into a noncentral chi-square (χ2) test. We find that the distribution of the sample SSR based on the regression error is to the left of the F-distribution when assuming the returns' normality. Compared to two benchmarks that use the noncentral F-distribution and the central F-statistic, the χ2-statistic is more effective, competitive, significant, and locally robust when used to reject the upper-tailed mean-variance efficiency test using the usual parameters (sample size, portfolio size, and SSR).
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