Construction and Evaluation of Optimal Portfolio Using Sharpe'S Single Index Model

Abstract

This paper attempts to construct an optimal portfolio by using Sharpe's Single Index Model of Capital Asset Pricing and farther to evaluate the performance of the portfolio by Sharpe's Ratio, Treynor's Ratio and Jenson Alpha. For this purpose, BSE SENSEX and all the 30 scrips which are part of it have been used as market index for preparing portfolio. The monthly data for all the scrips and index for the period April 2006-March 2011 have been considered. The proposed method formulates a unique cut off point (Cut off rate of return) and selects stocks having excess of their expected return over risk-free rate of return surpassing this cut-off point. Percentage of investment in each of the selected stocks is then decided on tlte basis of respective weights assigned to each stock depending on respective beta value, stock movement variance representing unsysternatic risk, return on stock and risk free return vis-a-vis the cut off rate of return. As per our findings, our optimal portfolio consists of seven scripts, selected out of 26 short listed scripts, giving the return of 46.54% with the portfolio standard deviation of 15.2%. The Sharpe ratio, Trynor's ratio and Jenson alpha for the same optimal portfolio is 2.63, 0.38 and 0.28 respectively.