Is a pure TIPS strategy truly risk free?

• DOI: http://doi.org/10.1016/j.rfe.2015.09.003
• Date: 01 January 2016
• Published date: 01 January 2016
• Author: Paul J. Haensly

Is a pure TIPS strategy truly risk free?

Paul J. Haensly ⁎

Collegeof Business and Engineering,The University of Texas of the PermianBasin, 4901 E. University Blvd.,Odessa, TX 79762, USA

abstractarticle info

Articlehistory:

Received17 June 2014

Receivedin revised form 8 March 2015

Accepted24 September 2015

Availableonline 3 October 2015

JEL classification:

G2

Keywords:

Inflation-indexed bonds

TIPS

Shortfallrisk

Portfoliomanagement

Inflation

ATreasuryInflation-ProtectedSecurity (TIPS) is virtuallyrisk free. As an obligationof the U.S. Treasury,it is most-

lyfree of default risk. As an inflation-indexedsecurityheld to maturity,it is risk free in terms of purchasingpower.

However,investing in a TIPS-onlyportfoliofor retirement is not riskfree. This paper presentsthe results ofa sim-

ulationanalysis designed toevaluate the performanceof a portfolio of inflation-indexed Treasurycoupon bonds.

This study demonstrates that significant shortfall risk exists for TIPS-only portfolios across a range of savings

plans and thesecurities selection rules.

© 2015 ElsevierInc. All rights reserved.

1. Introduction

A portfolio of TreasuryInflation Protected Securities(TIPS) appears

to be an ideal candidate for achievinga target level of real consumption

in retirement.TIPS have virtuallyno default risk and are indexedfor in-

flation.By comparison, stocksexpose investorsto considerable risk,and

even conventionalTreasury bonds held to maturityhave inflation risk.

For thesereasons, ProfessorZvi Bodie argues thatmost investors should

invest most if not all of their retirementsavings in Treasury inflation-

indexed bonds (e.g.Bodie & Clow es, 2003, Chevreau, 2009a, 2009b,

Light, 2009).

This paperevaluates the shortfallrisk of TIPS-onlyportfolios heldfor

retirement.Consider a household earning an incomeat the median for

U.S. households in 2012. Suppos e that their objective is to maintain

the corresponding level of re al income in retirement. This pa per

shows that, across a range of savin gs plans and security selection

rules, the probability is significant that this householdwill not accumu-

late sufficientwealth in a TIPS-only portfolioto achieve its goal.

The mostobvious reason is thatTIPS offer relativelylow real returns.

An investor could boost the levelof savings in the TIPS-only portfolio.

But this paperdemonstrates that an investorwould need to save prodi-

giouslyin order to reduce shortfallrisk to minimal levels. Anothersolu-

tion is to delay retirement. But th e reduction in the probability of a

shortfallgenerally comes at a significantcost in the form of lowerutility

of consumption in retirement as well as loss of leisure time (i.e., less

time in retirement). Social Security benefits reduce shortfall risk, but

an investor who savesfor retirement in a TIPS-only portfoliostill must

contributeat high levels in order to minimize thisrisk.

Low real returns are not the only factor. Uncertainty about future

real yields creates uncertainty in how much real savings are required

to meet the investor's objectives. The analysis in this paper takes this

factor into account by simulating uncertain real yieldsover time. This

paper also examinesthe effects on shortfall risk of market friction and

risk of involuntary, early permanentretirement (e.g., due to disability).

In addition, not all TIPS selection str ategies perform the same. This

paper shows that the choice of security selection rules can have a signif-

icant effecton shortfall risk.

