Expected Shortfall Analysis on Optimal Portfolios Using the Downside Deviation Method

(Case Study: Jakarta Islamic Index (JII) Sharia Stocks for the 2020–2024 Period)

Abstract

Portfolio optimization is crucial in financial management to maximize expected returns while minimizing downside risks. Traditional portfolio models often assume that asset returns are normally distributed, which fails to capture extreme market risks (tail risk) in empirical stock data. This study aims to construct an optimal portfolio of Jakarta Islamic Index (JII) stocks using the Downside Deviation method and evaluate its extreme loss potential using Expected Shortfall (ES). The dataset consists of daily stock returns from 17 sharia-compliant companies consistently listed in JII during the 2020–2024 period. The empirical results show that the stock returns are non-normally distributed, justifying the use of downside risk measures. Out of 17 stocks, 8 exhibited positive expected returns and were selected for optimization. The optimal portfolio formed by the Downside Deviation method yields a daily expected return of 0.0196% with a portfolio standard deviation of 0.8185%, with the largest asset allocations assigned to ICBP (45.828%), UNTR (16.451%), and TPIA (12.676%). Furthermore, risk estimation using Expected Shortfall with an initial capital of IDR 100,000,000 for a 1-day holding period reveals maximum average losses of IDR 2,206,782 (2.21%) at the 99% confidence level, IDR 1,712,351 (1.71%) at the 95% confidence level, and IDR 1,459,819 (1.46%) at the 90% confidence level. These findings suggest that combining Downside Deviation with Expected Shortfall provides a more realistic and comprehensive risk assessment framework for sharia stock investors under non-normal market conditions.