Managing Systematic Mortality Risk With Group Self‐Pooling and Annuitization Schemes

• Date: 01 December 2013
• Author: Chao Qiao,Michael Sherris
• Published date: 01 December 2013
• DOI: http://doi.org/10.1111/j.1539-6975.2012.01483.x

© The Journal of Risk and Insurance, 2013, Vol. 80, No. 4, 949–974

DOI: 10.1111/j.1539-6975.2012.01483.x

949

MANAGING SYSTEMATIC MORTALITY RISK WITH

GROUP SELF-POOLING AND ANNUITIZATION

SCHEMES

Chao Qiao

Michael Sherris

ABSTRACT

Group self-annuitization (GSA) schemes are designed to share uncertain fu-

ture mortality experience including systematic improvements. Challenges

for designing group pooled schemes include decreasing average payments

when mortality improves significantly, decreasing numbers in the pool at

older ages, and the impact of dependence from systematic mortality im-

provements across different ages of members in the pool. This article uses

a multiple-factor stochastic mortality model in a simulation study to show

how pooling can be made more effective and to quantify the limitations of

these pooling schemes arising from the impact of systematic longevity risk.

INTRODUCTION

Internationally there has been a significant shift to defined contribution schemes to

fund retirement and a reduction in pension funds providinglongevity protection post

retirement. Increasingly, attention has been turned to the postretirement phase and

financial arrangements to convert accumulated lump sums into retirement incomes.

These policy issues are well covered in recent World Bank discussion papers (Rocha

and Vittas, 2010; Vittas et al., 2010). The ideal post retirement income provides con-

sumption income with both longevity insurance and inflation indexation. Yaari(1965)

demonstrates the welfare benefits of ordinary life annuities because of the longevity

Chao Qiao works at PricewaterhouseCoopers Australia, 201 Sussex Street, Sydney NSW 2000.

He can be contacted via e-mail: chao.qiao@au.pwc.com. Michael Sherris is at CEPAR, AIPAR,

Australian School of Business, University of New South Wales. He can be contacted via

e-mail: m.sherris@unsw.edu.au. The authors acknowledge the financial support of ARC Link-

age Grant ProjectLP0883398 Managing Risk With Insurance and Superannuation as Individuals

Age with industry partners PwC and APRA and the Australian Research Council Centre of

Excellence in Population Ageing Research (Project No. CE110001029). Comments on an earlier

version from Bruce Gregor,Katja Hanewald, and Ralph Stevens are gratefully acknowledged.

Comments from seminar and conference participants at the Institute of Actuaries of Australia

2011 Biennial Convention, 19th Annual Colloquium of Superannuation Researchers UNSW,

HEC University of Lausanne, Seventh International Longevity Risk, and Capital Markets Solu-

tions Conference, Southern Finance Association 2011 Annual Meeting, and the Southern Risk

and Insurance Association 2011 Annual Meeting are gratefully acknowledged.

950 THE JOURNAL OF RISK AND INSURANCE

insurance protection provided under a standard life-cycle consumption model with

perfect markets, actuarially fair annuities with no loadings and rational individuals

with no bequest motives. Davidoff et al. (2005) show that there are benefits from some

level of annuitization under more general assumptions. Although annuity prices are

not actuarially fair, risk-averse individuals will still value annuities (Mitchell, 2001).

Stevens (2010), among others, includes analysis of annuity decisions showing how

systematic mortality risk reduces the attractiveness of life annuities.

There are many reasons advanced as to why there is a lack of well-developed an-

nuities markets despite the potential longevity risk benefits. From a demand per-

spective, these include lack of liquidity, bequest motives, poor value for money, and

availability of public pensions (Friedman and Warshawsky,1990; Hurd, 1989; Mitchell

et al., 1999). From the supply perspective, insurers incur significant capital costs in

guaranteeing lifetime incomes because of the significant uncertainty of individual

longevity prospects. Adverse selection and lack of underwriting in the life annu-

ity market also leads to significant costs for suppliers of life annuities. Evans and

Sherris (2010) review demand and supply factors in developing a life annuity market

in Australia.

An approach to the management of uncertain future longevity, presented in Piggott,

Valdez, and Detzel (2005), is referred to as group self-annuitization (GSA), which

is designed to pool idiosyncratic risk with individuals bearing systematic risk. In-

dividuals invest into the pool and are paid an annuity income that varies with the

realized mortality experience. As individuals exit the pool from death, their remain-

ing capital is shared among the survivors in the pool in the form of mortality credits.

GSAs do not involve payment guarantees and do not require costly capital to sup-

port guarantees as compared to an ordinary annuity. They are designed to generate a

retirement income similar to a life annuity. They are not designed as investment ve-

hicles, as are variable annuities, so that investment risk including interest rate risk is

minimized. Variable annuities are products designed to generate variable retirement

income through exposure to investment markets. GSAs are not designed as variable

annuities.

Valdez, Piggott, and Wang (2006) addressed adverse selection and demand is-

sues for GSAs. Arrow (1969) provides an early discussion of the Pareto optimal-

ity of pooling differing risk types. Abel (1986) and Sinha (1989) consider adverse

selection for ordinary annuity funds with known heterogeneous mortality prob-

abilities. Valdez, Piggott, and Wang apply a similar utility framework to GSAs

to show that annuitants will naturally adversely select against both conventional

annuities and GSAs. The extent to which adverse selection is exercised against

GSAs is lower than that of conventional annuities given certain utility function

conditions.

Stamos (2008) extends Valdez, Piggott, and Wang (2006) by investigating the opti-

mal consumption problem for fund participants in a portfolio choice framework.

He shows that the expected mortality credit achieved by members who survived

increased with the number of members in the pool. The expected optimal con-

sumption as a proportion of initial wealth increased with the number of fund mem-

bers. A similar pooling scheme is presented by Sabin (2010) known as Fair Tontine