Research

Abstract: We propose a novel method for estimating mean-variance efficient portfolios in the presence of heteroscedasticity and heavy-tailedness in asset returns. We utilize robust regressions and a self-normalization technique to address the challenges posed by heteroscedasticity and heavy-tailedness, and construct our portfolio by integrating these elements with MAXSER, an estimation method for mean-variance optimal portfolio with sparse regression, proposed in Ao et al. (2019). We call our method \emph{MAXSER for heteroscedastic returns} (MAXSER-H). Under mild assumptions, we prove that the MAXSER-H portfolio asymptotically achieves the maximum expected return while satisfying the risk constraint. As part of our proofs, we establish the consistency of Huber regression under elliptical factor model, which can be of considerable interest to the broader statistical community. We further develop an estimator of the optimal \emph{conditional} portfolio to account for time-varying parameters, which we call MAXSER-H-TV. Through extensive simulation and empirical studies, we demonstrate both the statistical and economic significance of MAXSER-H and MAXSER-H-TV. Empirical results show that MAXSER-H-TV delivers a higher Sharpe ratio than MAXSER-H before transaction costs, while the advantage vanishes when fees are considered.

Abstract: This paper introduces a method named CORE (COnstrained sparse Regression for Efficient portfolios), designed to estimate large mean-variance efficient portfolios consisting of only risky assets. These portfolios collectively form an estimated efficient frontier. Our method relies on a novel linear constrained regression representation of the mean-variance optimization problem. We establish the CORE portfolio's asymptotic mean-variance efficiency under a high dimensional setting where both the number of assets and the sample size can go to infinity. We also consider a scenario where factors involve long-short portfolios and develop CORE-LS (CORE for Long-Short factors) to estimate the efficient portfolios in this scenario. Extensive simulation and empirical studies demonstrate the favorable performance of our proposed method.