On the Financial Interpretation of Risk Contribution: Risk Budgets Do Add Up

Abstract

Due to a lack of clear financial interpretation, there are lingering questions in the financial industry regarding the concepts of risk contribution. This paper provides as well as analyzes risk contribution's financial interpretation that is based on expected contribution to potential losses of a portfolio. We show risk contribution, defined through either standard deviation or value at risk (VaR), is closely linked to the expected contribution to the losses. In addition, for VaR contribution, our use of Cornish-Fisher expansion method provides practitioners an efficient way to calculate risk contributions of portfolios with non-normal underlying returns. Empirical evidences are provided with asset allocation portfolios of stocks and bonds.

Keywords: risk management, risk budgeting, risk contribution, VaR contribution