Parameter Uncertainty in Asset Allocation

This article reviews the simulation competition and the set of utility functions with the equivalent resampled efficient frontier approach and also discusses the modification of the specification of the Bayesian investor. The Bayes investor finds the weights, which maximize the expected utility with respect to the predictive moments for each history, while the Michaud investor finds the weights using the resampling scheme. The Bayes investor uses a utility function based on predictive returns and the Michaud investor uses a utility function based on parameter estimates. The Markov Chain Monte Carlo (MCMC) algorithm generates samples from the predictive density and uses the draws to approximate the expected utility integral. The Importance Sampling scheme generates draws from an alternative density and reweights these draws in order to approximate the integral with respect to the predictive density. An important difference between the implementation of the MCMC algorithm and the implementation of the Importance Sampler has to do with the number of samples that are used. The resampling approach maximizes and then averages instead of maximizing an average. There are three components that are considered for both the approaches that include the generation of random parameters, the optimization framework used to determine an optimal set of investment weights, and the investment scenario used to determine how well the resulting weights perform.