2. Material andmethods

2.1. Simulatedinvestors

This paper evaluates investment performance in terms of shortfall

risk.This approach isconsistent with Bodieand Clowes (2003),whojus-

tify anall-TIPS portfolio on thegrounds that it minimizesthe risk of fall-

ing short of one'sretirement goals. Supposethat investors are savingto

buy an inflation-indexed annui ty at retirement. Shortfall risk can be

measured as P{ω:C

t(S;ω)

(S;ω)bχ}, where Sis a strategy in the invest-

ment strategy space, Θ;ωis a simulated histo ry for one investor;

t(S;w) is the actualdate of retirement; C

τ

(S;w)istheinflation-indexed

monthly consumption supported by an immediate inflation-indexe d

annuity purchased at time τ,givenstrategySfollowed by the investor;

Reviewof Financial Economics28 (2016) 1–20

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E-mailaddress: haensly_p@utpb.edu.

http://dx.doi.org/10.1016/j.rfe.2015.09.003

1058-3300/©2015 Elsevier Inc. All rightsreserved.

Contents listsavailable at ScienceDirect

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journal homepage: www.elsevier.com/locate/rfe

and χis the minimumacceptable levelof real monthly consumptionin

retirement.Equivalently,we can reformulatethis probabilityin terms of

actual pre-tax real retirement incomeversus an income target. In this

paper,the latter interpretation generallyis more convenientfor the pur-

pose of comparingretirement outcomes withthe level of monthly sav-

ings beforeretirement.

For consistency when comparing simulatedinvestor histories, real

values arein terms of purchasing powerat the investor's 25thbirthday,

regardlessof when the investorstarts and stopssaving. Hence, through-

out this paper, theterm “real value”refers to the investor's purchasing

power at age 25 unlessI specify otherwise.

This paperaddresses a claim about shortfallrisk of TIPS-only portfo-

lios.However, expectedutility of each strategyis reported as an alterna-

tive measure of the relative benefits when comparing two strate gies

with different shortfall risk. Results are for a time separable utility of

consumption in retirement, whe re the utility function is the natural

log of consumption. Expected utility at retirement is discounted back

to theinvestor's 25th birthdayin all cases (using the sametime discount

factor applied to calculate the expected utility) for consistency when

comparing investors withdifferent retirement dates. In order to focus

on standard of living in retirement, b equests have no utility in the

analysis.

For convenience in the analysis,I replace monthlyreal after-tax con-

sumption in retirementwith monthly real pre-tax retirement income.

Thisincome may arise solelyfrom a TIPS-onlyretirement portfolioliqui-

dated to purchase an inflation-indexed annuity, or it may also include

other inflation-indexed retirement income such as Social Security ben-

efits. With the natural log of utility and th e size of payments in this

study,the effect of shifting fromafter-tax consumptionto before-tax in-

come on utility is small. For example,if monthly pre-tax annuity pay-

ments are $4000 and the effective average tax rate is 10%, then the

ratio of the log of consumptionto the log of annuity payment is 0.987.

Moreover, the effectis proportional and thus does not change relative

ordering of expected utilities. Hen ce, an analysis of shortfall risk in

terms of pre-tax retirement inc ome at the median household leve l

willlead to approximatelythe same conclusionsin this paperas an anal-

ysis in terms of after-tax consumption.

A simulated investor adopts a lifetim e investment strategy that

consists of a savings plan and a securitiesselection rule. A savings plan

eitherconsists of constantmonthly real dollar contributions or monthly

real dollar contributions that gr ow at a constant rate. Each month

duringthe accumulation phase,the investor pools the newcontribution

withcash flowsfromcouponpaymentsandparfrommaturingTIPSand

attempts to invest in TIPS that satisfy the securityselection rule. In all

cases, the investor buys an in flation-indexed immediate ann uity at

retirement.

Each investment strategy isevaluated under three scenarios: (a) no

secondary market frictionand no risk of involuntary early retirement;

(b) secondary market friction and no risk of involuntary early retire-

ment;and (c) secondarymarket friction andrisk of involuntaryearly re-

tirement. When the simulated investor is at risk of involuntary early

retirement, therisk begins at age 52. This risk is based on theNational

Institute on Agingsurvey data reported by Hodes and Suzman (2007).

