Research Paper No. 2003-01 

Annuity Risk: Volatility and Inflation Exposure 

in Payments from Immediate Life Annuities 

Chris Soares 

Mark Warshawsky 

January 2

Abstract:

003 

 Some researchers have raised concerns about significant volatility in 

init l payments from fixed immediate life annuities and the subsequent inflation risk 

dur g the retirement period. This paper investigates these concerns using recent high 

frequency data. It finds that while there is significant volatility in initial payments from 

no inal fixed annuities, phased purchases of fixed annuities can reduce their volatility. 

It a t an i

inf

Se

Pre

“D

The thors are with the US Department of the Treasury. Any views expressed, however, are those of the 

aut rs alone and not necessarily those of the Treasury Department. We appreciate helpful comments from 

conference participants and John Ameriks, Jeffrey Brown, James Duggan, and Kent Smetters, and 

assi ance with data from Norman Carleton and Ron Koenecke at Treasury, and Stephen Goss, Alice Wade 

and elicitie Bell at the Social Security Administration. 

ia

in

m

lso finds tha nflation-adjusted annuity may address both the volatility and 

lation risk problems. The results are applicable to current discussions about Social 

curity reform and trends toward the defined contribution type of pension plan. 

sented at the conference sponsored by the Center for Research in Pension and Welfare Policies, 

eveloping an Annuity Market in Europe,” Turin, Italy, June 21, 2002 

 au

ho

st

 F
2

Trends in Retirement Plans: Defined Benefit to Defined Contribution

 Over the last two decades, there has been a steady movement, gathering speed, 

around the 

of 

on

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risks being assumed, perhaps unknowingly, by holders of defined contribution retirement 

pla s? Are

av , a

acc

fro

an articipants in 

def We examine a 

recent time horizon, 1983 through 2002, as relevant to current and likely future economic 

and policy 

beg

20

inc

ret

sim

pay

rou

inc

inf two products do not currently widely exist in the 

United States, but certainly are within the realm of practical and technical possibility, and 

are shown to illustrate methods of handling post-retirement inflation risk. We also 

consider a phased purchase of fixed nominal annuities over a three-year period pr r to 

 

world, in both public and private sectors, toward the defined contribution type 

retirement plan and away from the defined benefit type. Much research has been done 

 the reasons for this shift; the primary causes have been identified as increased labor 

bility, the possibility of higher returns on assets held in a defined contribution plan 

ount, fewer distortions in work incentives, reduction in regulatory burden, and the 

xibility usually gained in the distribution of assets during the working and, especially, 

irement years. The defined benefit plan type generally offers the promise of lifetime 

nuity) benefit payments during retirement, closely related to the level of earnings 

perienced during the working years (most typically, in the years just before 

irement).1

 Defined contribution plans, on the other hand, offer market returns on 

tributions and broader options for distribution of accumulated balances. 

In the face of the strong forces leading to the dominance of the defined 

ntribution plan type, a legitimate set of questions can be posed: are certain types of 

n these risks, in some measurable sense, unduly large? Are there mechanisms 

ailable t reasonable cost-benefit ratios, to control or modify these risks? Are the risks 

eptable in light of the additional flexibilities obtained? 

This short paper focuses on the volatility, over time, of initial monthly payments 

m individual immediate life annuities, as well as the inflation risk experienced after 

nuitization. Such annuities are those most relevant and available to p

ined contribution pension plans and individual retirement accounts. 

conditions. We also record high frequency results – monthly since the 

inning of 1983 through December 2002 and daily since the beginning of February 

02 through December 2002 – in order to get a better sense of the actual volatility of 

ome from life annuities that might be experienced by households timing their 

irement and purchase of life annuities, or who are aware of the outcomes of other 

ilarly situated individuals. The daily simulations are also compared to actual daily 

ments over the period from a AAA-rated life insurance company, which provides a 

gh gauge of how well our model tracks actual market outcomes. 

We examine fixed nominal annuities, fixed increasing annuities (whose payments 

rease with the rate of inflation expected at the time of annuity issue), and since 1998, 

lation-adjusted annuities. The latter 

io

 

hese annuity payments are sometimes fixed in nominal terms or sometimes increase, usually with some 

asure of consumer prices. 

1

 T

me
3

retirement. Volatility is measured primarily by the standard deviation of monthly 

pay ir percentage change over one-year periods. 

 It should be noted that the evaluation of risk for the defined contribution plan type 

is r ative b

sub

red

ris

de

the

con

spo

sponsored by private sector entities for their employees, or those purchased by 

individuals

to 

ma

spo

an

De

ments, and the

el ecause, despite its notional stability, the defined benefit plan type is also 

ject to risk. In the case of private plans, insolvency or inadequate prefunding can 

uce pension payments. In the case of government plans, demographic and political 

k could result in reductions to expected benefits. In either case, contributions to a 

fined benefit retirement plan that are made prior to vesting or retirement can be lost in 

 event an individual dies or no longer works. By contrast, in most defined 

tribution plans, contributions are generally quickly vested and bequeathable. 

