Portfolio Selection with Estimation Risk: A Test-Based Approach

An important challenge of portfolio allocation arises when the (true) characteristics of returns' distribution are replaced by sample estimates. Such substitutions introduce estimation risk, which adds to traditional financial risk. I develop a new framework to provide a feasible optimal investment rule that accounts for estimation risk. In borrowing from practitioners, I evaluate funds' allocations through their probability of defeating a chosen benchmark. More precisely, the P-value investment rule maximizes the p-value of a one-sided test, ensuring that the portfolio performance is above the given threshold. When the portfolio performance is measured by the Markowitz mean--variance criterion and when the estimation risk of the variance is ignored, the optimal investment rule is known in closed form. The P-value investment rule is a two-fund rule when the benchmark is fixed and a three-fund rule when the benchmark is estimated. In addition, ten investment strategies are compared on simulated and empirical data. Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.