Portfolio selection and risk sharing via risk budgeting

Risk budgeting is an effective risk management tool that a decision-maker uses to create a risk portfolio with a pre-determined risk profile. This paper provides a rich discussion about the theory and practice on how to construct risk budgeting portfolios in a variety of settings. We revisit the usual portfolio selection setting with and without clustered risk budgeting targets, and we then provide an approach on how to extend the usual setting to situations in which a non-hedgeable risk is present or fixed sub-portfolios are aimed by the decision-maker. Another study of this paper is how to include risk budgeting targets in risk sharing, which has not been discussed in the literature. Implementation issues are also discussed, and some bespoke algorithms are provided to identify such risk budgeting portfolios. Numerical experiments are performed for real-life financial data, and we explain the risk mitigation effect of our proposed portfolio. Specifically, financial risk budgeting portfolios with social responsibility targets are constructed.