Mean-Value-at-Risk Portfolio Optimization Based on Risk Tolerance Preferences and Asymmetric Volatility

Yuyun Hidayat (), Titi Purwandari, Sukono, Igif Gimin Prihanto, Rizki Apriva Hidayana and Riza Andrian Ibrahim
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Yuyun Hidayat: Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Titi Purwandari: Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Sukono: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Igif Gimin Prihanto: Research Center for Testing Technology and Standards, National Research and Innovation Agency, Jakarta 10340, Indonesia
Rizki Apriva Hidayana: Magister Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Riza Andrian Ibrahim: Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia

Mathematics, 2023, vol. 11, issue 23, 1-26

Abstract: Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks’ asymmetric return volatility and investors’ risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors’ risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia’s capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible.

Keywords: portfolio optimization; mean-value-at-risk model; asymmetric return volatility; risk aversion preferences; ARMA-GJR-GARCH (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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