Working Paper: NBER ID: w8922
Authors: Ravi Jagannathan; Tongshu Ma
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 covariance 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 nonnegativity constraint is imposed, minimum variance portfolios constructed using the monthly sample covariance matrix perform as well as those constructed using covariance matrices estimated using factor models, shrinkage estimators, and daily data. When minimizing tracking error is the criterion, using daily data instead of monthly data helps. However, the sample covariance matrix without any correction for microstructure effects performs the best.
Keywords: No keywords provided
JEL Codes: C49; G11; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Imposing nonnegativity constraints on portfolio weights (G11) | Reducing sampling error (C83) |
| Reducing sampling error (C83) | Improving efficiency of optimal portfolios (G11) |
| Imposing nonnegativity constraints on portfolio weights (G11) | Improving efficiency of optimal portfolios (G11) |
| Imposing nonnegativity constraints on portfolio weights (G11) | Mitigating effects of sampling error in estimation of covariances (C83) |
| Upper bounds on portfolio weights (C46) | Increasing sample covariances of corresponding assets (C10) |
| Increasing sample covariances of corresponding assets (C10) | Affecting performance of portfolios (G11) |
| Imposing nonnegativity constraints on portfolio weights (G11) | Performance improvement of minimum variance portfolios (G11) |