Bootstrap-based bias correction for the out-of-sample Sharpe ratio

Abstract

Looking for making an investment, one objective could be to find a portfolio where the Sharpe ratio for in the future, known as the out-of-sample Sharpe ratio, is maximized. Since future data is not avail-able, the Sharpe ratio needs to be predicted using historical data, the in-sample data. This is often done using the Sharpe Ratio Information Criterion, which determines the bias for the in-sample Sharpe ratio to es-timate the out-of-sample Sharpe ratio. However, this approach assumes that the covariance matrix is known. In portfolio management, the covariance matrix is typically unknown and can only be estimated. This project will use the bootstrap method to estimate the out-of-sample Sharpe ratio using the estimated co-variance matrix and analogous methods used for the Akaike Information Criterion. By eliminating the assumption of a known covariance matrix, this method becomes more applicable. Simulations will also be done with a known covariance matrix, demonstrating that the bootstrap method is an effective approach for estimating the out-of-sample Sharpe ratio. We then look at some extensions for the bootstrap method and finally we will apply the bootstrap method to stocks in the Dutch and American stock markets, showing that the in-sample Sharpe ratio is often overly optimistic compared to the out-of-sample Sharpe ratio. We reached our goal that we found an effective way to estimate the out-of-sample Sharpe ratio without the assumption that the covariance matrix is known, resulting this method becomes much more suitable for predicting the Sharpe ratio in the future.
1