There is a strong public policy interest in retirement plans, whether those directly 

nsored by public sector entities for all workers and families or their employees, those 

 and households for themselves. The public interest can be stated as a desire 

assure financial security in retirement, at a reasonable cost and level of risk, with the 

ximum possible flexibility. This public interest is implemented in the form of direct 

nsorship, tax incentives, insurance guarantees, and regulatory restrictions, guidelines, 

d oversight. 

fined Contribution Plans: The Distribution Phase and Immediate Life Annuities

The defined contribution plan type is subject to certain risks, potentially borne by 

the lan beneficiary, both in the accumulation and distribution phases. In the 

acc

an

on a primary pension plan: financial security in retirement. 

pla

an

sta ehold to the 

ris ed benefit 

pla or does not have a significant stock of asset holdings. As has been formally 

de nstrat

Ve

me

ann

ho

hav

pri

(ex

pla

Se rity system by establishing personal accounts, annuities are prominently mentioned 

 p

umulation phase, these risks include the possibility of poor investment performance 

d, depending on plan rules, the use of assets for purposes other than the fundamental 

e of 

The distribution phase is less studied and understood. Most defined contribution 

ns in the United States offer little structure to the distribution of assets. Although life 

nuities are sometimes offered by the plan, they are almost never mandated. Clearly this 

te of affairs offers maximum flexibility, but it also exposes the retired hous

k of outliving its assets if the household is not otherwise covered by a defin

n

mo ed by Mitchell, Poterba, Warshawsky and Brown (1999) and by Ameriks, 

res, and Warshawsky (2001) using expected utility and asset return simulation 

thodologies, respectively, longevity risk is substantial and the insurance value of a life 

uity is significant compared to the alternate strategy of phased withdrawals of assets. 

Moreover, there is a potential moral hazard problem in old age: if the retired 

usehold mistakenly employs its assets in excess spending or poor investments, it will 

e to fall back on a social safety net provided by government welfare programs or 

vate charity. In fact, largely to prevent these problems and to reduce adverse selection 

plained below), life annuities are mandated in primary defined contribution pension 

ns in the United Kingdom. In discussions of reforming of the United States Social 

cu
4

as a distribution mechanism (Report of the President’s Commission, December 2001, p. 

56)

 Whether made available in a defined contribution pension plan or purchased as an 

individual p

hig

an

igated intensively in a series of published 

articles, many collected in the volume by Brown, Mitchell, Poterba, and Warshawsky 

(20 1). Th

are

im

in 

ex

are

an

fin

ann

fin

ann

the

19

tha

Ra hat at the poi f

pur ic e sense, too high 

(owing to interest rates being, in some sense, too low). Also, if they purchase fixed 

nominal an

Bu

the

a p

rep

an

rat

Bu

 

. 

roduct sold in the voluntary market, two specific areas of concern have been 

hlighted about fixed immediate life annuities: they are costly for many potential 

nuitants, and they are risky. 

The first concern has been invest

0 ese authors confirm that immediate life annuities sold in a voluntary market 

 subject to adverse selection: that is, the tendency of individuals in poor health (with 

paired longevity prospects) to avoid life annuities. This tendency leads to an increase 

annuity prices of about 10 percent as insurers must anticipate annuitants with a longer 

pected lifespan than average individuals in the general population. In addition, there 

 administrative and sales costs embedded in annuity prices, particularly for those 

nuities sold in the individual (as opposed to the group) market. Yet the authors also 

d that an index of actuarial fairness (or money’s worth as they call it) of individual 

uities has improved substantially over the decades of the 1980s and 1990s. A recent 

ding on this score, in Poterba and Warshawsky (2000), indicated that, using projected 

uitant mortality and government bond rates as the benchmark, life annuities issued in 

 individual market in the United States, by some hundred insurance companies, in 

98 have had an average money’s worth of nearly one. 2 

Burtless (2000) has expressed the second concern. The risk referred to here is not 

t, once a fixed life annuity is purchased, regular income payments will not be paid. 

ther, it is the risk t nt in time they retire, workers may ind it expensive to 

chase nominal fixed annuities because annuity pr es will be, in som

nuities, workers will be exposed to the risk of uncertain future inflation. 

rtless claims that these risks, combined with the more conventional investment risk in 

 accumulation phase, are so significant and daunting that “they challenge the ability of 

ension system based solely on individual accounts to deliver reliable income 

lacement in old age” (p. 9). 

