Some further ideas concerning the interaction between insurance and investment risks

For many years it has been a frequently discussed question which is more important: insurance or investment risk. Based on Bühlmann’s (1995) method to separate these two risks with the help of conditional expectations, this paper presents a decomposition of the prospective portfolio loss into a sum of three addends that uniquely correspond to unsystematic insurance risk, systematic insurance risk, and investment risk. Calculating their variances for homogeneous portfolios of term life and pure endowment insurances shows that answering the initial question is more complex than frequently thought. In a second step, an extended duration concept is introduced, which allows one to analyze the non-diversifiable investment and systematic insurance in view of parameter changes at certain points in time.