Abstract
Portfolio weights solely based on risk avoid estimation errors from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation, and the Exponential Weighted Moving Average target matrices. Using an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance (MV), Inverse Volatility (IV), Equal-Risk-Contribution (ERC), and Maximum Diversification (MD) portfolios. We find out that the Identity and Variance Identity have very good statistical properties, also being well conditioned in high-dimensional datasets. In addition, these two models are the best target towards which to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps to reduce weight misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification and so benefit less from shrinkage.
Highlights
The seminal contributions of Markowitz (1952, 1956) laid the foundations for his well-known portfolio building technique
Each column corresponds to a specific target matrix: from left to right, the Identity (Id): blue circle-shaped; the Variance Identity (VId): green square-shaped; the Single-Index (SI):blue red circle-shaped; the Variance
Each column corresponds to a specific target matrix: from left to right, the Identity (Id), the Variance Identity (VId), corresponds to a specific target matrix: from left to right, the Identity (Id), the Variance Identity (VId), the Single-Index (SI), the Common Covariance (CV), the Constant Correlation (CC), and the EWMA, the Single-Index (SI), the Common Covariance (CV), the Constant Correlation (CC), and the EWMA, respectively
Summary
The seminal contributions of Markowitz (1952, 1956) laid the foundations for his well-known portfolio building technique. There is a large consensus on the fact that sample estimators perpetuate large estimation errors; this directly affects portfolio weights that often exhibit extreme values, fluctuating over time with very poor performance out-of-sample (De Miguel et al 2009) This problem has been tackled from different perspectives: Jorion (1986) and Michaud (1989). Chopra and Ziemba (1993), who clearly demonstrated how the mean estimation process can lead to more severe distortions than those in the case of the covariance matrix Following this perspective, estimation error can be reduced by considering risk-based portfolios: findings suggest they have good out-of-sample performance without much turnover (De Miguel et al 2009). Qian (2006) designed a way to select assets
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