Research on Improving Markowitz Portfolio Optimization

Chen-Yan Luo

Abstract

This study is focused on how mean, covariance shrinkage and regularization methods works within Markowitz Portfolio Optimization based on a micro asset pool, in which return dispersion can be extreme and one or two winners can dominate the cross-section. The analysis proceeds in two stages. Firstly, this study is focused on how to make the estimation of mean and covariance matrix more accurately, including historical estimates, James-Stein mean shrinkage, Ledoit-Wolf covariance shrinkage, joint shrinkage, confidence-bound robust means, and Michaud resampling are compared over risk-aversion coefficients of 2, 3, and 5 and estimation windows of 1, 2, and 5 years. Secondly, based on estimation window of 1 year with risk-aversion coefficients of 2, this study introduced different regularization methods including higher moments, an L2 weight penalty, a 25% position cap, a turnover penalty, and short selling with gross exposure limited to 1.5. Every test includes an equal position sizing portfolio and S&P 500 ETF as baselines. Furthermore, to avoid the bias of asset choosing manually, this study made 500 resampled asset pool with 7 stocks from a 36-stock historical Dow Jones constituent union. The result shows that Ledoit-Wolf shrinkage increases little in performance in the chosen asset pool while 25% position cap attains the highest median Sharpe ratio, 0.724, and exceeds the 1/N Sharpe ratio in 70.0% of samples across random pools, which indicates that model complexity is not uniformly valuable in a micro-universe: a method improves performance only when its reduction in estimation error exceeds the cost of suppressing informative cross-sectional signals.

Source: semanticscholar

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