To back up this claim, Burtless produces calculations of account balances and 

nuity income, based on certain assumptions and annual data on asset returns, interest 

es, and price inflation over the period from 1871 through 1999. In his empirical work, 

rtless emphasizes the variability of asset returns, and hence the variability of account 

 2

 A escription for reducing the cost of adverse selection in immediate annuities is to combine long-term 

car nsurance

attr

oth

this

4

 O

for

investigated. See http://www.phil.frb.org/files/spf/cpie10.txt. 

 pr

e i (“LTCI”) with the life annuity. The reduction in cost occurs because the integrated product 

acts those individuals with lower-than-average life expectancies so that they gain access to LTCI not 

erwise available to them. See Murtaugh, Spillman, and Warshawsky (2001) for empirical evidence on 

 point. 

ur inflation forecast series uses the Blue Chip survey for 1983 through 1991Q1, the Livingston survey 

 1990Q2 and 1991Q2, and the Survey of Professional Forecasters for the remainder the time period 
5

balances at the point of retirement. He also mentions, however, the importance of 

flu

sim

ret

the

abo

hig

Em y

ctuations in long-term interest rates which determine annuity prices. He notes that the 

ulated account balance/ labor earnings ratio was about the same for a worker who 

ired in 1982 as one who retired during the Great Depression. Yet Burtless found that 

 replacement rate provided by the defined contribution plan of the 1982 retiree was 

ut two-thirds larger because interest rates (and hence, annuity income) were so much 

her in the early 1980s than in the early 1930s. 

pirical Evidence: Simulated and Actual, Monthly and Dail

inal 

annuity pays a constant stream of payments, generally monthly, to an individual, or, in 

the ase of 

no inal an

pur

of 

wi

an

str

month (or day) during the period of our analysis. (See the Appendix for more details.) 

For the mo

life

fre

im

det

mo

an

of 

wi

gu

ann

Mo

im

65- on the joint-andsur ivor annuity because most households enter retirement as married couples. For 

ex ivor annuity issued to a 

65- er 2002. Over the entire 

tim period, the monthly nominal initial payment for a joint-and-survivor annuity 

av ed $7

pay

In return for a single premium to the insurance company, the fixed nom

 c a joint-and-survivor annuity, a couple. An increasing annuity is also a 

m nuity, but its payments increase at a fixed rate determined at the time of 

chase. Finally, an inflation-adjusted annuity has payments that increase with the rate 

inflation actually experienced. Obviously, increasing and inflation-adjusted annuities 

ll have lower initial payments than the fixed annuity for a given premium. 

Our simulated annuity payments are produced by a model which considers the 

nuitant mortality rates projected using Social Security cohort tables and the full term 

ucture of implied spot interest rates based on Treasury securities at the end of every 

st part, we use simulated annuity payments because data on actual prices on 

 annuities issued to 65-year-olds is not available for most of the time horizon for the 

quencies we desire, nor for the annuity types (increasing and inflation-adjusted) we 

agine for the United States. The simulated annuity payments reflect the factors 

ermining the changes in annuity prices over time – interest and mortality rates. For the 

nthly simulations shown below, we consider only straight life annuities, that is, those 

nuities whose payments stop when the annuitant dies. In the daily simulations, because 

the nature of the product for which we have actual payment data, we consider annuities 

th guarantee periods; that is, annuities whose payments continue for the length of the 

arantee period if the annuitant dies before the end of the period and for life if the 

uitant dies after the end of the guarantee period. 

nthly Simulations: Volatility in Initial Payments 

Figure 1 shows the monthly payment per $100,000 single premium for nominal 

mediate fixed life annuities, simulated over the period 1983 through 2002, issued to 

year-old male and female individuals and couples. We focus 

v

ample, the payment was as high as $1,148 for a joint-and-surv

year-old couple in May 1984, and as low as $535 in Septemb

e

erag 42 and had a standard deviation of $131. 

Besides range and deviation, another way of showing the volatility of annuity 

ments is to calculate one-year differences in monthly payments from nominal 
6

immediate fixed joint-and-survivor annuities simulated over the 1983-2002 period. This 

sta

pur

be 

Although in our simulated pricing for nominal and increasing annuities we employ the 

en e horiz

Tr

fig

the

ach

fai

ch investigate whether a nominal 

fix annuity with monthly payments increasing based on a forecast of experts of longrange (10-y

add

inf

no

sim

individuals and couples. We again focus on the joint-and-survivor annuity because most 

households

hig

an

ini

de

ind

in 

inc

co he one-year differences can be large – as high as +26% in 

September 1994 and as low as -33% in March 1986 – actually greater volatility than the 

nominal fix

no

fro

tim

av

ye

thr ominal joint-and-survivor immediate fixed annuities. The 

vo tility is reduced considerably – the worst observation is about -13% in June 1987, 

tistic might also be considered a measure of envy or regret resulting from the ill-timed 

chase of a life annuity. As seen in Figure 2, one-year differences are volatile and can 

large – as high as +21% in September 1994 and as low as -28% in March 1986. 

