Asset Allocation with Aversion to Parameter Uncertainty: A Minimax Regression Approach
AbstractThis paper takes a minimax regression approach to incorporate aversion to parameter uncertainty into the mean-variance model. The uncertainty-averse minimax mean-variance portfolio is obtained by minimizing with respect to the unknown weights the upper bound of the usual quadratic risk function over a fuzzy ellipsoidal set. Beyond the existing approaches, our methodology offers three main advantages: first, the resulting optimal portfolio can be interpreted as a Bayesian mean-variance portfolio with the least favorable prior density, and this result allows for a comprehensive comparison with traditional uncertainty-neutral Bayesian mean-variance portfolios. Second, the minimax mean-variance portfolio has a shrinkage expression, but its performance does not necessarily lie within those of the two reference portfolios. Third, we provide closed form expressions for the standard errors of the minimax mean-variance portfolio weights and statistical significance of the optimal portfolio weights can be easily conducted. Empirical applications show that incorporating aversion to parameter uncertainty leads to more stable optimal portfolios that outperform traditional uncertainty-neutral Bayesian mean-variance portfolios.
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Bibliographic InfoPaper provided by University of Paris West - Nanterre la Défense, EconomiX in its series EconomiX Working Papers with number 2011-1.
Length: 32 pages
Date of creation: 2011
Date of revision:
Asset allocation; estimation error; aversion to uncertainty; min-imax regression; Bayesian mean-variance portfolios; least favorable prior;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-05 (All new papers)
- NEP-ECM-2011-02-05 (Econometrics)
- NEP-UPT-2011-02-05 (Utility Models & Prospect Theory)
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