Optimization of Stock Diversification with Quadratic Programming Method Using Lingo

Abstract

Portofolio theory emphasizes the search for the optimal combination of investments that gives the maximum profit rate at a particular level of risk. Portfolios are formed by investors in general is a portfolio based on the investor preferences. Portfolios are formed based on the preferences of the portfolio is not really optimal. To determine the composition of shares that must be invested in order to generate optimal portfolios with constraints is by way of optimization techniques. In investing, the investor’s expectation is to obtain a return that is as large as possible or at least greater than the interest rate of deposits. In reducing investment risk, the better investment is done not only in one area. The expectation is if the loss of investment in a field then the loss is expected to be reduced or eliminated from investment in other areas (diversification). When diversifying, investors usually confuse in selecting and determining the proportion of investment he has to do (Optimal). Therefore, investors need to have a grip in diversification so that investor expectations can be fulfilled. One of them is by diversifying with quadratic programming method. Quadratic programming processes conducted based on Markowitz’s model approach using LINGO. The results of this research in the form of investment proportions on some stocks. The research method used is a descriptive and verification method with techniques aimed at sampling such as sampling. The description of the calculations in this study uses secondary data with a sample of historical data shares included in the LQ45 index list during the period February 2004 to July 2009. The data is then processed using the quadratic programming method The results showed that the optimal diversification by using the quadratic programming method will be achieved when the investment made in the shares of Indosat Tbk (ISAT) of 13,2%, Indofood Sukses Makmur Tbk (INDF) of 4,12%, Bank Central Asia Tbk(BBCA) of 37,55%, Astra International Tbk (ASII) of 4,11%, Aneka Tambang (Persero) Tbk (ANTM) of 0,91%, Astra Agro Lestari Tbk (AALI) of 5,73%, Telekomunikasi Indonesia Tbk (TLKM) of 31,9% and shares of Holcim Indonesia Tbk (SMCB) of 2,45%. Risks arising from the limitations of existing investments and amounted to 0,14%.