Research. Michigan. Center. Retirement. Understanding Individual Account Guarantees Marie-Eve LaChance and Olivia S. Mitchell. Working Paper MR RC

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1 Michigan Universiy of Reiremen Research Cener Working Paper WP Undersanding Individual Accoun Guaranees Marie-Eve LaChance and Olivia S. Michell MR RC Projec #: UM02-D2

2 Undersanding Individual Accoun Guaranees Marie-Eve Lachance Universiy of Pennsylvania Olivia S. Michell Universiy of Pennsylvania and Naional Bureau of Economic Research January 2003 Michigan Reiremen Research Cener Universiy of Michigan P.O. Box 1248 Ann Arbor, MI Acknowledgemens his work was suppored by a gran from he Social Securiy Adminisraion hrough he Michigan Reiremen Research Cener (Gran # 10-P ). he opinions and conclusions are solely hose of he auhors and should no be considered as represening he opinions or policy of he Social Securiy Adminisraion or any agency of he Federal Governmen. Regens of he Universiy of Michigan David A. Brandon, Ann Arbor; Laurence B. Deich, Bingham Farms; Olivia P. Maynard, Goodrich; Rebecca McGowan, Ann Arbor; Andrea Fischer Newman, Ann Arbor; Andrew C. Richner, Grosse Poine Park; S. Marin aylor, Gross Poine Farms; Kaherine E. Whie, Ann Arbor; Mary Sue Coleman, ex officio

3 Undersanding Individual Accoun Guaranees Marie-Eve Lachance Olivia S. Michell Absrac Demographic aging renders workers vulnerable o he inheren uncerainy of unfunded social securiy sysems. his realizaion has se off a global wave of social securiy reforms, and more han 20 counries have se up Individual Accouns (IA) plans in response. Srenghs of IAs are ha paricipans gain ownership in heir accouns, and hey also may diversify heir pension invesmens; addiionally hey produce a capialized, funded sysem ha enhances old-age economic securiy. While IAs reduce he risk paricipans face due o unfunded social securiy sysem, holding capial marke invesmens in IAs could expose paricipans o flucuaions in he value of heir pension asses. Concern over marke volailiy has promped some o emphasize he need for guaranees of pension accumulaions. his paper offers a way o hink abou guaranees in he conex of a reform ha includes Individual Accouns. We illusrae ha guaranee coss can be imporan and hey can vary significanly wih ime horizon, invesmen mix, and guaranee design. he findings indicae ha plan designers and budge analyss would do well o recognize such coss and idenify how hey can be financed. Auhors Acknowledgemens he auhors are graeful for commens provided by Zvi Bodie, Neil Dohery, Alex Muermann, and Ken Smeers. hey also benefied from research suppor provided by he Michigan Reiremen Research Cener, he Shannon Schieber Memorial Fund, and he Sociey of Acuaries (Lachance); he Pension Research Council (Michell); and he Deparmen of Insurance and Risk Managemen a he Wharon School of he Universiy of Pennsylvania (boh auhors). Opinions remain solely hose of he auhors. Lachance and Michell, 2002.

4 Demographic aging is promping workers everywhere o realize ha hey are vulnerable o he inheren uncerainy ha arises from unfunded social securiy sysems. his realizaion has promped a global wave of social securiy reforms, resuling in over 20 counries seing up Individual Accoun (IA) plans. Ineres in his movemen has recenly gained srengh in he Unied Saes wih he release of he Presiden s Commission o Srenghen Social Securiy (CSSS) Final Repor, in which volunary individual accouns (IAs) are proposed as a componen of a reformed sysem. 1 Key srenghs of IAs are ha paricipans gain ownership in heir accouns and may diversify heir pension invesmens. Bu in view of he recen demise of Enron, some have argued ha access o capial marke invesmens migh impose new risk on IA paricipans. 2 Concern over capial marke volailiy has consequenly promped some policymakers o propose guaranees for defined conribuion pension accumulaions. 3 Abroad, such guaranees have already been adoped in several Lain American counries undergoing reform, 4 and more recenly, in Japan and Germany. 5 he purpose of his chaper is o illusrae how one migh evaluae pension guaranees in he conex of an Individual Accoun componen of a social securiy reform. 6 Plan designers and budge analyss should recognize guaranee coss and idenify how hey can be financed. Sensible public policy ha proposes new guaranees mus idenify who will pay for hem and why. In wha follows, he firs secion surveys he major guaranee designs adoped or suggesed in a social securiy conex. he nex secion provides he background necessary o analyze guaranee coss. he hird secion provides five examples of guaranee designs and heir 1