The probability of involuntary retire ment in each month after the

investor's52nd birthdayis determined bya quadratic modelfittoannu-

al data from Figure 2-2, “Retirement Pattern for Career Workersin the

First HRS Cohort: 1992–2002.”Although this data includes retirement

for all reasons, health was the primary f actor in early retirement for

more than half of all men and more than one thi rd of all women in

the survey. Achieving sufficien t financial wealth does not appear to

have been a significant factor in the reported retirement rates,because

morethan one third of respondentssaid that theyhad saved nothing for

retirement,and three-fourthssaid that they had not savedenough. The

survey data is for retirement in the age range 5 2 to 70 years; in the

simulation, the probability of in voluntary early retirement aft er the

70th birthdayis assumed to be the same as the rate at age 70.

To determinethe monthly inflation-indexed annuitypayment that a

given level of wealth can buy, the simulator calculates the immediate

pension annuity factor, assuming disc rete, real monthly payouts

conditionalon the investor's age at retirement. (Pleasesee Appendix A

for details.) To determine the re al payout, the simulator divides the

investor'swealth by the immediatepension annuity factor.The follow-

ing simplifyingassumptions apply to all cases.

•The investor saves in a tax-deferre d retirement account, and the

annuity at retirement is held in this account. Th is assumption is

consistentwith the growing roleof tax-deferred definedcontribution

plans in the UnitedStates.

•The investor has an accumula tion phase before retirement and a

payout phase after retirement.The investor has earned income only

during the accumulation phase. This assumption is reasonable,

because earnedincome typically falls sharplyat retirement.

•The investoruses all wealthin the retirement accountto purchase the

annuity at retirement. Henc e, strategies only concern in vestment

decisionsin the accumulation phase.

•The annuityis indexed with no lag to the ConsumerPrice Index for All

Urban Consumers,non-seasonally adjusted (CPI-U).The annuity has

no risk of default and no insurance featu res. Also, assume that the

CPI-U tracksthe investor's personal purchasing power in retirement.

•The annuityis the investor's only sourceof income in retirement with

one exception.Defined benefit pensionsand income from working in

retirement are notconsidered in this analysis. To the extentthat an-

other source of inflation-indexed incom e is available, the investor

could lower the target real consumption that must be supported by

the retirementaccount. Due to the importanceof Social Security ben-

efits tomany retirees, I evaluatethe effect on shortfallrisk if inflation-

indexed SocialSecurity payments are available.

•Probability of death is modeled as a random event c onsistent with the

mortality rates in the Society of Actuaries (2014). Mortality rates in

this simulation are unisexrates for the total U.S.population calculated

as a simple average of the Societyof Actuaries (SOA) mortality rates

for men and women.I splice the SOA series for juveniles, employees,

and healthy annuitants.

•Calculationof shortfall risk isbased on real annuity paymentsexpect-

ed at time of retirement.

2.2. Target savings

In the simulation, I set the target realdollar, pre-tax retirementac-

count payout equal to $51,915 per year or, equivalently,$4326.25 per

month. This value is the median pre-tax annual income among U.S.

households in 2012 (Noss, 2014). Throughout this paper, “median pre-

tax family income”refers to this dollar amount which also is defined to

be in age 25 dollars from the perspective of the simulated investor.

A pair of important relatedquestions arises concerning therealism

of this target.What, in fact, is the retirementincome target for a family

retiring with a medianincome; and does a retired household needthe

same real incomein retirement as beforeretirement?

Interpolating from survey data reported by the Employee BenefitRe-

search Institute (Fig. 27 in Helman, Adams, Copeland, & VanDerhei,

2014), the median amount of savings that workers in 2012 thought

they need for retirement was $368,056. Assuming a continuously

compoundedannual real rate of returnof 3% and retirement at age 65,

the correspondingannual real annuity would be $24,657. For the sake

of argument, assume also that this value is the target for workers earning

the median family income just prior to retirement. Although Helman et al.

do not report whether respondents considered Social Security benefits to

count as savings, it is reasonable to assume that the respondents excluded

those benefits when asked about anticipated savings needed.

Expected Social Security benefits co uld range widely. Consider a

worker who began earning the minimum wa ge in 1973 at age 25

2P.J. Haensly/ Review of FinancialEconomics 28 (2016) 1–20