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Contributions Ameriks

Making Retirement Income Last a Lifetime

by John Ameriks, Ph.D., Robert Veres

and Mark J. Warshawsky, Ph.D.

Dr. Ameriks is a research economist at the TIAA-CREF

Institute, the research and education arm of TIAA-

CREF, in New York City, New York, ond is also editor of

Research D\a\ogue, an institute publication. Address

all inquiries to Dr. Ameriks at 730 Third Avenue, New

York, NY WOT7-3206;jameriksmiaa-cref.org.

Mr. Veres is the editor and publisher of \r\5\6e

Information, a newsletter for financial advisors.

Dr. Warshawsky is visiting researcher with the National

Bureau of Economic Research and the Columbia

University School of Business in New York and formerly

director of research at the TtAA-CREF institute.

What portfolio withdrawal ratesh(Hild advisors recommendduring the retirement years—

and how can they make the resultingincome flows last as long as possible?

The reliability of professional retirement|)l;inning advice depends to a great extent onthe integrity of one number: the amount ofan investment portfolio that can be safelyliquidated each year to provide income inretirement. That estimated number,

Acknowledgments

We thank tht- nieiiilK;rs of the TIAA-CRKKInstitute iMnancial AdviHor Advisory- Board,especially Janet Briaud; attendees at a session <ifthe KPA eonfcrcncc in Septemher 20(K): iindthree anonymous referees, ffir valiiahle com-ments and di.scussiuTis. The opinions expressedin this doeumt-nt arc chose of the authors alone,and not necessarily those of TIAA-f^REK. Theauthors are solely responsible for any errors.

The goal of this article is to explore the sustainability of

investment portfolio withdrawals using two distinct

methodologies—historical analysis and Monte Carlo

simulations—to address the risk of extreme longevity.The

article also examines whether annuitizing a portion of client

assets makes it more likely that retirees can enjoy higher

incomes over longer retirements.

expressed either in dollars or as a percentageof assets, fixed or (preferably) inflation-adjusted, determines the optimal size of aclient's target retirement portfolio and there-tV)re also defines the entire accumulationpnx'ess during the working years. On theother side of the retirement line, (tne needsto know how much income can be takenfrom a portfolio u ithout leaving retireesbroke or destitute in tbeir later years.

Unfortunately, professional advisorsdon't have certain knowledge of futureinvestment returns, inflation rates or thelength of their clients' lives. They are,

therefore, required to make educatedguesses about how much income a retire-ment portfolio can ultimately provide.

The goal of this paper is to explore theissue of portfolio liquidation using a com-bination of methods and tools, fromsimple analysis of past experience toMonte Carlo simulations of many thou-sands of hypothetical future scenarios. Inaddition, we explore several possible waysto make the liquidatirin process morestable and certain—in other « ords, toincrease the likelihood that an initial port-folio liquidation rate can be sustained allthe way out to the end of a retiree's life.

Some of this territory has already beenexplored in the professional literature. In his1994 article for this publication, financialadvisor Bill Bengen started with a com-pelling scenario. He noted that Money mag-azine had recommended that investorsspend 5.19 percent of their portfolios in thefirst year of retirement. The magazine alsorecommended that, in subsequent years,they take out the inflation-adjusted equiva-lent of this figure (keeping constant the pur-chasing power of the amount liquidatedfrom the yx)rtfolio) until death. Cnven thedouble-digit yearl)- returns that stock portfo-lios hii\c provided since 1936, tbis 5.29 per-cent figure might appear to IK; reswonableand even conservative. But w hen Bengenperformed a simple spreadsheet analysisusing the historical returns on the poitfolioswith asset mixes that he, himself, was rec-ommending, and assumed that a client hadretired in 1972, he found that the clientwould have completely run out of moneyafter 23 years. A client redrii^ in 1966,using the same strategy, would have beenbankrupted after 18 years.' Ciearl\\ if pastconditions repeated themselves, people whotook Money magazine's ad\ ice could havefound themselves in financial difficulty

Journal of Financial Planning/ December 2001

Ameriks Contributions

In f(illou-up analyses, Bengen foundchat if he changed the asset allocation mix.he chanyeil the sustainable 30-}-car with-drawal rates, w hich tended to peak ataround 4..1 jicrccnt at stock allocitions ofbetween 50 percent and 75 percent." Whenhe looked at rolling 3()-year periods taken(]uarterly rather than annually, he foundthat the highest sustainable withdrawalrates were almost exactly the same, butwere experienced in portfolios whosestoek allocations fell in a narrower rangelietween 55 percent and 65 percent.'

A subsequent analysis by Gordon Pyeoffered similar but not identical results.Insteaii of using actual historical returns,Pye created a Monte Carlo simulationmodel, which evaluated possible setjucncesof future returns on various asset cate-gories. The Monte Carlo simulation toolcreated by Pye basically takes the range;uid sranilard deviation of historical returns;ind inflation and simulates possible futureoutcomes of these variables. O\t'r a rela-tively short ten-) ear retirement period, Pyefound that a stock portfolio was able to sus-tain w ithdraw'uls of four percent of the ini-tial portfolio, inflation-adjusted, in 92 per-cent of the hypothetieal future sequences ofreturns- When the analysis was extended to20-year and 35-year time horizons, the 4percent liquidation rate succeeded morethan 8(1 percent of the time.'

As illustrated by these analyses, itappears that investors cannot be confidentof liquidating more than four percent(inflarion-adjustcd) of their retirement port-folios. It also apjiears that results derivedhom aii;il\sis ot the hi.storiea! sequence ofactual returns may be overly optimistic ifone admits die possibilit)' for a broaderI aiige of possible future return sequences.