Figure 3 shows the source of the volatility of annuity payments – interest rates. 

tir on of implied spot interest rates derived from the full maturity spectrum of 

easury securities traded at the end of the month over the period 1983-2002, in the 

ure we only show one illustrative rate – the implied spot rate for a bond maturing in 

 twentieth year. Here we convert the annuity payment from monthly to annual to 

ieve comparability with interest rates. Clearly, annuity payments track interest rates 

rly closely, and show similar volatility. 

 The volatility in nominal interest rates can come from many sources, including 

anging inflation expectations. Hence, we decided to

ed 

ear average) inflation at the time of purchase would exhibit less volatility.4

 In 

ition, we wanted to see whether this increasing annuity would adequately address 

lation risk during the retirement period, another aspect of annuity risk. 

Figure 4 shows the initial monthly payment per $100,000 single premium for 

minal immediate life annuities increasing with an initial 10-year inflation forecast, 

ulated over the period 1983 through 2002, issued to 65-year-old male and female 

 enter retirement as married couples. For example, the initial payment was as 

h as $779 for a joint-and-survivor annuity issued to a 65-year-old couple in May 1984, 

d as low as $406 in September 2002. Over the entire time period, the monthly nominal 

tial payment for a joint-and-survivor annuity averaged $526 and had a standard 

viation of $72. 

The increasing annuity does not reduce the volatility of initial payments. As 

icated above, the range and standard deviation of payments are large. Also, as shown 

Figure 5, the one-year differences in monthly initial payments from immediate fixed 

reasing joint-and-survivor annuities simulated over the 1983-2002 period exhibits 

nsiderable volatility. T

ed annuity. Of course, the increasing annuity has longer duration than the 

minal fixed annuity. 

Finally, we consider an alternate strategy to reduce volatility in initial payments 

m nominal fixed (and increasing) annuities, namely, phased purchases over a short 

e period. In particular, we consider a three-year purchase period, represented here by 

eraging the simulated nominal payments over the same month in three consecutive 

ars. In Figure 6, we show one-year differences in initial monthly payments from a 

ee-year phased purchase of n

la
7

and, more recently, one-year differences were rarely over 6% in either positive or 

ne

 Monthly Simulations: Inflation Risk 

ng annuity did during the 1983-2002 

period in covering inflation risk.5

 As indicated in the figure, forecasts by experts 

consistently

did

ex

init

inf xist in the United Kingdom 

and it is technically possible to issue them in the United States owing to the existence 

sin 1997 

the

by

mo

lik

be

na

mo

 

inf

be

rea et has somewhat 

lim d depth. Several important caveats result: Our estimates of prices of inflationad

ma

inf

the

ad

vo

ex e-year differences in initial monthly payments are 

shown for the inflation-adjusted annuity. The maximum one-year differences is under 

10% in eith

ma

tim

 

gative directions. 

Figure 7 illustrates how well an increasi

 overestimated 10-year inflation until late 1998. Hence, an increasing annuity 

 a more than adequate job of covering inflation risk, at least according to recent 

perience. The trade-off for a rate of increase above actual inflation would have been an 

ial monthly payment lower than necessary. 

An obvious solution to the problem of post-retirement inflation risk is an 

lation-adjusted immediate life annuity. Such annuities e

ce and 1998 of Treasury inflation-protected securities (TIPS). Nevertheless, 

se annuities are not widely issued in the United States.6

 Moreover, evidence produced 

 Brown, Mitchell, and Poterba (2001) from the United Kingdom indicates that the 

ney’s worth of inflation-adjusted annuities is worse than nominal annuities. This 

ely owes to the absence of inflation-protected corporate securities, whose yields would 

 higher than Treasury securities. Inflation-adjusted corporate securities would be the 

tural preference of insurance companies skilled in investing in the corporate bond and 

rtgage markets and issuing such insurance products. 

It should be noted that our annuity pricing methodology is more limited in the 

lation-adjusted case than in the nominal cases, because the time period of analysis only 

gins in 1998 when 30-year TIPS were first issued, and a full term structure of implied 

l spot rates is impossible to calculate. Also the current TIPS mark

ite

justed annuities are probably lower (payments higher) than would obtain in an actual 

rket, and the volatility of our simulation results might differ from that of an actual 

lation-adjusted annuity. 

In Figure 8, the initial monthly payment per $100,000 premium is compared with 

 payment on a nominal fixed annuity. Obviously, the initial payment for the inflationjusted annuity is lower, but it covers inflation risk and it is also substantially less 

latile, at least over the period for which we have data. This lower volatility is also 

hibited in Figure 9, where the on

er a positive or negative direction, a reduction of over 45% relative to the 

ximum one-year differences for the nominal fixed or increasing annuity over the same 

e period. 

 

ctually, for the years since 1993, the jury is still out, as we had to insert the forecasted inflation rate for 

rters where we do not yet have actual experience. 

he Thrift Savings Plan does offer US federal government employees the choice of annuities indexed to 

 CPI up to 3% annual changes, and one major insurer issues to the public an inflation-adjusted annuity. 

