Portfolio Mathematics with General  Linear and Quadratic Constraints

Stowe, David L.

doi:10.4236/jmf.2019.94034

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…Meanwhile, the variance return of the portfolio without risk-free assets can be briefly stated as follows [23,24]:…”

Section: The General Optimization Model Of the Investment Portfoliomentioning

confidence: 99%

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

Sukono,

Ghazali,

Johansyah

et al. 2024

Computation

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This paper aims to design a quadratic optimization model of an investment portfolio based on value-at-risk (VaR) by entering risk-free assets and company liabilities. The designed model develops Markowitz’s investment portfolio optimization model with risk aversion. Model development was carried out using vector and matrix equations. The entry of risk-free assets and liabilities is essential. Risk-free assets reduce the loss risk, while liabilities accommodate a fundamental analysis of the company’s condition. The model can be applied in various sectors of capital markets worldwide. This study applied the model to Indonesia’s mining and energy sector. The application results show that risk aversion negatively correlates with the mean and VaR of the return of investment portfolios. Assuming that risk aversion is in the 5.1% to 8.2% interval, the maximum mean and VaR obtained for the next month are 0.0103316 and 0.0138270, respectively, while the minimum mean and VaR are 0.0102964 and 0.0137975, respectively. The finding of this study is that the vector equation for investment portfolio weights is obtained, which can facilitate calculating investment portfolio weight optimization. This study is expected to help investors control the quality of appropriate investment, especially in some stocks in Indonesia’s mining and energy sector.

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“…Meanwhile, the variance return of the portfolio without risk-free assets can be briefly stated as follows [23,24]:…”

Section: The General Optimization Model Of the Investment Portfoliomentioning

confidence: 99%

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

Sukono,

Ghazali,

Johansyah

et al. 2024

Computation

View full text Add to dashboard Cite

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Reconciling Tracking Error Volatility and Value-at-Risk in Active Portfolio Management: A New Frontier

Lucchetti,

Nicolau,

Palomba

et al. 2024

Comput Econ

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This article introduces the Risk Balancing Frontier (RBF), a new portfolio boundary in the absolute risk-total return space: the RBF arises when two risk indicators, the Tracking Error Volatility (TEV) and the Value-at-Risk (VaR), are both constrained not to exceed pre-set maximum values. By focusing on the trade-off between the joint restrictions on the two risk indicators, this frontier is the set of all portfolios characterized by the minimum VaR attainable for each TEV level. First, the RBF is defined analytically and its mathematical properties are discussed: we show its connection with the Constrained Tracking Error Volatility Frontier (Jorion in Financ Anal J, 59(5):70–82, 2003. https://doi.org/10.2469/faj.v59.n5.2565) and the Constrained Value-at-Risk Frontier (Alexander and Baptista in J Econ Dyn Control, 32(3):779–820, 2008. https://doi.org/10.1016/j.jedc.2007.03.005) frontiers. Next, we explore computational issues implied with its construction, and we develop a fast and accurate algorithm to this aim. Finally, we perform an empirical example and consider its relevance in the context of applied finance: we show that the RBF provides a useful tool to investigate and solve potential agency problems.

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Portfolio Mathematics with General Linear and Quadratic Constraints

Cited by 2 publications

References 13 publications

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

Reconciling Tracking Error Volatility and Value-at-Risk in Active Portfolio Management: A New Frontier

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