These analyses raise some questions. Isit possible to maintain u ithdrawal rateshigher than about four percent, inflation-adjusted, in retirement? By varying themix of assets or by introducing othertypes of investments into the portfolio,can we make the \ earl\- w ithdrawals more

sustainable? Also, given the trend tow ard

earlier retirement dates and longer life

expectancies, and planning for a couple

rather than an individual, how confident

are we that a 30-year time horizon is long

enough? In retirement planning work,

shouldn't we consider sustainable with-

draw al rates over longer time horizons?

Past as Prologue

To start our own evaluation of portfolioliquidation options, we first define a rangeof investment portfolios for evaluation.The analysis that follow s is based on fourdifferent asset portfolios of retirees,defined by their holdings of, respectively,stocks (represented by the S&P 500),bonds (represented by intermediate-termgovernment bonds) and cash (30-day T-bills). We will hereafter refer to a "conser-vative" portfolio defined as one that holds20 percent stocks, 50 percent bonds and 30percent cash; a "balanced" portfolio w ith a40-40-20 mix; a "growth" portfolio allo-cated 60-30-10; and an "aggressive" port-folio allocated 85-15-0. (All return data arefrom Ibbotson Associates,)

1 he reader's eye is directed to FigureI, which shows the amount that couldhave been liquidated from portfolios overrolling monthly 30-year time periods. Thefigures shown are based on actual histori-cal t{)tal returns and inflation; the onlyadjustment is that we assessed a one per-cent annual portfolio management fee tocover the costs of professional manage-ment and advice.' In Figure I, we allowedeach portfolio to grow at the rate dictatedby the historical monthly returns of eachof its asset components. We then calcu-lated how much of the original value ofthe portfolio, expressed as a percentage,could have been taken out each year (inconstant purchasing pow er) so that theportfolio would be completely extin-guished after 30 years. Thus, if the figurew ere ten percent of a $ 1 million jxjrtfolio.

then the income figure in the fust year

would have been $I()O,(H1O a year ($1 mil-

lion times ten percent). l""or each subse-

quent year, we adjusted the dollar amount

being liquidated from the ponfolio to

account for effects of inflation.

This calculation w as made for retireeswho left work in January of 1946 and diedin December of 1976, and then again forretirees who retired in February- of 1946and died in January of 1977, and forroiling-monthl}' 3()-year periods there-after. The calculations in Table 1 end withpersons who retired in January' of 1970and extinguished their portfolio w ith theirlast income check in December 1999.

Figure 1 shows how much this "liqui-dation rate" can fluctuate over time. Aretiree holding an aggressive portfoliocould have retired in the summer monthsof 1949 and li(|uidated the inflation-adjusted equivalent of more than 11 per-cent of the initial amount of the portfolioeach year, for the next 30 years. A retireeholding a conser\'ative portfolio, by con-trast, could have barely taken out theinflation-adjusted equi\ alent of four per-cent of the original portfolio for the fol-lowing 360 months.

It is natural, when looking at graphslike Figure 1. for the reader's eye todefault to the top lines and calculate themaximum liquidation that was possiblewith each of the four portftjlios. But anequally important issue is the variabilityof that portfolio lit|uidation factor. Afterall, retirees standing on the threshold ofeach of these "conceptual" futures had noway of knowing what this graph linewould say about their future prosperity.

We can see that the aggressive portfoliooffered considerably more variability ofpossible liquidation rate than any of theother investment mixes. When comparedwith the alternatives, however, v\e findthat most of the variability w as on theupside, .Although the range of possible liq-uidation rates was much broader w ith tbeaggressive portfolio than the less-volatile

Journal of Financial Planning / December 2001


F I G U R E 1

Maximum Sustainable Inflation-Adjusted Withdrawals for Rolling 30-Year Periods, 1946-1970

100% Conservative (20-50-30)

100% Balanced (40-40-20)

100% Growth (60-30-10)

100% Aggressive (85-15-0)

Note: Fund returns reflect advisor fees of 1 percent annuallySouree:Aulhori'calculation5 based on Ibbotson data

Note:This exhibit shows the maximum inflation-adjusted withdrawals {vertical axis) that could have been taken from each portfolioover the 30-year period beginning at the date on the horizontal axis, given actual historical asset returns and inflation. For example,someone who retired in January 1958 and allocated her portfolio aggressively (85 percent stocks, 15 percent bonds) could havewithdrawn an amount equal to 6 percent of her initial accumulation each year for the next 30 years (adjusting each withdrawal to keepup with inflation), She would have ended up with exactly zero left at the end ol that period. Withdrawals are assumed to be taken at theend of each month, and are expressed on the chart as an annual rate. Data are based on monthly data from Ibbotson Associates.Portfolios rebalanced monthly. Portfolio rates of return reflect the deduction of a one percent annual fee for management expenses

portfolio;;, the aggressive portfolio almost

always outperformed the alternatives as an

income-producing vehicle, and where it

did undeqierform, the difference was rela-

tively small. The same is generally true of

rhe growth pfjrcfolio compared with the

halanced. and the balanced compared with

the conservative. Although investors may

have experienced very different income

results over different time periods, they

were almost always better off financially

with the more volatile portfolios than with

the portfolios that offered more year-to-

year certainty but generally low er returns.

These results, of course, are a reflection (jf

the historical return premium on equities.

There is no guarantee that this pattern

will repeat itself into the future.

Also striking about Figure 1 is how all

of the four (very different) asset mixes

converge sometime in earl)' 1965^and

how the convergence persists through the

end of the graph. Here we are seeing the

effect of the timing of investment returns.

