Optimal Portfolio Formation Using Markowitz Model and Value at Risk Measurement with Extreme Value Theory Approach on JII Stocks

Abstract

Sharia-compliant stocks, particularly those listed in the Jakarta Islamic Index (JII), represent a significant component of Indonesia’s Islamic capital market. To minimize investment risk, investors often construct diversified portfolios. This study aims to form an optimal portfolio using the Markowitz mean-variance model and assess its risk using Value at Risk (VaR), integrated with Extreme Value Theory (EVT) to capture extreme losses often missed by traditional methods. Among the selected stocks, MDKA showed the highest average return (0.112%), while UNVR had the lowest (-0.096%). ICBP exhibited the lowest volatility (1.732%), and BRPT the highest (3.350%). The optimal portfolio allocation consists of MDKA (63%), CPIN (7%), BRPT (17%), and ADRO (13%), indicating effective risk diversification. The portfolio’s standard deviation (2.010%) is significantly lower than that of the most volatile individual asset, highlighting the benefit of diversification. EVT analysis identified the Generalized Extreme Value (GEV) distribution as the best fit for modeling tail risks. The estimated portfolio VaR at 90%, 95%, and 99% confidence levels were -3.64%, -3.91%, and -4.28%, respectively. These results underscore the importance of integrating modern portfolio optimization techniques with robust risk assessment tools like EVT for enhancing decision-making in sharia-compliant investment.