Portfolio selection by GJR-GARCH model and Gaussian Mixture model

In financial markets, asset prices constantly change and volatilize due to various factors such as economic conditions, politics, and significant global events. Volatility is one of the key factors that influences investor’s decisions. Using models that are able to estimate such volatility is important in constructing investment portfolios. This research aims to construct portfolio based on the mean-variance theory by utilizing the Gaussian Mixture model (GMM) and the GJR-GARCH model with constant conditional correlations. Both models are used to estimate covariance matrices which are used for constructing portfolios. Daily asset price data from 2014 to 2024 were used in this study. Additionally, the portfolio allocation was adjusted every 10 days. The performance of the two portfolios is compared based on cumulative amount of money, standard deviation of return rate, and Sharpe ratio. The results of the study indicated that the portfolio created using the GJR-GARCH model achieved a cumulative amount of growth of 4.211739 times the initial capital, which is higher than the GMM. However, the 10-day return standard deviation was 0.041234 which is slightly higher than that from GMM. Additionally, the GJR-GARCH model exhibited a superior Sharpe ratio.