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Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach

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Author Info
Garlappi, Lorenzo
Uppal, Raman
Wang, Tan
Abstract

In this paper, we show how an investor can incorporate uncertainty about expected returns when choosing a mean-variance optimal portfolio. In contrast to the Bayesian approach to estimation error, where there is only a single prior and the investor is neutral to uncertainty, we consider the case where the investor has multiple priors and is averse to uncertainty. We characterize the multiple priors with a confidence interval around the estimated value of expected returns and we model aversion to uncertainty via a minimization over the set of priors. The multi-prior model has several attractive features: One, just like the Bayesian model, it is firmly grounded in decision theory. Two, it is flexible enough to allow for different degrees of uncertainty about expected returns for different subsets of assets, and also about the underlying asset-pricing model generating returns. Three, for several formulations of the multi-prior model we obtain closed-form expressions for the optimal portfolio, and in one special case we prove that the portfolio from the multi-prior model is equivalent to a ‘shrinkage’ portfolio based on the mean-variance and minimum-variance portfolios, which allows for a transparent comparison with Bayesian portfolios. Finally, we illustrate how to implement the multi-prior model for a fund manager allocating wealth across eight international equity indices; our empirical analysis suggests that allowing for parameter and model uncertainty reduces the fluctuation of portfolio weights over time and improves the out-of sample performance relative to the mean-variance and Bayesian models.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5041.

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Date of creation: May 2005
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Handle: RePEc:cpr:ceprdp:5041

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Related research
Keywords: ambiguity; asset allocation; estimation error; portfolio choice; robustness; uncertainty;

Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

This paper has been announced in the following NEP Reports:

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  1. Bryan R. Routledge & Stanley E. Zin, 2001. "Model Uncertainty and Liquidity," NBER Working Papers 8683, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 293-305, September. [Downloadable!]
  3. Larry Epstein & Martin Schneider, 2006. "Learning Under Ambiguity," RCER Working Papers 527, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
    Other versions:
  4. Larry G. Epstein & JianJun Miao, 2001. "A Two-Person Dynamic Equilibrium under Ambiguity," RCER Working Papers 478, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
    Other versions:
  5. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
  7. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
    Other versions:
  8. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December. [Downloadable!] (restricted)
  9. Hansen, Lars Peter & Sargent, Thomas J & Tallarini, Thomas D, Jr, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Blackwell Publishing, vol. 66(4), pages 873-907, October. [Downloadable!] (restricted)
    Other versions:
  10. 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. [Downloadable!] (restricted)
  11. Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 18(2), pages 673-705. [Downloadable!] (restricted)
  12. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February. [Downloadable!] (restricted)
  13. Alan Greenspan, 2004. "Risk and Uncertainty in Monetary Policy," American Economic Review, American Economic Association, vol. 94(2), pages 33-40, May. [Downloadable!]
  14. Robert F. Stambaugh, 1997. "Analyzing Investments Whose Histories Differ in Length," NBER Working Papers 5918, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  15. Marco Cagetti & Lars Peter Hansen & Thomas Sargent & Noah Williams, 2002. "Robustness and Pricing with Uncertain Growth," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(2), pages 363-404, March.
  16. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(01), pages 40-84, February. [Downloadable!]
  17. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December. [Downloadable!] (restricted)
    Other versions:
  18. 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. [Downloadable!] (restricted)
    Other versions:
  19. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July. [Downloadable!] (restricted)
    Other versions:
  20. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(5), pages 937-74.
  21. Heath, Chip & Tversky, Amos, 1991. " Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
  22. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  24. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  25. Best, Michael J. & Grauer, Robert R., 1992. "Positively Weighted Minimum-Variance Portfolios and the Structure of Asset Expected Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(04), pages 513-537, December. [Downloadable!]
  26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  27. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December. [Downloadable!] (restricted)
    Other versions:
  28. Truman F. Bewley, 1988. "Knightian Decision Theory and Econometric Inference," Cowles Foundation Discussion Papers 868, Cowles Foundation, Yale University. [Downloadable!]
  29. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-22, May. [Downloadable!] (restricted)
  30. Pastor, Lubos & Stambaugh, Robert F., 2000. "Comparing asset pricing models: an investment perspective," Journal of Financial Economics, Elsevier, vol. 56(3), pages 335-381, June. [Downloadable!] (restricted)
    Other versions:
  31. repec:cup:macdyn:v:6:y:2002:i:1:p:40-84 is not listed on IDEAS
  32. Fox, Craig R & Tversky, Amos, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 585-603, August. [Downloadable!] (restricted)
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