Risk Reduction in Large Portfolios: A Role for Portfolio Weight Constraints
43 Pages Posted: 10 Dec 2001
Date Written: January 7, 2002
Abstract
Mean-variance efficient portfolios constructed using sample moments often involve taking extreme long and short positions. Hence practitioners often impose portfolio weight constraints when constructing efficient portfolios. Green and Hollifield (1992) argue that the presence of a single dominant factor in the covariance matrix of returns is why we observe extreme positive and negative weights. If this were the case then imposing the weight constraint should hurt whereas the empirical evidence is often to the contrary. We reconcile this apparent contradiction. We show that constraining portfolio weights to be nonnegative is equivalent to using the sample co-variance matrix after reducing its large elements and then form the optimal portfolio without any restrictions on portfolio weights. This shrinkage helps reduce the risk in estimated optimal portfolios even when they have negative weights in the population. Surprisingly, we also find that once the non-negativity constraint is imposed, minimum variance and minimum tracking error portfolios constructed using the sample covariance matrix perform as well as those constructed using covariance matrices estimated using factor models and shrinkage estimators.
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Portfolio Selection and Asset Pricing Models
By Lubos Pastor
-
A Test for the Number of Factors in an Approximate Factor Model
-
Comparing Asset Pricing Models: an Investment Perspective
By Lubos Pastor and Robert F. Stambaugh
-
Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps
By Tongshu Ma and Ravi Jagannathan
-
On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model
By Louis K.c. Chan, Jason J. Karceski, ...
-
Honey, I Shrunk the Sample Covariance Matrix
By Olivier Ledoit and Michael Wolf
-
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
By Lorenzo Garlappi, Tan Wang, ...
-
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
By Lorenzo Garlappi, Tan Wang, ...
-
Portfolio Constraints and the Fundamental Law of Active Management