Evaluating Various Portfolio Optimization Strategies using High-Dimensional Covariance Matrix Estimators

Abstract

We compare the performance of multiple covariance matrix estimators for the purpose of portfolio optimization. This evaluation studies the ability of estimators like Sample Based Estimator (SCE), Ledoit-Wolf Estimator (LWE), and Rotationally Invariant Estimators (RIE) to estimate covariance matrix and their competency in fulfilling the objectives of various portfolio allocation strategies. In this paper, we have captured the effectiveness of strategies such as Global Minimum Variance (GMVP) and Most-Diversified Portfolio (MDP) to produce optimal portfolios. Additionally, we also propose a new strategy inspired from MDP: Most-Diversified Portfolio (MMDP), that enables diversification upon minimizing risk. Empirical evaluations show that by and large, MMDP furnishes the maximum returns. LWE are relatively more robust than SCE and RIE but RIE performs better under certain conditions.