On the unbiased efficient frontier: some analytical and computational remarks

Abstract

One of the most important and influential economic theories dealing with finance and investment is Modern Portfolio Theory. MPT has its roots in the work developed by Markowitz, resumed by Merton, and then studied and revisited by many authors, which still try to deal with the weaknesses of the theory. Starting from the approach proposed by Bodnar and Bodnar, which tries to correct the bias witnessed in the classical formulation of the sample efficient frontier, the scope of this work will be that of analyzing whether the unbiased estimator of the efficient frontier respects the properties which have been attributed to it by Corazza and Pizzi, if it is operationally effective and if it is robust to small departures from the assumption of independence. In order to do this, we will make exploratory analysis on our dataset and we will construct the different frontiers and confidence intervals with the use of the programming language and statistical software R. We will also apply differential sensitivity analysis to formulate a new proposition related to the unbiased estimator proposed by Bodnar and Bodnar. What we obtain is that the model is able to correct the bias of the classical sample efficient frontier, but also that it is not robust when changes to the degree of independence are introduced.