A1069
Title: Estimation of out-of-sample Sharpe ratio for high dimensional portfolio optimization
Authors: Weichen Wang - The University of Hong Kong (Hong Kong) [presenting]
Xuran Meng - The University of Hong Kong (Hong Kong)
Yuan Cao - The University of Hong Kong (Hong Kong)
Abstract: Portfolio optimization aims at achieving a portfolio with good out-of-sample performance, 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 high-dimensional settings. A novel method is proposed to estimate the out-of-sample Sharpe ratio using only in-sample data based on random matrix theory. Specifically, the classical framework of Markowitz mean-variance optimization is considered with a known mean vector under the high dimensional regime of $p/n$ goes to $c > 0$, where $p$ is the portfolio dimension and $n$ is the number of samples or time points. Correcting the sample covariance is proposed by a regularization matrix, and a consistent Sharpe ratio estimator is provided. The new estimator works well under either of the three conditions: (1) bounded covariance spectrum, (2) arbitrary number of diverging spikes when $c < 1$, and (3) fixed number of diverging spikes when $c \ge 1$. The results can be extended to the global minimum variance portfolio and the construction of the out-of-sample efficient frontier. The effectiveness of the approach is demonstrated through numerical experiments and real data. Results highlight the potential of the new methodology as a powerful tool for portfolio managers to estimate the out-of-sample Sharpe and to decide the optimal parameter to construct their portfolios.
