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

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  • Lorenzo Garlappi
  • Raman Uppal
  • Tan Wang

Abstract

We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive features: (1) it has a solid axiomatic foundation; (2) it is flexible enough to allow for different degrees of uncertainty about expected returns for various subsets of assets and also about the return-generating model; and (3) it delivers closed-form expressions for the optimal portfolio. Our empirical analysis suggests that, compared with portfolios from classical and Bayesian models, ambiguity-averse portfolios are more stable over time and deliver a higher out-of sample Sharpe ratio. (JEL G11) Copyright 2007, Oxford University Press.

Suggested Citation

  • Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    • Handle: RePEc:oup:rfinst:v:20:y:2007:i:1:p:41-81
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    1. Pascal J. Maenhout, 2002. "Discussion of "Robustness and Pricing with Uncertain Growth"," The Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 405-412, March.
    2. Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 673-705.
    3. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February.
    4. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    5. Marco Cagetti & Lars Peter Hansen & Thomas Sargent & Noah Williams, 2002. "Robustness and Pricing with Uncertain Growth," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 363-404, March.
    6. 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.
    7. 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.
    8. 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 1651-1683, August.
    9. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-522, May.
    10. Stambaugh, Robert F., 1997. "Analyzing investments whose histories differ in length," Journal of Financial Economics, Elsevier, vol. 45(3), pages 285-331, September.
    11. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    12. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    13. repec:cup:macdyn:v:6:y:2002:i:1:p:40-84 is not listed on IDEAS
    14. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    15. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    16. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    17. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    18. 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.
    19. 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.
    20. Bryan Routledge & Stanley Zin, 2009. "Model Uncertainty and Liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 543-566, October.
    21. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    22. Truman F. Bewley, 1988. "Knightian Decision Theory and Econometric Inference," Cowles Foundation Discussion Papers 868, Cowles Foundation for Research in Economics, Yale University.
    23. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    24. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-278, July.
    25. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    26. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    27. 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.
    28. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    29. Alan Greenspan, 2004. "Risk and Uncertainty in Monetary Policy," American Economic Review, American Economic Association, vol. 94(2), pages 33-40, May.
    30. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 40-84, February.
    31. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    32. 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(3), pages 293-305, September.
    33. 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, August.
    34. 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 937-974.
    35. 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.
    36. 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(4), pages 513-537, December.
    37. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    38. 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.
    39. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
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    More about this item

    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

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