The objective of this study is to create optimal two-asset portfolios consisting of stocks from Western Europe, the United States, and the BRICS (Brazil, China, India, Russia, and South Africa), as well as sixteen commodity types during the BREXIT period. We utilized dynamic variances and covariances from the GARCH model to derive weights for the two-asset portfolios, with each portfolio consisting of one equity factor and one commodity factor. Subsequently, hedge ratios were calculated for these various assets. Our findings indicate that portfolios consisting of European stocks do not require the inclusion of commodities, whereas the other equities do.

Abstract: It is negative risk if there is a good chance of coming out better than our reference level. This paper proposes a general risk measure: bilateral partial moment, where downside risk is supplemented with the "upside potential". Variance, mean absolute deviation, semi-variance and other downside risk definition are all incorporated in this framework. The portfolio selection problems in this general class of risk model are discussed. The portfolio optimization provides the flexibility for the selection of an appropriate target return and the weightiness of upside potentials.