Academic journal article Journal of Risk and Insurance

Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities

Academic journal article Journal of Risk and Insurance

Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities

Article excerpt

ABSTRACT

We compute the optimal dynamic annuitization and asset allocation policy for a retiree with Epstein-Zin preferences, uncertain investment horizon, potential bequest motives, and pre-existing pension income. In our setting the retiree can decide each year how much he consumes and how much he invests in stocks, bonds, and life annuities, while the prior literature mostly considered restricted so-called deterministic or stochastic switching strategies. We show that postponing the annuity purchase is no longer optimal in the gradual annuitization (GA) case since investors are able to attain the optimal mix between liquid assets (stocks and bonds) and illiquid life annuities each year. In order to assess potential utility losses, we benchmark various restricted annuitization strategies against the unrestricted GA strategy.

INTRODUCTION

In this article, we solve the optimal asset allocation problem of life annuities with fixed benefits, stocks, and bonds in the presence of pre-existing pension income for a retiree with Epstein-Zin preferences. In our setting, the retiree can decide each year how much he consumes and how much he invests in stocks, bonds, and life annuities. We refer to this unrestricted case as gradual annuitization (GA). We compare the results to restricted annuitization strategies where the retiree is only allowed to switch from a phased withdrawal plan into life annuities once (so-called switching strategies). We quantify the utility costs when the retiree is forced to follow a switching strategy for various specifications of the Epstein-Zin utility function. Using Epstein-Zin preferences, we are able to disentangle the implications of varying the relative risk aversion (RRA) and elasticity of intertemporal substitution (EIS).

Our study contributes to the literature along two essential dimensions. First, the literature has been almost entirely devoted to restricted switching strategies shifting the whole remainder of a withdrawal plan into annuities. We relax this restrictive assumption by analyzing GA and by introducing a less restrictive switching strategy that shifts an optimal wealth fraction to annuities only once (partial switching, PS). (1) Second, Epstein-Zin preference, pre-existing pension income and bequest have not been analyzed in the dynamic asset allocation literature with annuities so far.

Exploring the utility impact of restricted switching restrictions can be justified from a practical viewpoint since some countries in Europe require a mandatory annuitization age for tax-induced saving plans. For instance, in the United Kingdom, accumulated assets have to be annuitized by age 75. In Germany, "Riester" plans offer a tax inducement if life-annuity payments start from age 85 on and the withdrawn amounts are either constant or increasing prior to age 85. The analysis of the optimal annuitization strategies itself is important because there is an overall increase in general awareness for longevity risk: while nations worldwide are moving from public pay-as-you-go schemes to privately funded pension systems, employers are shifting from defined benefit plans to either hybrid or defined contribution plans. The unrestricted optimal dynamic annuitization and asset allocation policy shows how longevity risk can be managed best by purchasing life annuities with constant payouts.

The constant payout or fixed benefit life annuity is a bond-based investment including longevity insurance protecting the retiree from outliving his resources (Mitchell et al., 1999). (2) Not only do life annuities with fixed benefits capture the largest annuity market share, but they also play an important role in tax-induced private or corporate savings schemes. In what follows we will exclusively focus on the single premium immediate payout annuity with fixed real benefits. Such life annuities are almost identical to public pensions with respect to their payout structure. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.