The paper aims at constructing an optimal portfolio by applying Sharpe’s single index model of capital asset pricing in different scenarios, one is ex ante stock price bubble scenario and stock price bubble and bubble burst is second scenario. Here we considered beginning of year 2010 as rise of stock price bubble in Dhaka Stock Exchange. Hence period from 2005 -2009 is considered as ex ante stock price bubble period. Using DSI (All share price index in Dhaka Stock Exchange) as market index and considering daily indices for the March 2005 to December 2009 period, 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. Here, risk free rate considered to be 8.5% per annum (Treasury bill rate in 2009). Percentage of an investment in each of the selected stocks is then decided on the basis of respective weights assigned to each stock depending on respective ‘β’ value, stock movement variance representing unsystematic risk, return on stock and risk free return vis-à-vis the cut off rate of return. Interestingly, most of the stocks selected turned out to be bank stocks. Again we went for single index model applied to same stocks those made to the optimum portfolio in ex ante stock price bubble scenario considering data for the period of January 2010 to June 2012. We found that all stocks failed to make the pass Single Index Model criteria i.e. excess return over beta must be higher than the risk free rate. Here for the period of 2010 to 2012, the risk free rate considered to be 11.5 % per annum (Treasury bill rate during 2012).