Portfolio Selection using Best Beta

Abstract

An investor, who will make decision on investing his capital, usually considers a model. This model is called Capital Assets Pricing Model (CAPM). This model explains how an investor can calculate his expected returns. The CAPM gives prediction about relationship between risk and expected returns. The CAPM has beta parameter which refers to a measure of risk. By incorporating a target variable into the investor preferences, a best-beta CAPM (BCAPM) can be derived. BCAPM maintains the CAPM’s theoretical properties and analytical simplicity, yet unambiguously improves its pricing accuracy. By calibrating the US historical data to the model, it is found that the BCAPM typically improves the pricing accuracy of the CAPM by 20% to 30% annualy. Both the CAPM and the BCAPM predict a linear relation between assets’ risk premiums and beta. The aim of this study is to derive a simple variation of the CAPM, which called BCAPM. In both models there are possibly pricing errors. Alpha is defined as pricing errors between the true expected returns and predicted expected returns. This model gives a relationship between alpha on CAPM and alpha on BCAPM. If there are pricing errors, this model shows that alpha on BCAPM is smaller than alpha on CAPM for all assets.