Risk Aggregation, Dependence Structure and Diversification Benefit

Benefit Roland Bürgi, Michel Dacorogna and Roger Iles

Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include diversification in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits. To compute the total risk of a portfolio, it is important to establish the rules for aggregating the various risks that compose it. This can only be done through modelling their dependence. It is a well known fact among traders in financial markets that “diversification works the worst when one needs it the most”. In other words, in times of crisis the dependence between risks increases. Experience has shown that very large loss events almost always affect multiple lines of business simultaneously. September 11, 2001, is an example of such an event: when the claims originated simultaneously from lines of business that are usually uncorrelated, such as property and life, at the same time that the assets of the company were depreciated due to the crisis on the stock markets. In this chapter, we explore various methods of modelling dependence and their influence on diversification benefits. We show