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Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps

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  • 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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8922.

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Date of creation: May 2002
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Publication status: published as Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, 08.
Handle: RePEc:nbr:nberwo:8922

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  1. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
  2. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  3. Elton, Edwin J & Gruber, Martin J, 1973. "Estimating the Dependence Structure of Share Prices-Implications for Portfolio Selection," Journal of Finance, American Finance Association, vol. 28(5), pages 1203-32, December.
  4. Alexander, Gordon J., 1978. "A Reevaluation of Alternative Portfolio Selection Models Applied to Common Stocks," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(01), pages 71-78, March.
  5. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
  6. A. Craig MacKinlay & Lubos Pastor, . "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," Rodney L. White Center for Financial Research Working Papers 13-99, Wharton School Rodney L. White Center for Financial Research.
  7. Elton, Edwin J & Gruber, Martin J & Urich, Thomas J, 1978. "Are Betas Best?," Journal of Finance, American Finance Association, vol. 33(5), pages 1375-84, December.
  8. Elton, Edwin J & Gruber, Martin J, 1977. "Risk Reduction and Portfolio Size: An Analytical Solution," The Journal of Business, University of Chicago Press, vol. 50(4), pages 415-37, October.
  9. Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-91, September.
  10. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July.
  11. Gregory Connor and Robert Korajczyk., 1987. "Risk and Return in an Equilibrium APT," Research Program in Finance Working Papers 174, University of California at Berkeley.
  12. Cohen, Kalman J. & Hawawini, Gabriel A. & Maier, Steven F. & Schwartz, Robert A. & Whitcomb, David K., 1983. "Friction in the trading process and the estimation of systematic risk," Journal of Financial Economics, Elsevier, vol. 12(2), pages 263-278, August.
  13. Kalman J. Cohen & Jerry A. Pogue, 1967. "An Empirical Evaluation of Alternative Portfolio-Selection Models," The Journal of Business, University of Chicago Press, vol. 40, pages 166.
  14. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
  15. Ron Bird & Mark Tippett, 1986. "Note---Naive Diversification and Portfolio Risk---A Note," Management Science, INFORMS, vol. 32(2), pages 244-251, February.
  16. Bloomfield, Ted & Leftwich, Richard & Long, John Jr., 1977. "Portfolio strategies and performance," Journal of Financial Economics, Elsevier, vol. 5(2), pages 201-218, November.
  17. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
  18. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 353-363, September.
  19. Wallingford, Buckner A., 1967. "A Survey and Comparison of Portfolio Selection Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 85-106, June.
  20. Jorion, Philippe, 1991. "Bayesian and CAPM estimators of the means: Implications for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 15(3), pages 717-727, June.
  21. Shanken, Jay, 1987. " Nonsynchronous Data and the Covariance-Factor Structure of Returns," Journal of Finance, American Finance Association, vol. 42(2), pages 221-31, June.
  22. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-74.
  23. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
  24. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
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