Portfolio management with semi-parametric bootstrapping

Abstract

Estimation risk is an important topic within the area of risk management. Uncertanties on the parameter estimates carry on to the ¯nal statistical product, for example to the investment strategies, and need to be estimated and accounted for. Unless the exact expressions for the estimators' variances are known, the product's variability will be assessed through bootstrap techniques. We address this issue in this paper and propose a semiparametric bootstrap method for reproducing the data, a method which parametrically takes care of all marginal characteristics of the returns data, and also takes care of the dependence structure existing in the data in a very simple and clever non-parametric way. The technique is applied to the problem of assessing variability of the Markowitz e±cient frontier. Simulation experiments are conducted to assess the out-of-sample forecasting usefulness of the semi-parametric bootstrap methodology.