This study attempts to construct an optimal portfolio by using Sharpe's Single index model. For this purpose NSE, NIFTY and all the 25 stocks have been used as market index for preparing portfolio. The daily data for all the stocks and index for the period of 2015 to December 2021 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 selected stocks is then decided on the basis of respective weights assigned to each stock depending on respective beta value, stock movement variance unsystematic risk, return on stock and risk free return visa- vis the cut off rate of return. The optimal portfolio consists of four stocks selected out of 25 short listed scripts. Investment in stocks may be made individually or through portfolio managers. This study attempts at selecting an optimal portfolio for investment in Indian equity stocks belonging to specific economic sectors. After reviewing the relevant literature, the objectives and research methodology of the study have been spelt out. This is followed by a coverage of the concepts and definitions which are relevant for this study. A comparison of the different approaches to select an optimum portfolio has been made to get an overview of the relative measures. In this paper, an optimum portfolio of economic sectors in India, in which the investments could be made, has been constructed, using Sharpe's index model and Treynor's index as appropriate. The choice of individual stocks within each the selected sectors could be done by the individuals or portfolio managers based on any subsequent analysis which generally aims at accrual of higher returns, given a risk level.