Valuation of Portfolio Risk and Performance of Several Blue Chip Stocks in Indonesia using Value-at-Risk based on n-Dimensional Geometric Brownian Motion

Abstract

Blue Chips are stocks of leading companies with good management and strong financial performance. History of financial market data shows that Blue Chip stocks have stable stock price volatility, have a strong effect on the Composite Stock Price Index (CSPI), but the performance of these companies is mutually independent. Therefore, modeling the prices of Blue Chip stocks uses n-dimensional geometric Brownian motion which describes volatility and data which follows stochastic processes. In addition, by the presence of negative relationship between stock prices, it is necessary to build portfolio to minimize risks. This article aimed to model the stocks of BCA, PT Telekomunikasi Indonesia, and PT Unilever. This year, these stocks were recorded to increase the CSPI which fell dramatically in mid-October 2019. Stock data were taken from 30 November 2018 to 29 November 2019. The results showed that forecast which used 3-dimensional GBM was very accurate to predict stock prices, evident by MAPE less than 5%. Portfolio risk was measured using VaR, showing a value of 0.003295758% at a confidence level of 95%. In addition, the Sharpe Index resulted in a value of 20.437, indicating profits that exceeded investment in a risk-free interest rate. This indicates that it is very appropriate for investors to invest in BCA, TLKM and UNVR stock portfolios with the proportions of 0.000006%, 10.265098% and 89.734895%, respectively.