5

 A

qua

6

 T

the
8

Table 1 summarizes the main results of our monthly simulations. 

Da y Simulations and Actual Observations 

 To get a rough idea of how well our model simulates payment amounts, we 

co are our results to actual annuity payment data. In Figure 10, we show simulated 

monthly payment rates from annuities issued on a daily basis. In particular, we show the 

monthly initial payment per $100,000 single premium for nomin

an

to 

Fig

10 

sur

im

insurance company. Clearly rates are changed frequently, but not as often as daily 

(al ough t

vo

cal

Fig

relatively small band around 1.0. As interest rates increase, the money’s worth ratios 

de s in interest rates 

slightly in its annuity pricing. A money’s worth ratio so close to one is surprising 

be ses and make a profit. It is feasible 

her

sec

we

mo

int

sim

Str

il

mp

al immediate fixed life 

nuities, simulated over the period February 1, 2002 through December 31, 2002, issued 

65-year-old male and female individuals and couples. Unlike the monthly statistics in 

ures 1 through 9, here we consider immediate life statistics with guarantee periods – 

years for individuals and 20 years for couples. We again focus on the joint-andvivor annuity because most households enter retirement as married couples. 

In Figure 11, we show monthly payment rates on joint-and-survivor nominal fixed 

mediate life annuities actually available over the Internet issued by an AAA-rated life 

th he frequency does appear to pick up toward the end of the period), and hence 

latility is somewhat lower than we have simulated. We use a money’s worth 

culation to judge how close our payments come to those of this particular company. 

ure 12 shows the money’s worth ratios (actual payment over simulated payment) in a 

cline somewhat; apparently, this insurance company lags change

cause the insurance company must cover its expen

e, however, because the insurance company likely invests in long-term corporate 

urities earning yields higher than the interest rates based on Treasury securities that 

 use. It is also possible that this insurance company has alternative, less conservative, 

rtality views than ours, which are based on the Social Security Administration’s 

ermediate projections of improvements in life expectancy. In any case, our 

ulations follow the level and trend in the actual payment data very closely. 

ategies and Possible Policy Implications

We posed a set of questions at the beginning of this paper, on whether the risks 

arising from defined contribution plans are too large, are avoidable, or are worth the 

trade-off for other advantages obtained. As applied to life annuities, we transposed these 

qu ainly in terms of the volatility of initial retirement payments, over time, 

pro nd increasing annuity income over 

the ecent time horizon is generally not as large as that cited by Burtless when he 

co ared t

ex

red

def

rat

estions m

duced by annuities. Clearly the volatility of fixed a

 r

mp he early 1930s and early 1980s. Nevertheless, by some measures (for 

ample, annual differences), it can be significant. What are the options available to 

uce the effect of this volatility, while still obtaining the considerable advantages of 

ined contribution plans? 

As we saw in the prior section, because of the lower volatility of real interest 

es, inflation-adjusted annuities have much lower volatility than nominal fixed and 
9

increasing annuities, and hence represent lower risk in the sense that we are discussing. 

In 

for

an

ov

cu

the

by

pay

res

tion is to phase the purchase of fixed annuities over a short period of 

tim the prior section, this smoothing of purchases reduces the volatility 

of initial annuity payments over time. There is presumably some increase in 

ad nistrat

co

lab

pur

A 

life

fix

acc

sm ment rates by basing annuity prices on moving averages 

of long-term interest rates over short time periods, say three or four months. Although it 

ma be diff

to achieve t

som

wi

he

its

the

bid

int

and

va

co

the

vo annuities occurs after the initial payment, when the underlying asset 

portfolio ch ges value, and indeed that is the advantage of fixed annuities, whether 

nominal or i

rec

addition, these annuities have the obvious advantage of providing excellent coverage 

 post-retirement inflation risk. Probably an important challenge to inflation-adjusted 

nuities is public understanding and appreciation of the size and scope of inflation risk 

er a potentially extended retirement period. Another challenge to these annuities is that 

rrently the only securities that are inflation-protected in the United States are issued by 

 Federal Government; owing to lower returns on government securities than yielded 

 private securities, annuities backed by these securities would tend to offer lower 

ments. This is an area worthy of further exploration by financial engineers and 

earchers. 

Another op

e. As we saw in

mi ive costs and complexity from this strategy, but automation could reduce these 

sts substantially. It is consistent with phased retirement, an important new trend in 

or force participation at older ages. Moreover, it can be implemented with the 

chase of annuities with staggered deferral periods, so that payments begin all at once. 

close variant of this strategy would be a one-time purchase of an immediate variable 

 annuity with the underlying investment pool a diversified collection of medium-term 

ed income securities. 

