Optimal Diversification in the Presence of Parameter Uncertainty for a Risk Averse Investor

41 Pages Posted: 6 Aug 2014 Last revised: 18 Apr 2015

See all articles by Mathieu Dubois

Mathieu Dubois

London School of Economics & Political Science (LSE)

Luitgard Anna Maria Veraart

London School of Economics & Political Science (LSE) - Department of Mathematics

Date Written: August 4, 2014

Abstract

We consider an investor who faces parameter uncertainty in a continuous-time 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.

Keywords: optimal investment, power-utility, parameter uncertainty, risk aversion, L1-norm constraint, sparse portfolio

JEL Classification: C00, C4, C61, G11, D81

Suggested Citation

Dubois, Mathieu and Veraart, Luitgard Anna Maria, Optimal Diversification in the Presence of Parameter Uncertainty for a Risk Averse Investor (August 4, 2014). Available at SSRN: https://ssrn.com/abstract=2476053 or http://dx.doi.org/10.2139/ssrn.2476053

Mathieu Dubois

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Luitgard Anna Maria Veraart (Contact Author)

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom

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