Optimal Diversification in the Presence of Parameter Uncertainty for a Risk Averse Investor
41 Pages Posted: 6 Aug 2014 Last revised: 18 Apr 2015
Date Written: August 4, 2014
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
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