The retirees who left work at any point in

calendar 1964 thnuigh calendar 1969

(when the graph runs out of 30-year peri-

Journal of Financial Planning/December 2001

Ameriks

ods to measure) would have experiencedthe 1973-74 bear market early in theirretirement, The earlier significant negativereturns hit a retirement portfolio, theharder it is to sustain higher liquidationrates, even though, as was the case forpeople retiring in the late 1960s, they ulti-mately experienced some of the highestinvestment returns in history. By the timethose high returns occurred, they didn'thave enough of their [ jortfolio left for it utmatter much.

Based on the historical record, we seethat more conservative portfolios seem tohave offered only limited downside pro-tection and to have severely constrainedthe upside. This may come as someu hatof a surprise to the investment commu-nity', because choosing a more conser\ a-tive portfolio mix has generally been themethod of choice for financial advisors tostabilize future investment returns, and,therefore, the amount that can be takenout of portfolios safely. If this hasn't beeneffective historicalh, then it raises theobvious t|uestion; Is tliere a better way toensure a portfolio u ill be able to provideadequate income throughout retirement?

Back to the (Possible) Future

Before we consider that question, how-ever, « e should recognixe the limitation ofthe historical record, « hich gives us only asingle sequence of returns to evaluate.While we examine data beginning in everymonth from 1946-1999, these data are allbased on the same historical sequence ofreturns, which « ill almost certainly not heexacti)' replicated with any likelihood inthe future. Another, and perhaps superior,way to analyze withdrawal rates is to per-form a Monte Carlo analysis of a largenumber of possible future sequences ofinvestment returns and inflation, based ondata fnmi the past.

In our method of analysis, possiblefuture returns are simulated by randomly

drawing return and inflation data onemonth at a time, with replacement, fromthe historical monthly data (1946-1999)and using these draws to construct a largenumber of possible return sequences. Thisprocedure overcomes the statistical prob-lems of using overlapping multi-periodreturns. We note, however, that in thistype of analysis, returns and inflation fig-ures in different periods are implicitlyassumed to be statistically independent ofeach other.

In the analysis that follows, we listedthe asset class returns and inflation ratesfor each month in the historical recordfrom January 1946 to January 2()()(), andalso each month's change in the Cdnsumcrprice index {CP\). We then drew out, atrandom and with replacement, lO.OOOsequences of up to 50 years of annual his-torical events (involving a total of six mil-lion random draws from the monthly his-torical data). We then measured, invarious ways, how the various [X)rtfolioswould liave evolved over time if we hadwithdrawn 4.5 percent of each portfolio inthe first year, and adjusted the withdrawalamount for inflation thereafter. This 4.5percent figure is chosen based on theBengen and Pye analjses and also on theresults of Figure !, in order to test w hatap|K;ars to be a somewhat aggressive, butputeinially sustainable, withdrawal rateover a variety of historical periods andconditions.

Table I shows a variety of statistics forthe four portfolio mixes under examina-tion." The first column shows the actualcomposition of the portfolio; the readerwill note that these are the same asset classpercentages that w ere used to createFigure 1. 'I he second column lists thenumber of years of portfolio liquidation:the range of retirement periods, in five-)'ear increments, is from 20 years to 40.

The third column shows the meanamount of the original portfolio that thehypothetical retiree has left after with-drawals are made over each time period—

that is, the average amount of wealthremaining in the portfolio. In the case ofthe aggressive portfolio, the mean portfo-lio si/.e of the H),O(K) trials, after 40 yearsof liquidation in retirement, was morethan six times the original portfolio.

I he fourth column calculates the stan-dard deviation of the means shown incolumn three. 'Fhis is an indication of therange of results. Standard deviation is onemeasure of the broad up-and-downswings, as seen in Figure 1. If the meanportfolio value were 0.42 {as it is for the.'0-year liijuidvition of the balanced portfo-lio in 1 able 1). and the standard deviationis O..' 9, then it means that r{)iiyhly two-thirds of thf trials fall hetuccn -.17 (0.42- 0.59) and l.OI (0.42 + 0.59)." In somecases, this is a highly significant figure tow atch, because it measures the certaintyor uncertainty of the mean figure. Forexample, before we take t(K) much comfortfrom the fact that the mean portfolio valueafter 40 years of liquidation is 6.17 timesthe original value, it is helpful to notice,by kH)king at the standard deviationfigure, that at least two-thirds of the trialsresulted in terminal portfolio valuesdefined by an exceptionally high range:-2.S2 to 15.16. Clearly there was plenty ofopportunity for failure.

How should the negative numbers onthe table be interpreted? These are pcrliapsbest thought of as measuring tbe extent towhich a retiree would ha\e to rcK" onfamily or other external sources of fumiingto maintain his or her lifestyle. In much ofw hat follows, the discussion focuses mainlyon the likelih(HKl that a portfolio runs oLitof money. However, one should alsoremember that the rclati\ e size of shortfallsis important: A portfolio that has a modestprobability of being just barely exhaustedafter 40 years of w ithdraw als may be per-cei\ ed as very different from one tbat has asmall chance of leaving retirees with adeficit of two or three times their initialwealth after 4<) ) ears.

The figures presented in the fifth

Joumal of Financial Planning/December 2001


Inflation-Adjusted ^l i f l lHI iptist ics for WealthBased on Annual Witharawafsof 4.5 PercentPortfolio Year Mean Std. Dev. Pr(<0) 5th 10th 50th

Conservative

20% Stock50% Bonds30% Cash

Balanced




Note; All statistics aie inflation-adjusted multiples of the initial accumulation amount. Withdrawals are intl a I ion-adjusted.Source: Authors'calculations based on Ibbotson data.

