Risk parity: An alternative formulation for risk-averse stochastic optimization in presence of heavy-tailed distribution of losses

Abstract

The concept of Risk Parity (or Equal Risk Contribution), which has been widely used in financial portfolio management, aims at explicitly enforcing diversification in a portfolio by ensuring equal contribution from each asset to the total volatility. While the Risk Parity condition has a straightforward use case in finance, several other application areas can be found in engineering and operations research. In these settings, the Risk Parity condition can be interpreted as enforcing the fairness of a decision or as a way to balance between a number of candidate solutions. In this paper, we consider Risk Parity in conjunction with modern risk-averse stochastic optimization (namely coherent measures of risk), study a generalized Risk Parity model, and propose a combined two-stage diversification-risk framework. We also introduce a bi-level formulation in a case when hierarchical decision-making is enforced. An approach to reformulate the Risk Parity problem as second-order cone programming is also proposed. We assess the performance of the proposed models based on a case study in hazardous materials transportation. The results show their effectiveness in terms of fairness and risk equity for decision-making under uncertainty with heavy-tailed distribution of losses.