Bootstrap estimation of the efficient frontier

In this paper, we propose a bootstrap resampling methodology to obtain the confidence intervals for efficient portfolios weights and the sample characteristics of the mean-variance efficient frontier. We provide an estimate of efficient portfolios, compute the confidence region of the efficient frontier and get the prediction densities of the future efficient portfolio returns without distributional assumptions on returns. An extensive simulation study evaluates the finite-sample performance of these bootstrap intervals and stresses the advantages of such approach. Interestingly, the methodology can be easily modified to make inferences that incorporate our modelling of returns in the predictive efficient frontier estimation with or without additional managerial restrictions.