Notes for Table 1: Table 1 shows the results of a Monte Carlo simulation of 10,000 hypotheticalasset return histories for each of four investment portfolios listed in Column 1. Each history isconstructed by drawing,at random with replacement, 600 months of returns and inflation fromthe actual historical record from 1946-1999, using monthly data from Ibbotson.

The statistics shown describe the remaining wealth portfolio at each point in time (Column 2),assunning annual withdrawal of 4.5 percent of the initial accumulation amount each year, adjustedfor inflation.

The numbers in Columns 3-4 and 6-8 are expressed in multiples of the initial accumulationamount (e.g., for the conservative portfolio, after 20 years, the table shows that the mean amountin the left portfolio is .35. or 35 percent of the initial accumulations).

Column 5 is in percentage points."Mean" is the arithmetic average of the remaining wealthamounts at each point in time across the 10,000 simulations. "Std,Dev."is the standard deviationacross the 10,000 simulations. "Pr(<0)" is the "failure rate," or percentage of simulations in whichthe portfolio had run out of money,

Thecolumnslabeled5th, 10th, and 50th show the amount of wealth in the portfolio at thebottom 5th, 10th and 50th percentile of the 10,000 simulations. Thus, the 50th percentile is theamount of wealth at the exact middle of the distribution of the 10,000 simulations: In half of thesimulations, portfolios had more wealth than is indicated; in the other half, the portfolios had lesswealth than is indicated in this column.

column of the tables are likely to be ofcon.siderable interest to financial advLsorsbecause they sliuw the "failure rate": thepercentage of trials in which the portfolioran out of money before various periodswere concluded. For example, in thegrow th portfolio, the reader can turn tothe 3()-year line, read across to the rightand see tliat at a 4..'i percent (inflation-adjusted) liquidation rate, 12.6 percent ofthe trials result in portfolio extinctionbefore the ->0 years were up. In the aggres-sive portfolio, only 8.4 percent of the trialsrun out of money before the end of 30years, while 14.7 percent of the aggressiveportfolio trials experience failure by theend of 40 years.

The last three columns show the frac-tion of the pnrttolii) that remains at the 5th,10th and 50th percentiles of all trials. Thenumbers in this section are multiples of theinitial portfolio value (adjusted for infla-tion), so numbers larger than one indicatevalues above the starting \ alue, and anumber less than one indicates a smallervalue. Positive numbers (blue) indicate thatthere was still at least some of the [ Mjrtfolioicmaining; negative numbers (red) indicatethat the pt)rttolio has been exhausted.

The pereentile values provide anotherway to assess the likelihood of particularoutcomes. For example, if the . th [xrcentilefigure is equal to one, then in 5 pereent ofthe I(),(K)() trials, the portfolio had a valueless than or equal to its starting value(implying, of course, that in the other 95percent of the trials, the [xirtfolio had anequal or higher value). Of particular note isthe rightmost column. It shows the 50thpercentile, or the median, of the distributionof portfolio values. This is the "halfwayjwint" of the distribution of returns. Asmentioned earlier, if this figure is negative,that means that at least half of the trialsresulted in the poitfolio running out ofmoney before the end of the time period. Anumber greater than /x ro indicates that atleast half of the portfolios were able to sur-vive despite the yearly liquidation.

Joumal of Financial Planning/December 2001

Ameriks Contributions

As the reader explores Table 1, weshould sound ;i notf of caution. Theiiivestiiicnt and infliitioii figures used togenerate these results were taken frompast historical events; there c;in be noassurance that unforeseen economic condi-tions will not change the parameters ofinvestment experience going forward.V\ ith that caveat in mind, the reader cansee thcit these simulations tend to confirmBcngen's and Pye's analyses. The aggres-sive portfolio fails in just H.4 percent of the3()-year Monte Carlo trials, meaning thatit \\ as able to sustain a 4.5 pereent distri-Inition factor in 91.6 pereent of the trials.

I able I expand.s the field of vision con-siderably by examining various time peri-ods and portfolio mixes. We can see. fort'.\;un[)le, that the 4.5 percent liquidationrate begins to look increasingly aggressiveas you move toward less stock-heavy port-folio mi.\es, and it looks nearly .suicidal fortbe conservative portfolio, where the pos-sibility of portfolio extinction before K)years is more tlian 67 percent.

Interestingly enough, the pattern of1 able 1 shov\ .s that for shorter retirementperiods, tlie less volatile (less stock-ori-ented) portfolios offer better ehances ofsur\ ival than the more aggressive alterna-tives. .\fter 20 years, the conservative andbalanced portfolios have a failure rate ofless than I percent, compared with the 1.2percent and 1.7 percent failure rates of thegrow til and aggressive portfolios.

A.S people live longer into retirement,houever, the nioie volatile asset mixesoffer much higlier probabilities that theportfolio will sustain rbc 4.5 pereent infla-tion-adiusted withdrawal rate. Indeed, theaggressive portfolio will support a 4()-yearretirement period, at this liquidation rate,roughly H5 percent of the time. A look atcolumn 6 of Table 1 shows that the fifthpercentage of trials—which defmes theglnoniiest tn'e percent (tf these hypotheti-cal outcomes—are not dramaticalh- differ-ent for the aggressive portfolio than theless stock-heavy portfolios.

However, the appearance of stabilit)' canbe misleading for two rea.sons. First, asmentioned earlier, the projected futuresequenees/trials are derived from historicaldata, which Incorporate the historical equitypremium, which may not be replicated inthe future. Second, even if the premiumsomehow were to remain stable into thefuture, a look at the standard deviations incolumn 4 show s that the more stock-heav)-portfolios come \\ ith a risk of much lower,as well as much higher, potential outeomes.

