Optimization of the Mean-Variance Investment Portfolio of Some Stocks under Market Sentiment and the ARMAX-GARCH Model

Abstract

Stock returns are assumed to follow the model of the time series. To determine stock returns is done by using the log-return model. It is assumed that the stock price was affected by market sentiment, so in this paper the mean stock returns is estimated using a model Autoregressive Moving Average exogenous (ARMAX) which is inserted exogenous variables such as indicator of market sentiment. While volatility is estimated using a model Generalized Autoregressive Conditional Heteroscedastic (GARCH). In this paper discussed about the mean and variance portfolio optimization several Sharia stocks where its prediction  of stock return model is using ARMAX-GARCH models where the optimization is done is to use the method of Lagrange Multiplier. Numerical results obtained by using the data several Sharia stocks in Indonesia where the expected results are obtained proportion appropriate investment for shares of sharia in Indonesia.