5 cos esimaes, using he mehodology and assumpions developed in he Appendix. A fourh secion discusses alernaive financing opions for he pension guaranee, and a final secion concludes. An Overview of Pension Guaranees While many alernaive pension guaranee mechanisms could be envisaged, hey may be classified ino wo general caegories: minimum rae of reurn guaranees, and minimum benefi guaranees. Under a minimum rae of reurn guaranee, plan paricipans would be eniled o receive paymens a leas equal o heir lifeime conribuions o he sysem plus some rae of reurn. One varian on his heme is a principal guaranee which is equivalen o guaraneeing a nominal rae of reurn of zero percen. his approach has been adoped recenly in Germany and Japan, under which paricipans mus receive a leas heir plan conribuions a reiremen (bu no before). A more generous design proposed by Feldsein and Samwick (2001) involves a real principal guaranee, under which paricipans would be guaraneed heir lifeime conribuions adjused according o an inflaion index. Sill a more generous guaranee migh promise paricipans heir conribuions plus some minimum rae of reurn. For example, paricipans could be old ha hey would always receive heir conribuions plus he reurn on a governmen bond (e.g. he 10-year reasury bond). 7 Irrespecive of he paricular guaraneed rae of reurn adoped, cos will depend in par on how ofen he guaranee hreshold is esed. In many designs, as in he German and Japanese cases, he guaranee is evaluaed only once, a he end of he plan paricipan s worklife. In oher insances, he minimum rae of reurn is imposed annually. In Uruguay, for insance, he invesmen-based sysem provides pension paricipans a minimum annual real rae of reurn of 2

6 2 percen. In Chile, pension funds mus pay an annual real rae of reurn ha is a funcion of he average annual real rae of reurn earned by he enire se of pension funds and in Colombia, he guaraneed rae of reurn is evaluaed over hree-year periods (Pennachi, 1999; Fischer, 1999). A prominen alernaive o a minimum rae of reurn guaranee is a minimum benefi guaranee. In his second approach, plan paricipans are promised ha he benefis hey will receive from social securiy a reiremen will be a leas as high as a minimum annuiy, irrespecive of heir accoun s acual invesmen performance. For insance, he Chilean reform provides a minimum annuiy o defined conribuion paricipans, financed by a pay-as-you-go program (Zaria, 1994; Pennachi, 1999). Some social securiy sysems have adoped a mulipillar srucure of benefis in which he paricipan receives he combinaion of a defined benefi annuiy (firs-pillar) and an Individual Accoun (second-pillar). Under his design, evaluaing possible program coss mus ake ino accoun he sum of hese benefis, and compare hem o he minimum annuiy. In he Unied Saes conex, Feldsein and Samwick (2001) describe a mixed sysem where par of he paricipan s social securiy ax could be conribued o an Individual Accoun while he remainder is used o finance he pay-as-you-go program. heir suggesed model also includes a guaranee ha paricipans would receive benefis a leas as grea as under he presen law benefi formula. 8 3

7 he Moral Hazard Issue. In addiion o he guaranee formulas described above, anoher facor influencing he cos of he guaranee is he level of invesmen risk aken by he Individual Accoun paricipan. Paricipans may boos he cos of he guaranee, if hey elec o hold riskier invesmens in heir porfolios. Naurally his can give rise o a moral hazard problem, as recognized by Bodie and Meron (1993) and Smeers (2002), among ohers. Several ools are available o address he moral hazard problem. One would be o specify a sandard invesmen porfolio and provide he guaranee only o hose paricipans who eleced ha sandard porfolio. Anoher approach would le paricipans inves in he porfolio of heir choosing, bu hen guaranee paymens would be compued using he sandard porfolio as a benchmark, raher han he paricipan s acual invesmen reurns. his second approach leaves paricipans wih more invesmen flexibiliy, hough i would no proec hem agains invesmen risk greaer han experienced by he sandard porfolio. Models for Cosing Pension Guaranees his secion models guaranee oucomes under he wo approaches oulined above, and i furher illusraes likely guaranee coss using financial echniques for deermining he economic cos of guaraneed pension paymens. Guaraneeing Reiremen Income. I is useful o develop a simple noaion for cosing boh he minimum rae of reurn and minimum benefi guaranee approaches. Denoe by he number of years over which a plan paricipan conribues o his IA. For a young worker (i.e. a new sysem paricipan), he period corresponds o he lengh of he full worklife. By conras, when he sysem is firs inroduced, a more senior worker would have a much shorer window during which he could conribue o his Individual Accoun. Furher, le IA and respecively, he value of he IA and of a given guaranee formula a reiremen. G denoe, 4