Making Withdrawals Last

At this point, it seems reasonable to return toone of our original questions: Is there an}-wa)' to make it more likely that a given with-drawal rate can be supported over a long[XTiod? If future returns are comparablew ith past (jnes, then raising the stock portionof the asset mixes appears to afford a higherliquidation factor over longer time [periods.But signifieant areas of unccitaint\- stillremain. The aggiessive portfolio, for exam-ple, fails in more tlian an cit;hth of all trialsover a 4()-year projected time hori/on. Thisis comparable to a 6()-year-old living to ageI(K)—which, given current trends inlongevity, may be an incR'asingly commonscenario for which professionals need to plan.

In addition, higher stoek allocationssignificantly increase the varialiility in theportfolio's value over the retirementperiod. On the downside, this meansincreased risk of portfolio extinction at anearlier age. On the upside, (tne wonderswhether, in the face of an enormous run-up in portfolio \alues, clients wouldn't betempted to abandon what [night seem atthe time to l)e an unnecessarily austere liq-uidation rate. In both eases, the feasibilityof the fixed withdi'a\\'al rate strateg)' isealled into question.

Some elients may be willing to over-look or accept these risks. But even forthose w ith the highest risk tolerance, atsome point, we can no longer raise the

percentage of the portfolio allocated tostocks. And for the more risk-averseelients, it may simply be too much to askthem to tolerate the volatility of an aggres-sive portfolio. In such situations, we needto tind other options that mav have differ-ent characteristics.

The Longevity Factor

Throughout the preeeding diseussion, wehave not really addressed the issue of uncer-tainty reg-arding length of life in retirement,despite the fact that it's hard to overstate theimportance of this souree of uncertainty. Toillustrate, suppose that 1(X) 65-year-oldfinancial planning clients, all ready to retire,all w ith the same investments, w ere facedwith the withdrawal problem we have beendiscussing. K ich could "conscr\'atively" planon living .?0 years in retirement and thenmake w ithdraw als from their resjiective}ioitfolios tliat were expected to stretch themoney out exactly that long (perhaps basedon an analysis similar to that above). Thiswould work well for members of the groupfor w hom this guess about the ultimatelength of life turns out to be exactly right.But for those who live longer than theyexpect, this pnxredure would result in real|iovem' after die "planned for" period.Meanwhile, those who end up living only ashort while in retirement will leave bebind alarge, unplanned estate.

One way to deal w ith this uncertaint)IS for retirees to pool their assets and,therefore, their longevity risk throughimmediate annuities, whieh can convertretirement assets into a guaranteed life-time income stream. Introducing animmediate annuity to a retirement portfo-lio raises a number of questions, but a cru-cial one v\ ould seem to be: Does the pur-chase of an immediate annuity with someof a person's retirement assets have a ben-eficial or deleterious effect on the sustain-ability of these liquidation rates that wehavf alreadv examined?

Journal of Financial Planning/December 2001 M-'Vi


Inflation-Adjusted StatisticsIn Conservative PortfolioAssuming Portfolio Withdrawals + Any Annuity Income = 4.5% Annually

. ... .. PercentileAnnuitizationRate Year Mean 50th

-0.14 -0.09

-0.39 -0.34

-0.67 -0.61

-0.99 ^ -0.91

Note: Statistics are Inflation-adjusted multiples/fractions of the initial accumulation amount. Annuity AiR is 7 percent.WiihdrawaIs/income are adjusted for inflation.Source: Authors'calculations based on ibbotson data.

To investigate tli;it qiicstion, theauthors ran the same 10,000 investment/inflation iterations on different time hori-zons for the same four asset niivcs, ;indextended the format of Table 1 to ineludeannnitizing 25 percent and 50 percent ofthe in\'cstnient portfoho. The monthlyineome pa}'ments from the fixed hfe annu-ity are based on the assumptions that theaniiiiity pool's assets will aehieve anannual rate of return of seven percent aiuithat mortality patterns among the annui-tants will match a recent mortalit)' table.CJiven these assumptions, for a 65-year-oldindividual, the annual annuity paymentsamount to 9.05 percent of the amountannuitized. Wbile prevailing interest rateshave declined in 2001 (making current!)'available annuities more costly), we

believe that this assumption is a reason-able estimate of rates t\'pically availablefrom reputable, competitive annuity-providers. For example, one weli-knownprovider offers (as of February 21, 2001) amonthly fixed annuity for age-65 malesvv'ith income of roughly H.S7 percent ofannuitized assets annually. Assuming thatthe relationship between this company'sproducts and those of other insurancecompanies has remained constant recently,we estimate that the average income pay-ment that a male, age 65, could obtainfrom a fixed annuity was roughly ').}(ipercent as of December 2000." We note,however, that there is considerable varia-tion in available annuity rates and it canpay to shop around. .Also, we note that theannuity provider's fees are already

reflected in the assumed total rate ofreturn, so there is no separate adjustmentfor cost in our analj^sis.

Tables 2. } , 4 and 5 show the results ofall trials tor conservative, balanced,grow th and aggressive portfolios, respec-ti\ ely, u ith 0 percent, 25 percent and 50percent of the initial portfolio used toobtain a fixed annuity. I he most compli-cated part of the calculations is keepingthe yearly amount that is taken out of theportfolio equal in constant dollars despitethe two sources of income (the [lortfoliowithdrawals and the annuity payments).Because we assumed that the annuit)' por-tion ot the ineome flow does not changew ith inflation, we had to raise the amountwithdrawn from the unnannuJtized por-lion of the portfiidio over lime in order tomaintaJEi a constant total amount of infla-lion-adjusied income. .As time gncs on andthe cumulative effects of inflatitin are feltmore strongly, a declining portion ofincome is c<)ming from the annuity and alarger portion from the non-annuitizedportion of the portfolio.

