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

Abstract

We consider the issue of optimizing an insurance company's asset allocation in the context of 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 insurers and run a quadratic optimization program to derive nondominated frontiers with budget, short-sale, and investment constraints. We then compute the respective 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 document that the standard formula is unable to distinguish investments on the basis of risk-return profiles and does hence not produce economically sensible results. Therefore, the introduction of Solvency II in its current form might cause severe asset management biases in the European insurance sector.