Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Articles

MODIFIED STATISTICAL-BASED VALUE AT RISK FOR MULTI-OBJECTIVE OPTIMAL-BASED PORTFOLIO ANALYSIS OF INDONESIAN STOCK RETURN DISTRIBUTION

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  • Wisnowan Hendy Saputra,
  • Hasri Wiji Aqsari
Wisnowan Hendy Saputra
Computer Science Department, School of Computer Science, Bina Nusantara University, Indonesia
Hasri Wiji Aqsari
Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia
DOI: https://doi.org/10.30598/barekengvol20iss1pp0287-0298
Published November 24, 2025
Keywords
  • Modified Value at Risk,
  • Multi-Objective Optimization,
  • Portfolio Risk Analysis,
  • Risk Averse,
  • Stock Portfolio
How to Cite
[1]
W. H. Saputra and H. W. Aqsari, “MODIFIED STATISTICAL-BASED VALUE AT RISK FOR MULTI-OBJECTIVE OPTIMAL-BASED PORTFOLIO ANALYSIS OF INDONESIAN STOCK RETURN DISTRIBUTION”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0287-0298, Nov. 2025.

Copyright (c) 2025 Wisnowan Hendy Saputra, Hasri Wiji Aqsari

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Abstract

Basically, all stock investments aim to obtain maximum profit with low risk. The formation of a stock investment portfolio is always accompanied by measuring returns and risks that show its performance. Portfolio risk measurement is often faced with the challenge that returns are not normally distributed, so that measurements using the normality assumption cannot be applied. This study proposes the development of a modification of stock portfolio risk measurement so that it is not limited to the normality assumption. The development is carried out by modifying the calculation of Value at Risk (VaR) to consider the skewness and kurtosis values ​​(hereinafter referred to as modified VaR), so that the normal distribution assumption can be eliminated. As a method for compiling a stock portfolio, the Multi-Objective Optimization technique was chosen because it can modify risk averse so that the risk can be adjusted to the risk profile of each investor and is able to stabilize the mean return value. For its implementation, this paper uses real stock data which of course has returns that are not normally distributed, namely the four Indonesian stocks based on the largest capitalization recorded in January 2025 (blue chip), namely BREN, BBCA, BYAN, and BBRI obtained through finance.yahoo.com. The analysis method is divided into three steps, including multi-objective optimization completion, portfolio return calculation, and finally modified VaR estimation. The results of the study show that BBCA has the largest weight with a portion of more than 40% of the four stocks, so BBCA will be the priority stock for this portfolio. The portfolio formed using multi-objective optimization is proven to have a stable mean return because the portfolio mean return is between several of its constituent stocks (vice versa) which is around 0.01%, and the smallest estimated value of the portfolio modified VaR is 1.67%. Thus, a portfolio based on multi-objective optimization is not only able to create a portfolio that provides a small risk in risk measurement without assuming a normal distribution, but at the same time multi-objective optimization is also able to provide competitive returns with its constituent stocks.

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