8 he guaranee paymens can hen be specified depending on he accoun s invesmen resul. No guaranee is paid a reiremen if, a ha ime, he Individual Accoun accumulaion exceeds he value of he guaranee: IA > G. Bu if he value of he Individual Accoun is below he guaraneed minimum, hen he guaranee paymen mus cover he difference (i.e. G IA ). he guaranee payoffs, illusraed in Figure 1, may be represened as follows: f [ 0 G IA ] = max,. (1) Figure 1 here I mus be noed ha equaion (1) is applicable in he case of a newly-creaed IA sysem, wih no legacy commimen from a prior sysem. More generally, individual accoun models someimes develop afer a parial or full conversion from a prior pay-as-you-go program. Under a full conversion, he paricipan would receive he sum of his IA and (possibly) an addiional benefi reflecing his paricipaion under he legacy sysem. Under a parial conversion (or mixed sysem), he paricipan would receive a combinaion of his Individual Accoun and also a defined benefi componen as specified under he old plan, perhaps subjec o adjusmen. hus under a minimum benefi guaranee, i is necessary o adjus equaion (1) by adding o he Individual Accoun value any addiional benefis. o illusrae his poin, we examine how one migh adjus equaion (1) for a mixed reform. Under he curren Unied Saes social securiy sysem, for insance, workers are promised a reiremen annuiy wih presen value, SS. If volunary IAs were o be permied, paricipan would likely be allowed o diver a porion (bu no all) of heir social securiy conribuions o a funded defined conribuion pension accoun. o compensae he rus Fund for he loss in conribuions, he promised social securiy annuiy would have o be reduced by an offse amoun. he Presiden s Commission (2001) proposed o calculae such an offse by 5

9 asking, in effec, how much Individual Accoun conribuions would be expeced o accumulae under a given rae of reurn. Leing Offse and RED SS represen, respecively, he offse and he reduced annuiy, hen a minimum benefi guaranee for a mixed social securiy sysem can be represened by: RED [ G ( IA SS )] f = max 0, +, (2) or equivalenly, f [ 0, G ( IA + ( SS Offse ))] = max. (3) Finally, we noe ha in (2) and (3), social securiy benefis are assumed o be paid wih cerainy. Poenial coss associaed wih he funding of social securiy benefis should be handled separaely; ha is, legacy sysem coss are properly aribued o he old sysem, and no o he guaranee. 9 Cosing Guaranee Payoffs wih Opion-Pricing echniques. he discussion above shows ha a pension guaranee can provide invesors wih a floor of proecion agains he chance of a capial marke loss. In urn, he guaranee represens a liabiliy o he sponsor, be i a privae secor group a plan sponsor, an insurer, a financial services firm or a governmen eniy. Over he las decade, as a resul of experience wih he Savings and Loan crisis as well as oher governmen guaranee programs, he Congressional Budge Office (CBO) and he General Accouning Office (GAO) have increasingly aken he posiion ha governmen guaranees should be evaluaed and cosed as o heir budgeary impac. If a pension guaranee were o be included in an IA plan proposal, i would be necessary o esimae and recognize he financial cos of such a promise. ha is, irrespecive of wheher guaranees are provided by a governmen eniy or privae secor firms, i is essenial o accoun properly for heir coss since real economic resources are required o finance hem. 6

