Optimal Portofolio Analysis with Risk-free Assets using Index-tracking Portfolio Optimization Model

Abstract

Constructing optimal portfolio to the desired expected return is one of the main concerns of every investor. This research aimed for constructing and comparing two approaches of stocks portfolio optimization model with an addition of risk-free assets on two different models. The classical Markowitz mean-variance model is further compared with an index-tracking model introduced by Edirisinghe. Additional risk-free asset in the portfolio is intended to give investors an option to lower the risk through diversification. The stocks analyzed for the research are stocks traded in Jakarta Composite Index (JCI) under the period of 2007 – 2012. Results shown that additional risk-free asset lowers the risk significantly for both Markowitz and the index-tracking portfolios, with the index-tracking diversified portfolio has a lower risk than the benchmark index. The index-tracking portfolio also gives a higher beta than the Markowitz MV portfolio. This increase in beta depends on the index variance, in this case JKSE variance, and also the asset covariance matrix. During the back testing, the performance of both Markowitz MV portfolio and index-tracking portfolio do not track the index performance. However, the portfolios which use index-tracking method outperform the portfolios constructed using the Markowitz MV model.

Keywords: Investment, Index-tracking, Portfolio Optimization, Mean-variance Optimization