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

Thomas M. Menino Convention & Exhibition Center 

Out-of-sample Sharpe ratio is a key metric for portfolio optimization, but in high-dimensional problems naive plug-in evaluation using the sample covariance is inconsistent. We develop an estimator of the out-of-sample Sharpe ratio using only in-sample observations based on random matrix theory. In the Markowitz mean–variance framework with p/n→c∈(0,∞), 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 the following conditions: (a) bounded covariance spectrum, (b) arbitrary number of diverging spikes when c<1 and (c) fixed number of diverging spikes with weak requirement on their diverging speed when c≥1. We can also extend the results to construct global minimum variance portfolio and correct out-of-sample efficient frontier. We demonstrate the effectiveness of our approach through comprehensive simulations and real data experiments. Our results highlight the potential of this methodology as a useful tool for portfolio optimization in high dimensional settings.

Efficient frontier recovery

High dimensionality

Portfolio allocation

Ridge regularization

Spiked covariance structure 

IMS