Portfolio Selection: A Statistical Learning Approach

Abstract

We propose a new portfolio optimization framework, partially egalitarian portfolio selection (PEPS). Inspired by the celebrated LASSO regression, we regularize the mean-variance portfolio optimization by adding two regularizing terms that essentially zero out portfolio weights of some of the assets in the portfolio and select and shrink the portfolio weights of the remaining assets towards the equal weights to hedge against parameter estimation risk. We solve our PEPS formulations by applying recent advances in mixed integer optimization that allow us to tackle large-scale portfolio problems. We also build a predictive regression model for expected return using two cross-sectional factors, the short-term reversal factor and the medium-term momentum factor, that are shown to be the more significant predictive factors among the hundreds of factors tested in the empirical finance literature. We then incorporate our predictive regression into PEPS by replacing the historical mean. We test our PEPS formulations against an array of classical portfolio optimization strategies on a number of datasets in the US equity markets. The PEPS portfolios enhanced with the predictive regression estimates of the expected stock returns exhibit the highest out-of-sample Sharpe ratios in all instances.