Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula

We optimize a life insurance company's asset allocation in the context of classical portfolio theory when the firm needs to adhere to the market risk capital requirements of Solvency II. The discussion starts with a brief review of the standard formula and the introduction of a parsimonious partial internal model. Subsequently, we estimate empirical risk–return profiles for the main asset classes held by European insurers and run a quadratic optimization program to derive nondominated frontiers with budget, short‐sale, and investment constraints. We then compute the capital charges under both solvency models and identify those efficient portfolio compositions that are permitted for an exogenously given amount of equity. Finally, we consider a systematically selected set of inefficient portfolios and check their admissibility, too. Our results show that the standard formula suffers from severe shortcomings that interfere with economically sensible asset management decisions. Therefore, the introduction of Solvency II in its current form is likely to have an adverse impact on certain parts of the European insurance sector.