By looking at columns ? and 4, thereader w ill quickl}' sec that the presence ofthe annuit\' does, indeed, offer somereduction in the number of trials thatresult in portfolio extinction. I-"or example,for the conservative portfolio with noimmediate annuity, almost 25 percent ofthe trials lead to failure at a 4.5 percentwithdrawal rate after 25 years. After . 0years, the failure rate is 67.4 percent. Yetif 25 percent of the portfolio is annuitized,those figures droj) to H.H percent and 46.7pereent. respectively. They fall to 1.1 jicr-cent and 1 K.7 percent wbcn 50 percent ofthe portfolio is annuiti/,ed.'

Similar increases in portfolio sustaln-ability can be seen in the other portfolio.The balanced portfolio, with zero annuiti-zation, fails in 23.7 percent of the trialsafter .10 years; with 25 percent and 50 per-eent of the portfolio annuitized, the 30-year failure rate falls to 14.9 (lercent and5.5 percent, respectively. In the growth


Coiilribiilioiis Ameriks

r A B L E 3

Inflation-Adjusted Statistics for WealthIn Balanced PortfolioAssuming Portfolio Withdrawals + Any Annuity Income = 4.5% Annually

AnnuitizationRate Year Mean

Percentile

5th ^ 10th

Note: Statistics are inflation-adjusted multiples/fractions of ihe initial accumulation amount. Annuity AIR is 7 percent,Withdrawals/income are adjusted for inflation,

luthors'calculations based on ibbcitson data;

jjortfolio. the clmnces of f;iiliire fiill from12.6 percent f)vcr 50 years with zero annu-itization to 7.H percent with 25 percentannuitization to 3.3 percent with 50 per-cent annuitization,

Notice that the reduction in unccr-taint)' for the aggressive portfolio isaccompanied h}- relatively modest dropsin the mean terminal wealth after 40years, from 6.17 times the original portfo-lio (with no annuity) to 5.44 (with 25 per-cent annuitized), to 4.72 times the originalportfolio when half the portfolio is annu-itized. There are, however, substantialdrops in the standard deviation of terminaluealth as well: from 14.7 in the unannu-itized case, to 10.9 with 25 percent annu-itized, to 7.4 with 50 percent annuitized.

In fact, while mean terminal wcaltli after40 years falls b)' 24 percent (comparingthe unannuitized case with the 50 percentannuitized case), the standard deviation ofending wealth falls by nearly 50 percent.F.ffeetiveiy, the retiree is trading the possi-bility of extreme!)' large accumulated>Aealth levels for a greater degree of cer-rainty that the portfolio can generateincome throughout his or her lifetime.This leads to an interesting observation:By providing a stable source of income,the fixed life annuity can effectively sub-stitute for the cash or hond part of aretiree's [wrtfolio. This may enable evenvery risk-averse retirees feel more secureabout investing their unannuitized assetsmore aggressively.

Comparing the Historical andMonte Carlo Approaches

Table 6 compares the results of the histor-ical and Monte Carlo approaches to exam-ining the sustainability of a 4,5 percentwithdrawal rate.'"

At first glance, the results of the two;malyses seem very different: For all of theportfolios and at all horizons, the historicalanalysis suggests that the failure rates aremuch higher than the Monte Carlo analy-sis in which there is no annuity. Here itmust be remembered that the historicalanalysis is based on a unique pattern ofevents, in which the bear market of theniid-l"J70s and the liigh inflation of thelate 1970s and early 1980s figure promi-nently. Whether these events will everoccur in the same \\ ay in the future is anopen question; the Monte Carlo analysisreduces the importanee of this historicalpattern. Note also that in the historicalanalysis, the failure rate for the aggressiveportfolio is higher over the 50-year periodsin the sample than it is over the 35-yearperiods. This result demonstrates animportant weakness of the historicalanalysis: there are more rolling 30-yearperiods over the span 1946-1999 than 35-year periods. Thus, the "sample" of 35-year periods does not include those peri-ods beginning in the late 1960s, w hile the"sample" of .30-year periods does. Given

the market performance in the early tomid-iy70s, the result in the table is under-standable. This again serves to highlightthe important advantage of the MonteCarlo analysis: the Monte C arlo examina-tion of the failure rates is based on thesame number of independent trials foreach time period.

Despite the difference in the absolutelevel of the "failure rates" in the twoanalyses, both point to one conclusion:Portfolios w ith a significant stock marketexposure had much higher probabilities ofsustaining systematic \\ itbdrawals longerinto retirement. In addition, the table

Joumalof FinancialPlanning/December 2001


Inflation-Adjusted StatisticIn Growth PortfolioAssuming Portfolio Withdrawals + Any Annuity Income = 4.5% Annually

PercentileAnnuitizationRate Year Mean Std. Dev. Pr(<0)

0% 20

25

30

35

40

25% 20

25

30

35

40

1.16

1.23

1.31

1.43

1.58

1.04

1.12

1.23

1.35

1.50

50% 20

25

30

35

40

0.93

1.04

1.16

1.30

1.46

0.81

1.09

1.44

1.94

2.57

0.65

0.89

1.20

1.59

2.10

0.51

0.72

0.97

1.28

1.71

1.2

5.8

12.6

20.1

26.8

0.4

2.6

7.8

14.3

21.2

5th 10th

0.0

0.6

3.3

8.0

14.1

0.18 t 0.31

-0.03 0.13

-0.29 -0.09

-0.62 -0.36

-1.03 '• -0.70

0.24 ^ 0.35

0.09 0.23

-0.10 I 0.07

-0.34 -0.14

-0.66 -0.39

0.38

0.31

0.20

0.06

0.29

0.19

0.06

-0.11

-0.34 -0.13

SOth

1.00

0.98

0.98

0.96

0.95

0,91

0.92

0.94

0.96

0.95

0.83

0.89

0.93

0.97

1.02

Note: Slatistics are infiation-adjusted multiples/fractionsof the initial accumulation amount. Annuity AIR Is 7 percent.Withdrawals/income ate adjusted for inflation.Source: Authors'calculations based on Ibbolson data.

clearly shows the significaiii: improvementin the "failure rate" that the annuity pro-vides: P'or all time peri(jd.s and for all port-folios, the addition of the annuity leads toa decline in the portfolio failure rates.

