Optimal diversification in the presence of parameter uncertainty for a risk averse investor

Dubois, Mathieu S. and Veraart, Luitgard A. M. ORCID: 0000-0003-1183-2227 (2015) Optimal diversification in the presence of parameter uncertainty for a risk averse investor. SIAM Journal on Financial Mathematics, 6 (1). pp. 201-241. ISSN 1945-497X

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Abstract

We consider an investor who faces parameter uncertainty in a continuoustime financial market. We model the investor's preference by a power utility function leading to constant relative risk aversion. We show that the loss in expected utility is large when using a simple plug-in strategy for unknown parameters. We also provide theoretical results that show the trade-off between holding a well-diversified portfolio and a portfolio that is robust against estimation errors. To reduce the effect of estimation, we constrain the weights of the risky assets with an L1-norm leading to a sparse portfolio. We provide analytical results that show how the sparsity of the constrained portfolio depends on the coefficient of relative risk aversion. Based on a simulation study, we demonstrate the existence and the uniqueness of an optimal bound on the L1-norm for each level of relative risk aversion.

Item Type:	Article
Official URL:	http://epubs.siam.org/loi/sjfmbj
Additional Information:	© 2015 Society for Industrial and Applied Mathematics
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	20 Feb 2015 15:05
Last Modified:	07 Jan 2024 04:18
Funders:	Jones / Markham scholarship, Jones/Markham scholarship
URI:	http://eprints.lse.ac.uk/id/eprint/61024

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