Research

Abstract: We propose MAXSER-H, a novel method for estimating large mean-variance efficient portfolios when dealing with asset returns that exhibit heteroscedasticity and heavy-tailedness. The approach integrates robust regressions and a self-normalization technique with the  MAXSER method proposed in Ao, Li, and Zheng (2019). We prove that as the number of assets and sample size grow, the MAXSER-H portfolio asymptotically maximizes expected return while adhering to the specified risk constraint. A conditional method, MAXSER-H-TV, is further developed to account for time-varying parameters, improving upon the original unconditional method. Extensive simulations and empirical studies confirm the superior performance of both MAXSER-H and MAXSER-H-TV.

Abstract: This paper addresses the challenge of estimating the efficient frontier when portfolios comprise only risky assets—a critical task in markets where risk-free assets are unavailable or for institutions with restrictive mandates. We introduce CORE (COnstrained sparse Regression for Efficient portfolios), a novel method for estimating large mean-variance efficient portfolios that collectively form an estimated risky efficient frontier. We develop two versions of CORE, one for the scenario that does not involve long-short factors, and the other for the scenario that does. Under a high-dimensional setting where both the number of assets and the sample size approach infinity, we establish the asymptotic mean-variance efficiency of CORE portfolios. We show in extensive simulations and empirical studies how collectively CORE portfolios form the efficient hyperbola where various risk constraints are respected while high Sharpe ratios are achieved.