Gaussian mixture distribution with expectation maximization algorithm for portfolio analysis

In addition to providing high profit opportunities (return), stock investment is also carrying a large risk of loss. Stock return distribution analysis can assist investors in measuring the risk of a stock. However, stock return distributions that are not normally distributed are often found, as well as extreme values at the left and right ends or fat tails. The Gaussian Mixture distribution of stock returns is proposed to capture the above-mentioned statistical characteristics of stock return distributions. The use of the Expectation Maximization (EM) algorithm to fit this Gaussian Mixture model is described and examples of its use are given in the context of portfolio analysis. The application of the method for 2 components of the Gaussian Mixture distribution on portfolio consisted of 3 stocks, namely PT Indofood Sukses Makmur Tbk (INDF), PT Semen Indonesia Tbk (SMGR), and PT XL Axiata Tbk (EXCL) is given as an illustration.