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All Journal Griya Journal of Mathematics Education and Application
Arlin Marsyanda
Universitas Bengkulu
Education Mathematics

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Optimasi Portofolio Mean-Conditional Value-At-Risk (MEAN-CVAR) untuk Saham Indeks IDXHIDIV20 di Bursa Efek Indonesia Arlin Marsyanda; Ani Sapitri; Siska Yosmar
Griya Journal of Mathematics Education and Application Vol. 6 No. 3 (2026): September 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

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Abstract

This study optimizes a portfolio of 20 IDXHIDIV20 constituent stocks listed on the Indonesia Stock Exchange using the Mean-Conditional Value-at-Risk (Mean-CVaR) model through Linear Programming (LP) in Python. Adjusted closing prices from 2 January 2020 to 28 April 2026, comprising 1,521 trading days, were divided into 1,216 in-sample and 304 out-of-sample observations. The Jarque-Bera test indicates non-normal return distributions for all stocks (p < 0.001), supporting the use of CVaR as a tail-risk measure. At α = 0.95, the Mean-CVaR model selects 9 active stocks and produces an in-sample CVaR of 2.5251% and an out-of-sample CVaR of 2.6992%. The out-of-sample CVaR is lower than the Equal-Weight portfolio (2.8311%) but higher than the Mean-Variance portfolio (2.5860%). Meanwhile, Equal Weight records the highest out-of-sample annualized return of 9.48%, compared with −10.19% for Mean-CVaR and −5.77% for Mean-Variance. Sensitivity analysis shows that increasing α from 0.90 to 0.99 increases out-of-sample CVaR from 2.0754% to 5.1917% and affects portfolio concentration. These results indicate that the choice of risk measure and confidence level influences portfolio composition and risk characteristics, while out-of-sample performance may differ from in-sample optimization results.
Co-Authors Ani Sapitri Siska Yosmar