Risk Comparison in Optimal Portfolios: A Study of Value at Risk (VaR) and Tail Value at Risk (TVaR)

Abstract

Considering investment risk is something that investors must do before deciding to invest; measuring risk provides an opportunity for investors to get the desired return and minimize losses. This study compares Value at Risk (VaR) and Tail Value at Risk (TVaR) methodologies for measuring portfolio risk. VaR is a commonly used method that provides the maximum loss at a certain confidence level and period. However, VaR is not an effective measure of risk because it does not satisfy one of the axioms of coherent risk measures, i.e., subadditivity. Subsequently, the TVaR measure emerged, which satisfies all the axioms of coherent risk measures, thereby providing a good and effective measure of risk. The optimal portfolio will be formed using the Single Index model, simplifying the Markowitz portfolio model. The Composite Stock Price Index will be the only factor influencing other stocks in this model. The data used data from stocks that were consistently listed on the IDX30 index from 24/10/2022 to 25/10/2024. Based on the result of the analysis of data, the optimal portfolio consists of 5 stocks, i.e., PT Bank Mandiri (BMRI.JK), PT Indofood Sukses Makmur (INDF.JK), PT Bank Central Asia (BBCA.JK), PT Bank Negara Indonesia (BBNI.JK), and PT Barito Pacific (BRPT.JK). Risk measures were compared on the optimal portfolio, using a confidence level of 1-α=95%, with a daily time period, and an initial investment capital of IDR 1 billion. The estimated VaR risk measure is IDR 15.38 million, while TVaR reaches IDR 23.25 million.