Risk Reduction in Large Portfolios: A Role for Portfolio Weight Constraints

43 Pages Posted: 10 Dec 2001

See all articles by Tongshu Ma

Tongshu Ma

Binghamton University

Ravi Jagannathan

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF); Indian School of Business (ISB), Hyderabad

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

Ma, Tongshu and Jagannathan, Ravi, Risk Reduction in Large Portfolios: A Role for Portfolio Weight Constraints (January 7, 2002). AFA 2002 Atlanta Meetings. Available at SSRN: https://ssrn.com/abstract=293579 or http://dx.doi.org/10.2139/ssrn.293579

Tongshu Ma

Binghamton University ( email )

PO Box 6001
Binghamton, NY 13902-6000
United States

Ravi Jagannathan (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
429 Andersen Hall
Evanston, IL 60208
United States
847-491-8338 (Phone)
847-491-5719 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF) ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

Indian School of Business (ISB), Hyderabad ( email )

Hyderabad, Gachibowli 500 019
India

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