Portfolio Optimization With Illiquid Life Insurance Investments

Abstract

Endowment life insurance products contain a collective component resulting in smoothed returns. By unsmoothing the data of German life insurers we are able to extract the risk/return pattern of the underlying financial assets. Thus, we can analyze mean-variance optimal portfolios including a smoothed with-profit contract compared to an unsmoothed unit-linked contract. We find that life insurance is attractive for conservative investors and cannot be easily replicated. Furthermore the investor cannot regain his expected utility when being allocated to an undesirable amount of the illiquid with-profit contract -- neither through reallocation of his liquid investments nor through collateral lending. Overall, the with-profit contract shows similar characteristics than other illiquid assets. The main difference is that the regulation by law allows the investor to participate in the smoothed returns -- contrarily to all other financial market products where the investor shall participate in his holding period returns.