The quantification of type-2 prudence in asset allocation by the trustees of a retirement fund

Abstract

In this paper, consideration is given to the normative use of expected-utility theory for the purposes of asset allocation by the trustees of retirement funds. A distinction is drawn between type-1 prudence, which relates to deliberate conservatism on the part of actuaries in the setting of assumptions and the determination of model parameters, and type-2 prudence, which relates to the risk aversion of the trustees. The intention of the research was to quantify type-2 prudence for the purposes of asset allocation, both for defined-contribution (DC) and defined-benefit (DB) funds. The authors propose new definitions of the objective variables used as the argument of the utility function: one for DC funds and another for DB funds. A new class of utility functions, referred to as the weighted average relative risk aversion class is proposed. Practicalities of implementation are discussed. Illustrative results of the application of the method are presented, and it is shown that the proposed approach resolves the paradox of counter-intuitive results found in the literature regarding the sensitivity of the optimal asset allocation to the funding level of a DB fund.