Quadratic investment portfolio based on value-at-risk with risk-free assets: For stocks of the mining and energy sector

The mining and energy sector is still the driving force for economic development and community empowerment, especially around mining and energy activities. Therefore, increased investment in the mining and energy sectors needs to be increased and balanced with stricter safety and environmental policies. This paper aims to formulate a quadratic investment portfolio optimization model, and apply it to several stocks in the mining and energy sectors. In this paper, it is assumed that risk is measured using Value-at-Risk (VaR), so that the optimization modeling is carried out using the quadratic investment portfolio approach to the Mean-VaR model with risk-free assets. Furthermore, the model is used to determine the efficient portfolio surface based on several values of risk aversion levels.