Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization.

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out- of-sample Sharpe ratio using only in-sample data, based on random matrix theory. Furthermore, portfolio managers can use the estimated out-of-sample Sharpe as a criterion to decide the best tuning for constructing their portfolios. Specifically, we consider the classical framework of Markowits mean-variance portfolio optimization with known mean vector and the high dimensional regime of p/n -> c, where p is the portfolio dimension and n is the number of samples or time points. We propose to correct the sample covariance by a regularization matrix and provide a consistent estimator of its Sharpe ratio. The new estimator works well under either of three conditions: (1) bounded covariance spectrum, (2) arbitrary number of diverging spikes when c < 1, and (3) fixed number of diverging spikes when c >= 1. We can also extend the results to construct global minimum variance portfolio and correct out-of-sample efficient frontier.

Recommended citation: Xuran Meng, Yuan Cao and Weichen Wang, "Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization." arxiv: 2406.03954, 2024.
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