Construction of an Optimal Portfolio Using the Single Index Model : An Empirical Study of Nifty50 Stocks

Abstract

It is Markowitz who introduced for the first time the modern portfolio theory which considers both risk and return for the selection of stocks required for an optimal portfolio. The Markowitz model is highly information intensive, conceptually very sound, and theoretically very elegant. However, it has serious practical limitations due to complexities involved in compiling the expected return, standard deviation, variance, and covariance. William Sharpe developed a model known as the Single Index Model, which is an extension of the model given by Markowitz. It is the simplest and the most widely used one. He simplified the amount and type of input data required in the selection of stocks for the portfolio construction. The model expresses the return on each stock as a function of the return on a broad market index to which the stocks are related. The current study was undertaken to construct an optimal portfolio using the Single Index Model for a sample of 50 stocks included in the NSE Nifty and the Nifty50 as the benchmark index. For the construction of the portfolio, average of daily opening and closing prices of the Nifty50 stocks and Nifty50 index were used for a 4 year period from 1/4/2014-31/3/2019; 364 days monthly treasury bill rates of the financial year 2014–19 were used as risk free rate of return. Though as many as 50 stocks were considered for the current study, only few stocks (i.e. eight) were selected for the construction of an optimal portfolio as per the Single Index Model. The stocks selected belonged to consumer non-durables (three), consumer durable (one), finance (three), and agro-based sectors (one). The consumer non-durables and finance companies dominated for the selection of stocks followed by consumer durables.