Optimal Time of Annuitization in the Decumulation Phase of a Defined Contribution Pension Scheme

We consider the problem of finding the optimal annuitization time in the decumulation phase of a defined contribution pension scheme, exploiting the model of Gerrard, Højgaard and Vigna (2010). We make extensive numerical investigations on the optimal annuitization time, size of final annuity upon annuitization, extent of improvement when annuitization is not immediate and comparison between optimal annuitization and immediate annuitization. We find that the optimal annuitization time depends on the retiree's risk aversion, on her perception of remaining lifetime and on the risk premium of the risky asset. Intuitively, optimal annuitization should occur a few years after retirement with high risk aversion, low risk premium and/or short remaining lifetime, and many years after retirement in an opposite scenario. We also measure the cost of sub-optimality of a pension system where immediate annuitization is compulsory, in terms of loss of expected present value of consumption from retirement to death. We find that this cost varies between 6% and 40% in relative terms, depending on the risk aversion.This paper is currently reserved to Carefin sponsors and will be made public on SSRN after a short embargo. Please visit the CAREFIN website to learn more on how to get the paper