TY - JOUR
AU - Jagannathan,Ravi
AU - Ma,Tongshu
TI - Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps
JF - National Bureau of Economic Research Working Paper Series
VL - No. 8922
PY - 2002
Y2 - May 2002
DO - 10.3386/w8922
UR - http://www.nber.org/papers/w8922
L1 - http://www.nber.org/papers/w8922.pdf
N1 - Author contact info:
Ravi Jagannathan
Kellogg Graduate School of Management
Northwestern University
2001 Sheridan Road
Leverone/Anderson Complex
Evanston, IL 60208-2001
Tel: 847/491-8338
Fax: 847/491-5719
E-Mail: rjaganna@northwestern.edu
Tongshu Ma
SUNY-Binghamton
E-Mail: tma@binghamton.edu
AB - 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.
ER -