A modest step toward smoothing the volatility of initial payments could be 

omplished without needing a phase-in purchase by having the insurance company 

ooth its immediate annuity pay

y icult to require this in the individual market, where the competitive pressure 

he highest possible current payment rates leads to mark-to-market pricing, 

e modest smoothing should be possible to achieve in immediate contracts negotiated 

th group retirement plans, at a cost. In particular, the insurance company can pursue 

dging strategies using interest rate futures and options extending three months, or alter 

 investment strategy appropriately. As explained in Poterba and Warshawsky (2000), 

 prices of annuities purchased by the Thrift Savings Plan for its beneficiaries through a 

-out group contract are based on a three-month moving average of government bond 

erest rates. 

Additional research is warranted into other approaches to mitigate annuity risk 

 promote investment diversification generally. There may be a place for immediate 

riable annuities based on more volatile asset classes, such as equities or real estate. Of 

urse, there is no volatility in the initial payments from immediate variable annuities, as 

 initial payment is based on a fixed assumed interest rate, usually four percent. The 

latility from such 

an

nflation-adjusted – they offer more predictability in the stream of income 

eived during retirement. 
10

Further research into the annuity risk and diversification properties of reverse 

annuity mo

div

ind

net

pa

int

por

rtgages could also prove fruitful. Finally, investigation is needed into the 

ersification effects of other asset classes in the accumulation phase, both in the 

ividual account held as part of the defined contribution plan, and in the household’s 

 worth held outside of formal retirement plans, especially owner-occupied housing. In 

rticular, it would be helpful to know more about the appropriate role of bonds and other 

erest-rate sensitive investments in a dynamic investment strategy for an accumulation 

tfolio, as retirement is approached. 
11

Appendix

We use the following formula to derive the monthly payment A from a $100,000

premium im

(1)

mediate annuity: 

100,000

∑= +

599

1 12

1

t [(1 ) ]

t

t

t

i

M

the probability that a 

ving lived to age 65, and it is th

A =

where Mt is person will live t months after exact age 65 conditional

on a e interest rate in period t. 

De treasury

sec rity yield curves. The file contains rates at six month intervals out to 30 years (we

use

W

ann

po

annuitant period tables to cohort tables. We assume that the ratio of cohort mortality risk 

(fo birt

ind

So

(2)

h

The nominal interest rates used in the annuity calculations come from a Treasury

partment summary file of implied spot rates derived on a daily basis from

u

 the last rate in the series to discount after age 95) for dates beginning in late 1982. 

e use the rates on the last business day of the month in our calculations. 

The appropriate mortality rates to use in the calculation are cohort rates for the

uitant population. Because the only published mortality tables for the annuitant 

pulation are period tables, we use the method of Mitchell et al. (1999) to convert the

r the h cohort age 65 in the reference year) to period mortality risk (in the year the

ividual turns 65) for a given age is the same for the annuitant population as that for the

cial Security area population. Specifically, 

a

a t

t

a

a t

t AP

SP

SC AC 65

65

+

+

=

where AC is the annuitant cohort mortality, SP is the SSA period mortality, and so on, a

is the age, t is the mortality table year, 65 ≤ a ≤ 115, and 1918 ≤ t ≤ 1937. (Note that this 

is equivalent to a cline in mortality risk between a person age x in year

y a e - 65) will be the same in the annuitant population as

projected population.) These assumed cohort annuitant 

mo ality rates are then converted to the conditional rates found in equation (1). 

bet

tab

app

tho

Se

 

ssuming that the de

rson age x in year y + (x 

for the Social Security area

nd a p

rt

We created annuitant period life tables for 1984-1999 by linearly interpolating

ween the published 1983 IAM Basic period life tables and the Annuity 2000 basic 

les.

7 We ‘grew’ annuitant tables for 2001 and 2002 from the Annuity 2000 table by

lying the same change in mortality at each age as found in the SSA period tables for 

se years. The SSA period tables came from the background data for the 2002 Social 

curity Trustees’ Report (TR02).8

 

7 D from S 8

 T

ata ociety of Actuaries web site: www.soa.org/tablemgr/tablemgr.asp.

R02 mortality tables include actual mortality for 1983-1999 and projected mortality for 2000-2001. 
12

 Because we want the calculations to represent the price of an annuity as it would 

ha been c

to 

the

20

be

coh

tab

app

int

Re

ve alculated at a particular date (i.e., without the benefit of hindsight with regard 

mortality outcomes), we need cohort tables that are generated from data available in 

 year of presumed purchase. We had cohort tables for 1935 to 1937 from the 2000 to 

02 Trustees’ Reports, respectively. We created a 1927 cohort table by interpolating 

tween 1925 and 1930 tables published in a 1992 SSA Actuarial Study. To anchor the 

ort series, we created a cohort table for 1983 by first interpolating between period 

les for 1980-2040 published in a 1983 SSA Actuarial Study, and then compiling the 

ropriate mortality rates for the 1918 (age 65 in 1983) birth year. Finally, we 

erpolated between the 1918, 1927 and 1935 cohort tables to fill in the missing years. 

ferences

John Ameriks, Robert Veres, and Mark Warshawsky, “Making Retirement Income Last a 

Lif l of Financial Planning, December 2001. 

