Optimal Portfolio Selection in Ex Ante Stock Price Bubble and Furthermore Bubble Burst Scenario from Dhaka Stock Exchange with Relevance to Sharpe’s Single Index Model


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).

Sharpe’s single index model, Sharpe ratio, optimal portfolio, cut-off rate

Ashraf, M. A., and Noor, M. S. I. (2010) Impact of Capitalization, on asset Price Bubble in Dhaka Stock Exchange. Journal of Economic Cooperation and Development, 31(4), pp. 127-152.

Bondt, De W. (2002) Bubble psychology. In W. Hunter and G. Kaufman (eds.), Asset
Price Bubbles: Implications for Monetary, Regulatory, and International Policies.

Chitnis, A. (2010) Performance Evaluation of Two Optimal Portfolios by Sharpe’s Ratio. Global Journal of Finance and Management, ISSN 0975-6477, Vol. 2, No. 1, pp. 35-46.

Dutt, D. (November, 1998) Valuation of common stock – an overview. The Management Accountant.

Elton, E. J., and Gruber, M. J. (2003) Modern Portfolio Theory and Investment Analysis. 6th ed., John Wiley and Sons Inc.

Elton, E. J., Gruber, M. J., and Padberg, M. W. (1976) Simple Criteria for Optimal Portfolio Selection. The Journal of Finance, Vol. 31, Issue 5, pp. 1341-1357. https://doi.org/10.1111/j.1540-6261.1976.tb03217.x

Fama E. F., and French K. R. (1992) The cross Section of Expected Stock Returns. The Journal of Finance, Vol. xlvii, No. 2, pp. 427-465. https://doi.org/10.1111/j.1540-6261.1992.tb04398.x

Fama E. F., and French K.R. (2004) The capital asset pricing model: Theory and evidence. The Journal of Economic Perspectives, Vol. 18, No. 3, pp. 25-46. https://doi.org/10.1257/0895330042162430

Kahneman, D., and Tversky, A. (March, 1979) Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), pp. 263-291. https://doi.org/10.2307/1914185

Levy, H., De Giorgi, E. G., and Hens, T. (2011) Two Paradigms and Nobel Prizes in Economics: A Contradiction or Coexistence? Journal of Financial Economics, 99, pp. 204-215.

Lintner. J. (February, 1965) The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, Vol. 47, No. 1, pp. 13-37 .This article can be retrieved from http://www.jstor.org/stable/1924119. https://doi.org/10.2307/1924119

Markowitz, H. (Mar., 1952) Portfolio Selection. The Journal of Finance, Vol. 7, No. 1, pp. 77-91.

Mossin J. (Oct., 1966) Equilibrium in a Capital Asset Market. Econometrica, Vol. 34, No., pp. 768-783. The Econometric Society. The URL for the article is http://www.jstor.org/stable/1910098. https://doi.org/10.2307/1910098

Perold, A. F. (2004) The Capital Asset Pricing Model. Journal of Economic Perspectives, Vol. 18, pp. 3–24. https://doi.org/10.1257/0895330042162340

Rahman, J. (2010) Bubble in DSE,World Press, Dhaka.

Rosser, J. B. (2000) From Catastrophe to Chaos: a General Theory of Economic Discontinuities. Kluwer Academic, 2nd ed.

Savabi, F., Shahrestani, H., and Bidabad, B. (May, 2012) Generalization and combination of Markowitz – Sharpe’s theories and new efficient frontier algorithm. African Journal of Business Management, Vol. 6 (18), pp. 5844-5851. Available online at http://www.academic

Sharpe, W. F. (Sep., 1964) Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, Vol. 19, No. 3, pp. 425-442.

Siegel, J. J. (2003) What is an asset price bubble; an operational definition. European financial management, Vol. 9, No. 1, pp. 11-24. https://doi.org/10.1111/1468-036X.00206

Tua, J, and Zhou, G. (2011) Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies. Journal of Financial Economics, 99, pp. 204-215. This journal can be retrieved from http://www.elsevier.com/locate/jfec. https://doi.org/10.1016/j.jfineco.2010.08.013

The data of market index (DSI all-share Price Index) have been retrieved from http://www.dsebd.org.