Analysis of portfolio optimization with and without shortselling based on diagonal model: evidence from indonesian stock market

Abstract

Markowitz (1952, 1959) and Roy (1952) proposed portfolio theory which narrate that risk of a portfolio is the variance of individual securities and covariances among those securities comprising the portfolio. The objectives of this research is to construct an optimized portfolio using Sharpe's diagonal model with and without short selling respectively, and to analyze the performance of less diversified optimal portfolios by investing in a single industry versus well diversified portfolio by investing across all industries. Finally to analysis the statistical properties of the estimates of diagonal model. Markowitz mean-variance portfolio optimization theory is implemented for all stocks listed in 9 sectors of Indonesian stock market during 2007-2011. However our model used 269 stocks which are not contradicting to the basic assumptions of the diagonal model. Diagonal model used in this research is a linear model and data used are time series secondary data. Firstly 9 optimal portfolios are computed for individual sectors with the assumption that short selling not permitted and then computation is done with assumption that short selling is permitted. Similarly 2 optimal portfolios are computed consisting of all stocks with assumptions mentioned above. Results showed that both well diversified short and long portfolios provide higher returns at a specified risk level compare to portfolios consist of individual sectors stocks. Largest weight in short portfolio is from infrastructure, utilities and transportation sector equaling 17.2 percent. Largest weight in long only portfolio are from trade, investment and services sector equaling 23.2 percent. The more diversified and larger portfolios provide better tangency portfolio. All stocks short and long portfolios performed better than any other individual sector portfolio. Standard error for and residual standard error for other portfolios are large compare to individual stocks indicating risk was not diversified away. Least square parameters estimates were not quite promising such as value of portfolio beta happened to be less than individual stocks as well as value of its coefficient of determination shows most of the systematic risk could not get eliminated as low values of R2 for portfolios shows that most of the variance in stock return as well as in portfolio return is not explained by market variance therefore unsystematic risk could not get eliminated despite of forming a portfolio encompassing all equities listed in Indonesian Stock Exchange as suggested by results of regression analysis.