Testing multiple investment strategies until you find one with a high Sharpe Ratio inflates the probability of finding something that looks good by pure chance (Type I error). This repository contains functions for evaluating investment strategies considering multiple testing.
Adjusted critical
The Sharpe Ratio measures the average return that exceeds the risk-free rate, relative to the volatility of the return. It is a commonly used metric to understand the risk-adjusted return of an investment.
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$\mu$ : Mean return -
$r_f$ : Risk-free rate -
$\sigma$ : Standard deviation of the return
When testing
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$\Phi$ : CDF of the standard normal -
$\gamma$ : Euler-Mascheroni constant -
$N$ : Number of returns -
$M$ : Number of tests
The
The Bonferroni Method is a conservative approach for multiple testing correction. It reduces the chance of type I errors (false positives) by dividing the significance level by the number of tests.
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$\alpha$ : Significance level
The Holm Method is a stepwise correction that is less conservative than the Bonferroni Method. It adjusts the
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$k$ : Index of the test sorted by ascending$p$ -value
The BHY Method controls the False Discovery Rate (FDR) and is less conservative than Family-wise Error Rate (FWER) methods like Bonferroni and Holm. FDR is the expected proportion of false discoveries among the rejected hypotheses.
The Sharpe Ratio is corrected by plugging the corrected
This function takes a