Optimization Stock Portfolio With Mean-Variance and Linear Programming: Case In Indonesia Stock Market


  • Yen Sun Bina Nusantara University




optimum portfolio, mean-variance, linear programming, LQ45, performance evaluation


It is observed that the number of Indonesia’s domestic investor who involved in the stock exchange is very less compare to its total number of population (only about 0.1%). As a result, Indonesia Stock Exchange (IDX) is highly affected by foreign investor that can threat the economy. Domestic investor tends to invest in risk-free asset such as deposit in the bank since they are not familiar yet with the stock market and anxious about the risk (risk-averse type of investor). Therefore, it is important to educate domestic investor to involve in the stock exchange. Investing in portfolio of stock is one of the best choices for risk-averse investor (such as Indonesia domestic investor) since it offers lower risk for a given level of return. This paper studies the optimization of Indonesian stock portfolio. The data is the historical return of 10 stocks of LQ 45 for 5 time series (January 2004 – December 2008). It will be focus on selecting stocks into a portfolio, setting 10 of stock portfolios using mean variance method combining with the linear programming (solver). Furthermore, based on Efficient Frontier concept and Sharpe measurement, there will be one stock portfolio picked as an optimum Portfolio (Namely Portfolio G). Then, Performance of portfolio G will be evaluated by using Sharpe, Treynor and Jensen Measurement to show whether the return of Portfolio G exceeds the market return. This paper also illustrates how the stock composition of the Optimum Portfolio (G) succeeds to predict the portfolio return in the future (5th January – 3rd April 2009). The result of the study observed that optimization portfolio using Mean-Variance (consistent with Markowitz theory) combine with linear programming can be applied into Indonesia stock’s portfolio. All the measurements (Sharpe, Jensen, and Treynor) show that the portfolio G is a superior portfolio. It is also been found that the composition (weights) stocks of optimum portfolio (G) can be used to predict the forward return (5th January – 3rd April 2009). It is shown that the stock portfolio return of 5th January – 3rd April 2009) has exceeded the market return for the same period of time based on Sharpe and Treynor measurement. 


Plum Analytics

Author Biography

Yen Sun, Bina Nusantara University

Accounting Department


Brealey, R. A., Myers, S. C., and Marcus, A. J. (2007). Fundamentals of corporate finance, New York: McGraw-Hill/Irwin.

Hull, J. (1995). Introduction to futures and options markets, Prentice Hall.

Indonesia Stock Exchange. (2008). Retrieved 2nd April 2010 from http://www.idx.co.id.

Konno, H. and Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market. Management Science, 37 (5), 519. Retrieved 30th March 2010 from http://proquest.umi.com/pqdweb?index=0&did=106523&SrchMode=1&sid=1&Fmt=6&VInst =PROD&VType=PQD&RQT=309&VName=PQD&TS=1272531141&clientId=68814.

Lintner, J. (1965). The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econ. Statist. 47.

Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments, New York: John Wiley & Sons.

Mossin, J. (1966). Equilibrium in capital asset markets. Econometrica. 34.

Mossin, J. (1968). Optimal multiperiod portfolio policies. J.Business. 41.

Reilly, F. K., and Brown, K. C. (2006). Investment analysis and portfolio management, 8 ed., USA: Thomson South-Western.

Sadewa, P. Y. (2009). Kredibilitas bursa saham perlu ditingkatkan. Danareksa Research Institute. Retrieved 2nd April 2009 from http://www.danareksa-research.com/economy/media- newspaper/242-kredibilitas-bursa-saham-perlu-ditingkatkan.

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. J. Financial, 19, 425-442.

Swisher, P., and Kasten G. W. (2005). Post-modern portfolio. FPA Journal. Retrieved 5th April 2010 from




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