A0436
Title: Estimation of out-of-sample Sharpe ratio for high dimensional portfolio optimization
Authors: Xuran Meng - The University of Hong Kong (Hong Kong)
Yuan Cao - The University of Hong Kong (Hong Kong)
Weichen Wang - The University of Hong Kong (Hong Kong) [presenting]
Abstract: 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. A novel method is proposed 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, the classical framework of Markowitz mean-variance portfolio optimization is considered under the high-dimensional regime of $p/n \to c \in (0, \infty)$, where $p$ is the portfolio dimension and $n$ is the number of samples or time points. It is proposed 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 the following conditions: (1) bounded covariance spectrum, (2) arbitrary number of diverging spikes when $c < 1$, and (3) fixed number of diverging spikes with weak requirement on their diverging speed when $c \ge 1$. The results can also be extended to construct a global minimum variance portfolio and correct out-of-sample efficient frontier. The effectiveness of the approach is demonstrated through comprehensive simulations and real data experiments.
