In a couple of recent papers of O. Bodnar and T. Bodnar on the estimation of the efficient frontier of a portfolio of risky assets ([1, 2]), 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. Furthermore, they highlight that the sample estimator of the efficient frontier is overoptimistic, in the sense that the latter systematically underestimates the variance of each efficient portfolio. 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 same unbiased estimator in correspondence of particular combinations of the means of the returns of the assets and of their variance-covariance matrix 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.
Marco Corazza (Corresponding)
|Titolo:||Some critical insights on the unbiased efficient frontier à la Bodnar&Bodnar|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||3.1 Articolo su libro|
File in questo prodotto:
|Corazza_Pizzi_MAF2018.pdf||Documento in Post-print||Accesso chiuso-personale||Riservato|