Asset selection based on high frequency Sharpe ratio

Abstract

In portfolio choice problems, the classical Mean–Variance model in Markowitz (1952) relies heavily on the covariance structure among assets. As the number and types of assets increase rapidly, traditional methods to estimate the covariance matrix and its inverse suffer from the common issues in high or ultra-high dimensional analysis. To avoid the issue of estimating the covariance matrix with high or ultra-high dimensional data, we propose a fast procedure to reduce dimension based on a new risk/return measure constructed from intra-day high frequency data and select assets via Dependent Sure Explained Variability and Independence Screening (D-SEVIS). While most feature screening methods assume i.i.d. samples, by nature of our data, we make contribution to studying D-SEVIS for samples with serial correlation, specifically, for the stationary α-mixing processes. Under α-mixing condition, we prove that D-SEVIS satisfies sure screening property and ranking consistency property. More importantly, with the assets selected through D-SEVIS, we will build a portfolio that earns more excess return compared with several existing portfolio allocation methods. We illustrate this advantage of our asset selection method with the real data from the stock market.