Discussion

It ;ippears that Bengen and Pye «LIC siih-stantially correct in their analysis of port-folio sustainahility. Tor 3()-vear retirementperiods, a 4.5 percent withdrawal rate suc-ceeds more than 91) percent of the timeonly if the asset mix is very heavilyweighted toward stocks. Retirees whoselect a more conservative (less stock-heavy) retirement mix might be al)le toachieve slightly more consistency if theyexpect a short retirement, but the proba-

liility of failure v\ ill be dramatically higherover time periods of 20 years or longer.

Our analysis also shows that the 4.5percent withdrawal factor can be sus-tained u ith more eertaintw for longertime periods, by adding the risk-poolingcharacteristics of an immediate annuity tothe overall retirement portfolio. In muclithe same way as asset classes are used toliedtje financial risks, immediate annuitiescan be used to hedye longovit\' risk. It isimportant to note, however, that tlie pool-iiiii of lontjevity risk has consei|iieiiLesother than portfolio withdraw al stability.If the retiree dies early in the retirementyears, after ha\'ing purchaseil an immedi-ate annuity, then tlie investment in thepool eontinues to pay other annuity hold-ers rather than the retiree s heir;*. This

opportunity cost should be assessed beforeany decision is reached regarding thestrucnire ot retirement portfolios."

In addition, the simple fact that theannuity dampens future uncertainty virtu-ally guarantees that there will be lessopportunity for the retiree portfolios toijrow as large as i[) the nnannuiti/.ed ease.The presence of the pooling arrangementiffectively compresses the tails of the dis-tribution ))f future portfolio wealth—making it less likel)' that the investor willgo broke, hut also reducing the size of theaccumulation that will be passed to heirs.

Cliven the trend toward increasedlongevity and the possiliilit\- of majormedical advances in the future, poolingthe risk of longevity offers potential hene-fils that have not been captured by thetables presented here. While tbe portfoliosthat contained no annuities actually ranout of money m tbe years indicatetl intables l-.\ the retirement portfolios thatv\ ere 25 percent or 50 percent inwsted in.iimuities were still making income pa\'-incnrs to the hyprthetical retirees 40 yearsafter they left w ork. l'"ven 50 or moreyears after retirement, the annuities viouldstill be generating income for life, albeiton a noninflation-adjusted basis.

Finally, v\e note that there are at leasttwo important way,s in which furtheranalysis could extend the initial resultspresented here. First, we have notattempted to model the impact of taxes onthe analysis. In some circumstances, theeffect of taxes is a straightforward exten-sion of our results. For example, if aclient's retirement assets were heldentirely in qualified retirement plans,income received would just he lower hy apercentage equal to the income tax rate.'But if assets are held in noru|ualified vehi-cles, the effects of hotli income taxes andcapital gains taxes need to he considered.Ihe interaction of these raxes ma\' haveimportant impMeations tor both the leveland sustainahility of retirement income,optimal portfolio choices and ihe use of

Joumalof Financial Planning/December 2001


Inflation-Adjusted Statistics for WeIn Aggressive PortfolioAssuming Portfolio Withdrawals + Any Annuity Income = 4.5% Annually

AnnuitizationRate Year Mean Std. Dev. Pr(<0}

0% 2.03

2.59

3.39

4.55

6.17

25% 1.77

2.28

3.02

4.02

5.44

50% 1.51

1.97

2.61

3.49

4.72

Percentile

5th 10th 50th

0.21 I " 0.42 [~ 1.60

0.01 0.28 1.87

-0.25 {; O.n I 2.25

-0.59 -0.12 2.78

-1.03 J -0.42 I 3.47

0.29 " 0.45 1.43

0.16 0.37 1.68

-0.02 I 0.26 I 2.07

-0.25 0.12 2.53

-0.57 I -0.07 I 3.17

0.32

0.26

0.15

0.00

-0.20

0.45

0.43

0.37

0.29

0.17

1.24

1.50

1.86

2.28

2.89

NoteiStatisticsaceinfiation-adjusled multiples/fractions of the initial accumulation amount, Annuiiy AIR is 7 percent.Withdrawals/into me ate adju5ted for inflation.Source; Aiithor5'calculfltions based on Ibbotson data.

Description of Tables 2-5: See note to Table 1. Tables 2-5 add an immediate fixed lifeannuity to the analysis. In these simulations, withdrawals are taken from theunnannuitized portfolio in each year only to the extent that annual annuity income inthat scenario falls short of equalling 4.5 percent of the initial total amount, adjusted forinflation.The statistics in the table describe the remaining unannuitized portfolio ineach year (Column 2), in multiples of initial total assets.

immediiite and deferred annuities. Ituould be useful tu examine these effectsin much greater detail.