Fe

Se

Se

Jef

An

Jeffrey Brown, Olivia Mitchell, and James Poterba, “The Role of Real Annuities and 

Ind

Ma

Ch

Ga

So

Jos

Stu ber 1983. 

Ol

on

December 1999, pp. 1299 – 1318. 

Ch

An

Ris and Insurance, 68(2), June 2001, pp. 225 – 254. 

Jam

Ind r, Administrative Aspects of Investmentetime,” Journa

licitie Bell, Stephen Goss, and Alice Wade, "Life Tables for the United States Social 

curity Area: 1900-2080," Actuarial Study No. 107, Office of the Actuary, Social 

curity Administration, August 1992. 

frey Brown, Olivia Mitchell, James Poterba, and Mark Warshawsky, The Role of 

nuity Markets in Financing Retirement, Cambridge, Mass.: MIT Press, 2001. 

exed Bonds in an Individual Accounts Retirement Program,” in John Campbell and 

rtin Feldstein, editors, Risk Aspects of Investment-Based Social Security Reform, 

icago: University of Chicago Press for the NBER, 2001. 

ry Burtless, “Social Security Privatization and Financial Market Risk,” Center on 

cial and Economic Dynamics Working Paper No. 10, February 2000. 

eph Faber and Alice Wade, "Life Tables for the United States: 1900-2050," Actuarial 

dy No. 89, Office of the Actuary, Social Security Administration, Decem

ivia Mitchell, James Poterba, Mark Warshawsky, and Jeffrey Brown, “New Evidence 

 the Money’s Worth of Individual Annuities,” American Economic Review, 89(5), 

ris Murtaugh, Brenda Spillman, and Mark Warshawsky, “In Sickness and In Health: 

 Annuity Approach to Financing Long-term Care and Retirement Income,” Journal of 

k

es Poterba and Mark Warshawsky, “The Costs of Annuitizing Retirement Payouts in 

ividual Accounts,” in John Shoven, edito
13

Based Social Security Reform, Chicago: University of Chicago Press for the NBER, 

20

Pre ident’s Commission to Strengthen Social Security, Report: Strengthening Social 

Se

00, pp. 173 – 200. 

s

curity and Creating Personal Wealth for All Americans, December 2001. 
14

Table 1. Simulated Initial Monthly Payments, Joint & Survivor Annuity, 1983-2002 

 

Nominal Increasing 

Phased 

Purchase 

InflationAdjusted* 

Average $742 $526 $736 $492 

Standard 

Deviation 

$131 $72 $104 $21 

Range $535 - $1,148 $406 - $779 $578 - $1014 $437 - $529 

Max. One-Year 

Difference 

-28% / +21% -33% / +26% -13% / +5% -10% / +7% 

* April 1998 to December 2002 
15

Figure 1

Monthly Payment per $100,000 Single Premium

Nominal Immediate Fixed Annuity: 1983-2002 Simulations

$0

$200

$400

$600

$800

000

200

400

Jan-83Jan-84Jan-85Jan-86Jan-87Jan-88Jan-89Jan-90Jan-91Jan-92Jan-93Jan-94Jan-95Jan-96Jan-97Jan-98Jan-99Jan-00Jan-01Jan-02

$1,

$1,

$1,

Male Individual

Female Individual

Joint & Survivor

Standard deviation of payment:

 Males: $ 142.80

 Females: $ 135.33

 Joint: $ 130.96

Figure 2

One-Year Differences in Monthly Payments

Nominal Immediate Fixed Joint & Survivor Annuity:

1983-2002 Simulations

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

Jan-84Jan-85Jan-86Jan-87Jan-88Jan-89Jan-90Jan-91Jan-92Jan-93Jan-94Jan-95Jan-96Jan-97Jan-98Jan-99Jan-00Jan-01Jan-02

Percentage
16

Figure 3

Interest Rates and Annual Payment as Percentage of Single Premium

Nominal Immediate Fixed Joint & Survivor Annuity:

1983-2002 Simulations

0

2

4

6

8

10

12

14

16

Jan-83

Jan-84Jan-85

Jan-86

Jan-87

Jan-88

Jan-89Jan-90

Jan-91Jan-92

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97Jan-98Jan-99

Jan-00

Jan-01

Jan-02

Percentage

Percentage of Premium

Spot Rate in 20th Year

Figure 4

Initial Monthly Payment per $100,000 Single Premium

Immediate Fixed Annuity Increasing with

Initial 10-year Inflation Forecast

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

Jan-83

Jan-84

Jan-85

Jan-86

Jan-87

Jan-88

Jan-89

Jan-90

Jan-91

Jan-92

Jan-93

Jan-94

Jan-95

Jan-96

Jan-97

Jan-98

Jan-99

Jan-00

Jan-01

Jan-02

Age 65 Male Individual

Age 65 Female Individual

Joint & Survivor (Age 65 Couple)

