Some critical insights on the unbiased efficient frontier à la Bodnar&Bodnar

In a couple of recent papers, Bodnar and Bodnar have tackled the estimation problem of the efficient frontier of a risky asset portfolio. The authors prove that the sample estimator of such a frontier is biased and provide, under proper but questionable hypotheses, an analytical expression for its unbiased estimator. In this contribution, first, we study the behavior of the unbiased estimator of the efficient frontier when the length of the return time series tends to infinity, then, we investigate a “strange” behavior of the unbiased estimator in correspondence of particular combinations of the means of the returns of the assets and of their variances and covariances with respect to the number of the assets and the length of the associated time series of returns; finally, we analyze the operational effectiveness of the proposed unbiased estimator by a bootstrap-based approach.