Second, when discussing annuities inthis article, we have focused exclusivelyon Immediate annuities that pay a guaran-teed, /7.vec/level of income (noninflation-adjusted) for the life of the annuitiint(s).While this type of fixed-income annuitymay be what immediately comes to mindwhen one hears the word "annuit}," othertypes of income-generating life annuitiesare currently available to retirees. In par-

ticular, immediate v;in;i6/t'annuities pro-vide inconif payments ft)r life that periodi-cally change (either up or dow n) to reflectthe realized recent perforniance of what-ever aJisets are held in the annuity's assetpool," Variable immediate annuities basedon stock market investments thereforeallow annuitants to hedge their longevityrisk without giving up exposure to theinvestment risks and returns of the stoekmarket. Further analysis shotild certainlyevaluate the usefulness of this type ofimmediate annuitv as vet another tool to

help retirees maximize their portfolio

income.The debate over how best to deter-

mine, maximize and stabilize the amountof a ponfoliu that can he liijuidarcd inretirement \\ ill eertainly lead pn)tcs,sionalretirement jilanners tow ard a betterunderstanding of the immediate annuityas iincstniLnt variable. This, in turn,should lead to better recommendations,decisions and, perhaps, more prosperousretirements for the clients of financialadvisors w ho v\ ill have to live with thenianv uneertainties of the future.

Endnotes

1. \\ iliiam P. Bengen, "DeterminingWithdrawal Rates Using HistoricalDam," Jouniiil of I-innncial Phmning,January 1994, pp. 14-24,

2. Throughout the Bengen analyses, infla-tion rates w ere measured using changesin the consumer price index.

3, William P, Bengen, "Conser\-ing ClientPortfolios LXiring Retirement, PartIII," journal of I'iniwciiil Phinning,December 1997, pp. 84-97.

4, See Figure 4 in (iordon B. Pye's "Sus-tainable Investment U ithdraw als,"jtHiriiiil of Portfolio Management.Summer 2000, pp, 73-S3, Pye has sul)-sequcntl\' extended his annlysis toincorporate the effects of managementexpenses and taxation on sustainablewithdraw als; see "Adjusting W ith-dravi al Rates for Taxes and Expenses,"Journal of Financial Plannitig, April2001, pp. 126-136.

5, Here, and in all subsequent analyses,no tax effects are calculated.

6. Note that in all analyses, we assumedthat the portfolio has an annualexpense of one percent a year.



What Is The Probability oWith a 4.5 Percent "Total'

Retirement NoPortfolio Period Annuity

ig Out of Moneywal"Rate?

Monte Carlo

No 25% 50%Annuity Annuitized Annuitized

Conservative 20 Years

25 Years

30 Years

35 Years

40 Years

0.9%

24.8%

67.4%

90.1%

97.1%


20 Years

25 Years

30 Years

35 Years

40 Years


3.4%

14.9% I30.3%

46.0%


Aggressive85% Stock15% Bonds0% Cash

Note: Annuity payments + portfolio withdrawals = 4.5 pertentonnitialattumulation.adjusted for inflation.

Description of Table 6: Table 6 compares the results of the historical analysis ofwithdrawal rates with the monte-carlo analysis. Results are shown for the fourportfolios in column 1, and withdrawal periods in column 2.The"Historical"columnshows the fraction of rolling historical periods in which withdrawing 4.5 percent of theinitial portfolio amount (adjusting for inflation with each withdrawal) would haveexhausted the portfolio before the end of the period. The "Monte Carlo" columns showthe fraction of simulations (in cases of 0 percent, 25 percent and 50 percentannuitization) in which the unnannuitized portfolio was exhausted before the end ofthe retirement period. Both the historical and Monte Carlo approaches reflect a1 percent asset management fee. Historical analysis for 40 year period was notconducted; there were not enough rolling 40-year periods for a meaningful analysis.

7. The portfolio return data arc almostcertainly not normally distributed, sotwo-thirds is, at l)cst, a rough iiitproxi-ni;itioii of variation around the mean.

H. This estimate is based on the averageannuit)' rate {for 50 insurance compa-nies) as reported in (JompnnitiwAnnuity Rcix)rts, Vol. 21, Issue 12,

December 2()00. This publicationreports that the average SPIA rate for amale, age 70, with a 10-year cenainperiod, is $8.19 a month per thou.sanddollars annuiti/,ed. On an annual l)asis.this is equivalent to *>.H2H jx-rcent ofthe annuitized amount.

9. The extinction percentages for theseportfolios were calculated as of thelime \i hen it was no longer possible totake income ei|uivalent tt» 4.5 percent(inflation-adjusted) of the originalretirement portfolio, even though someincome was being paid continuously.

10. We did not conduct the historicalanalysis for 40-year periods; we feltthere were not enough rolling 40-yearperiods for a meaningful analysis,

11. Retirees who are nervous about puttingtheir assets into the risk pool ean electfor a period-certain payout of 10 or 20years. This effectively renio\ es a por-tion of the annuity's value from therisk pool and addresses risk in the mostextreme cases of premature death.Because this option removes assetsfrom the pool, it also generates some-what lower payment am<iunts than thepurchase of a "straight" life annuity

w ithout the period-certain feature,especially at older ages.

12. Of course, this also assumes that asingle income tax rate applies and isconstant o\'er time.

13.In their most basic form, these annu-ities operate by guaranteeing thatsome set share ot the assets in theannuity pool \\ ill be distributed toeaeh annuitant for life. However,because the value of the investmentsin the pool fluctuates, the value of theannuity payments (which are propor-tional to each annuitant's share in thepool) also fluctuate. As a result, theannuitant hedges longevity risk (theywill alw ays get a payment), but notinvestment risk (the payment may goup or doun, depending on how theassets perform).

Journal of Financial Planning / December 2001

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