Standard deviation of payment:

 Males: $ 84.25

 Females: $ 75.51

 Joint: $ 72.03
17

Figure 5

One-Year Differences in Initial Monthly Payments

Immediate Increasing Joint & Survivor Annuity:

1983-2002 Simulations

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

35%

Jan-84Jan-85Jan-86Jan-87Jan-88Jan-89Jan-90Jan-91Jan-92Jan-93Jan-94Jan-95Jan-96Jan-97Jan-98Jan-99Jan-00Jan-01Jan-02

Percentage

Figure 6

One-Year Differences in Initial Monthly Payments

Nominal Fixed Joint & Survivor Annuities Purchased over Three Years:

1983-2002 Simulations

-15%

-10%

-5%

0%

5%

10%

15%

Jan-86

Jul-86

Jan-87

Jul-87

Jan-88

Jul-88

Jan-89

Jul-89

Jan-90

Jul-90

Jan-91

Jul-91

Jan-92

Jul-92

Jan-93

Jul-93

Jan-94

Jul-94

Jan-95

Jul-95

Jan-96

Jul-96

Jan-97

Jul-97

Jan-98

Jul-98

Jan-99

Jul-99

Jan-00

Jul-00

Jan-01

Jul-01

Jan-02

Percentage
18

Figure 7

Actual versus Forecast 10-year Average CPI Inflation

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Percentage

Projected 10yr Average

Actual 10yr Average

Note: Beginng in 92q3, actual average incorporates 02q2 forecast.

Figure 8

Initial Monthly Payment per $100,000 Premium

Inflation-Adjusted Annuity: 1998-2002 Simulations

$900

$0

$100

$200

$300

$400

$500

$600

$700

$800

Apr-98

Jun-98

Aug-98

Oct-98

Dec-98

Feb-99

Apr-99

Jun-99

Aug-99

Oct-99

Dec-99

Feb-00

Apr-00

Jun-00

Aug-00

Oct-00

Dec-00

Feb-01

Apr-01

Jun-01

Aug-01

Oct-01

Dec-01

Feb-02

Apr-02

Jun-02

Aug-02

Oct-02

Dec-02

Male Individual, Nominal

Male Individual, Inflation-Adjusted

Female Individual, Inflation-Adjusted

Joint & Survivor, Inflation-Adjusted
19

Figure 9

One-Year Differences in Initial Monthly Payment

Inflation-Adjusted Joint & Survivor Annuity:

1998-2002 Simulations

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

May-99

Jul-99

Sep-99Nov-99

Jan-00

Mar-00

May-00

Jul-00

Sep-00Nov-00

Jan-01

Mar-01

May-01

Jul-01

Sep-01Nov-01

Jan-02

Mar-02

May-02

Jul-02

Sep-02Nov-02

Percentage

Figure 10

Monthly Payment per $100,000 Premium, Nominal Fixed Annuity

(with 120 month guarantee period for individuals, 240 months for J&S)

Daily Simulations, 2/1/02 to 12/31/02

$800

$400

$500

$600

$700

2/1/02

2/15/02

3/1/02

3/15/02

3/29/02

4/12/02

4/26/02

5/10/02

5/24/02

6/7/02

6/21/02

7/5/02

7/19/02

8/2/02

8/16/02

8/30/02

9/13/02

9/27/02

10/11/02

10/25/02

11/8/02

11/22/02

12/6/02

12/20/02

Male Individuals

Female Individuals

Joint & Survivor
20

Figure 11

Monthly Payments per $100,000 Premium, Nominal Fixed Annuity

(120 month guarantee for individuals, 240 months for J&S)

Daily Internet Quotes, AAA-rated Life Insurance Company, 2/1/02 to 12/20/02

$400

$500

$600

$700

$800

2/1/2002

2/15/2002

3/1/2002

3/15/2002

3/29/20024/12/2002

4/26/2002

5/10/2002

5/24/2002

6/7/2002

6/21/2002

7/5/2002

7/19/2002

8/2/2002

8/16/20028/30/20029/13/20029/27/2002

10/11/2002

10/25/2002

11/8/2002

11/22/2002

12/6/2002

12/20/2002

Male Individuals

Female Individuals

Joint & Survivor

Figure 12

Daily Money's Worth Ratios, Nominal Fixed Annuity

(actual payment / simulated payment)

0.90

0.95

1.00

1.05

2/1/2002

2/15/2002

3/1/2002

3/15/2002

3/29/2002

4/12/2002

4/26/2002

5/10/20025/24/2002

6/7/2002

6/21/2002

7/5/2002

7/19/2002

8/2/2002

8/16/2002

8/30/2002

9/13/2002

9/27/2002

10/11/2002

10/25/2002

11/8/2002

11/22/2002

12/6/2002

12/20/2002

Male Individuals

Female Individuals

Joint & Survivor

1.10