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Abstract
We propose a novel methodology for constructing optimal portfolios in the presence of (i) model parameter uncertainty and (ii) user-specified constraints on the portfolio weights. This is a challenging problem, in large part because the constraint conditions generally preclude the derivation of closed-form solutions even in the absence of parameter uncertainty. Yet, in this article, we succeed in producing a practical solution, which is based on a herein proposed technique that we call a “perturbation method.” The method relies on a specially devised resampling procedure, whose performance is shown in simulations to compare favorably to other methods from the literature on portfolio optimization.
Acknowledgments
Our special thanks are due to Professor Sat Gupta and the participants of the International Conference on “Advances in Interdisciplinary Statistics and Combinatorics” for making such an inspiring atmosphere in the fall of 2012 at the University of North Carolina at Greensboro, where the current project had taken pivotal steps toward its fruition.
We are indebted to two anonymous referees for their constructive criticism, queries, and suggestions that guided our work on the revision of this article.
Funding
The second author thanks the Department of Economics, Vanderbilt University, for hospitality and the Grey fund for financial support during his research visit at the department. The research was also supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.