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

47 Pages Posted: 17 Aug 2005  

Lorenzo Garlappi

University of British Columbia (UBC) - Sauder School of Business

Tan Wang

University of British Columbia (UBC) - Division of Finance; China Academy of Financial Research (CAFR)

Raman Uppal

EDHEC Business School; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 3 versions of this paper

Date Written: July 2005

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.

Keywords: Portfolio choice, asset allocation, estimation error, uncertainty, ambiguity, robustness

JEL Classification: D81, G11

Suggested Citation

Garlappi, Lorenzo and Wang, Tan and Uppal , Raman, Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach (July 2005). CEPR Discussion Paper No. 5148. Available at SSRN: https://ssrn.com/abstract=774207

Lorenzo Garlappi

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

Tan Wang

University of British Columbia (UBC) - Division of Finance ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-822-9414 (Phone)
604-822-8521 (Fax)

China Academy of Financial Research (CAFR)

1954 Huashan Road
Shanghai P.R.China, 200030
China

Raman Uppal (Contact Author)

EDHEC Business School ( email )

58 rue du Port
Lille, 59046
France

Centre for Economic Policy Research (CEPR)

90-98 Goswell Road
London, EC1V 7RR
United Kingdom

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