The efficient frontier for a portfolio that includes one risk-free asset

摘要

This paper presents a description of the efficient frontier of a portfolio composed by three assets, including a risk-free asset. We use a data analysis method to obtain two classes of assets and then we estimate the risk of each asset corresponding to each class. Thus, we get the best two assets among those considered risky for which we build the efficient frontier if we consider that the portfolio consists of these two risky assets and a risk-free asset. The originality of our study lies in the combination of classification theory with risk estimation theory to determine the best assets. To illustrate the effectiveness of the method used, we present a case study that refers to the domestic financial market. We construct the efficient frontier, based on the correlation of the best stocks that we have obtained through data analysis (for classification), and by assessing the loss distribution (for risk assessment), taking into account that the portfolio contains an asset without risk.