Value-at-Risk and Minimum Variance in the Investment Portfolio with Non Constant Volatility
Sukono1, E. Lesmana2, D. Johansyah3, H. Napitupulu4, Y. Hidayat5, Diana Purwandari6
1Sukono, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia.
2E. Lesmana, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia.
3D. Johansyah, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia.
4H. Napitupulu, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia.
5Y. Hidayat, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia.
6Diana Purwandari, Department of Mining, Faculty of Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia.
Manuscript received on 03 August 2019 | Revised Manuscript received on 26 August 2019 | Manuscript Published on 05 September 2019 | PP: 197-202 | Volume-8 Issue-2S7 July 2019 | Retrieval Number: B10490782S719/2019©BEIESP | DOI: 10.35940/ijrte.B1049.0782S719
Open Access | Editorial and Publishing Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: One of the criteria for efficient portofilio is that it produces the same level of profit, but with minimum risk.This paper discusses the estimates Value-at-Risk and minimum variance on an investment portfolio.In this case it is assumed that the asset return follows the time series model. Therefore, non-constant meanis estimated using autoregressive moving average (ARMA) models.While non constant volatility is estimated using generalized autoregressive conditionaly heteroscedasticity (GARCH) models. To determine the minimum variance is done using Markowitz’s model optimization. Furthermore, Value-at-Risk is calculated based on the values of the mean and minimum variance. The result of return analysis of assets of BBRI, INCI, LPBN, and MPPA, obtained the minimum variance value of 0.011734775, and at the 95% confidence level obtained Value-at-Risk of 0.017873889.The minimum variance and Value-at-Risk are obtained on the vector of the investment weighted composition as x’ = (0.092827551, 0.212180907, 0.14631804, 0.548673502). So to get a minimum risk on the investment portfolio consisting of the four assets, the capital allocation must follow the vector of weighted composition produced.
Keywords: Asset Return, Time Series, Mean Model, Variance Model, Markowitz’s Model.
Scope of the Article: Cryptography and Applied Mathematics