Construction of Optimal Portfolio Using Sharpe’s Single Index Model and Markowitz Model

Author(s)

Subhodeep Chakraborty and Ajay Kumar Patel

Affiliations

1. PGDM Candidate, GL Bajaj Institute of Management and Research, Greater Noida
2. Assistant Professor, GL Bajaj Institute of Management and Research, Greater Noida

Abstract

The main focus of this research is to construct an optimal portfolio in Indian Market with the help of Sharpe Single index model. The construction of an optimal portfolio has become increasing challenging in recent years, as investors expect to maximize return and minimize risk from their respective investment therefor a good combination of portfolio will give maximum return for a particular level of risk. An investor need to have proper knowledge of security analysis and portfolio theory for making corrective investment decision. In 1950, Markowitz who was considered the father of modern portfolio theory, mainly because he is the first person who gave a mathematical model for portfolio optimization and diversification. Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of risk, or minimize the risk for a given level of expected return. Markowitz theory advise investors to invest in multiple securities rather than pulling all eggs in one basket. In order to overcome the Markowitz Model, William Sharpe, tried to simplify the process of data inputs and reaching a solution, by developing a simplified variant of the Markowitz model. In the Sharpe’s model, the desirability of any securities inclusion in the portfolio is directly related to its excess return- to-beta ratio. 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. Then they are ranked from highest to lowest order and then the Percentage of investment in each of the selected security is then decided on the basis of respective weights assigned to each security. In this research, all 50 stocks of NSE NIFTY 50 Index are taken into consideration and & Weekly data of all these stock for the period of September 14,2016 to September 15.2017 have been considered which further converted into annually. Further the proportion of investment of each 50 stock in the optimal portfolio was also calculated and along with risk and return of the selected stock are also been calculated with the help of Markowitz Model This study gains more importance as stocks included in Nifty 50 represent majority of market capitalisation of NSE. The Nifty 50 hold about 62.9% of the market capitalization of the stocks listed on NSE.

Keywords

Markowitz Theory, Sharpe’s Single Index Model, Optimal Portfolio, Cut Off Rate, Excess Return-to-Beta Ratio, Percentage of Investment, NSE NIFTY 50 Index, Market Capitalization.

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