10 In pracice, here is much confusion regarding how o compue he economic value of such guaranee paymens. One reason is ha he economic cos of providing he pension guaranee may no necessarily equal he recipien s valuaion of he guaranee. 10 In his chaper, we focus only on he economic value of he pension guaranee for he provider, 11 referred o as guaranee coss below. Anoher reason is ha more han one approach has been suggesed o evaluae pension guaranee coss. he simples approach is o projec wha pension guaranee paymens migh be according o a se of sochasic assumpions and ake heir expecaion (c.f. Feldsein and Samwick, 2001). his expecaion approach has he meri of being easy o apply and explain; i is paricularly useful when more sophisicaed echniques canno be adoped. On he oher hand his expecaion approach does no incorporae an adjusmen for he economic value of risk, so i would end o underesimae guaranee coss. An approach ha does adjus guaranee coss for risk recognizes ha he shape of he guaranee paymens in Figure 1 conforms o a pu opion. Indeed, he pension lieraure has long recognized ha opion-pricing echniques 12 can be used o value opions relaed o pension obligaions (e,g, Meron, Bodie, and Marcus, 1987). o apply his mehodology, one mus firs deail he sochasic processes for he guaranee formula and he invesmen porfolio. 13 hen, risk-neural valuaion 14 is used o obain he guaranee coss from his model. In he special case where he guaraneed porfolio consiss of a single conribuion ha grows wih invesmen reurns over ime and where he reurns follow a lognormal disribuion, he risk-neural valuaion echnique corresponds o he well-known Black-Scholes formula. he obvious advanage of his approach, as illusraed by Bodie (2001) and Smeers (2002), is ha i provides a closed-form soluion for he guaranee coss. 7

11 More realism in he pension plan design can be inroduced by permiing he pension invesmens o be deposied as a series of periodic conribuions, raher han as a one-ime invesmen. In his laer case, a closed-form soluion for he guaranee coss is more difficul o find, bu Mone Carlo simulaions and he risk-neural valuaion echnique can be used o model a wide variey of guaranee formulas and porfolio srucures. Analyss who have used riskneural valuaion echniques o value guaranees in his more complex pension framework include Pennachi (1999, 2000) who examined guaranees in Uruguay and Chile, Zaria (1994) who modeled guaranees in Chile, Fischer (1999) who evaluaed Colombia s pension guaranee, and Feldsein and Ranguelova (2000) who explored he feasibiliy of pension collars for he Unied Saes. In he presen chaper we also adop his echnique o evaluae he ypes of pension guaranees ha migh be suggesed in he conex of a possible Unied Saes social securiy reform, one ha combines a new defined conribuion individual accoun componen wih a more radiional defined benefi srucure. While specific model deails are provided in he appendix for ineresed readers, i is useful o provide a shor descripion of our applicaion of his process. As a firs sep, i is necessary o risk-adjus he probabiliy disribuions of he underlying securiies held in he pension porfolio. his probabiliy adjusmen is made such ha riskadjused reurn processes are expeced o yield he risk-free rae. Expecaions aken wih hese risk-adjused probabiliies are represened by he operaor Ê. Second, he pension guaranee paymens can be projeced o ime and discouned back a he risk-free rae using he appropriae formulas. hird, he value of he pension guaranee is obained by aking he riskadjused expeced value of he discouned guaranee paymens. he process may be summarized 8

12 analyically in equaion (4) below. Leing r represen he average risk-free rae over he period, he no-arbirage value f of a derivaive ha pays f a ime is given by:15 [ exp( r ] f = Eˆ ). (4) Naure of he Downside Risk. As was shown above, having a pension guaranee is poenially valuable because of he downside risk inheren in IA invesmens. I is ineresing ha popular belief regarding he naure of his downside risk ends o downplay he cos of such guaranees. For insance, i is ofen recommended ha invesors wih long invesmen horizons hold a larger proporion of socks in heir porfolios. his view is grounded in he argumen ha socks are less risky in he long run or, puing i anoher way, ha invesors have more ime o recoup heir losses wih longer invesmen horizons. Hisorically, socks have ouperformed bonds over long invesmen horizons, 16 so he belief is ha his rend will repea in he fuure, resuling in cosless guaranees. Empirical evidence on his poin is provided in Figure 2, which graphs hisorical annual nominal reurns payable o shor-erm invesors in Unied Saes sock and bond indexes over he period he figure confirms ha in he Unied Saes, a leas, sock reurns have hisorically exceeded bond reurns, bu wih higher volailiy. Over he period, he average annual (nominal) reurn was 14.6 percen on a sock index fund (S&P 500) compared o an average bond fund reurn of 5.8 percen. he volailiy of he sock index over he same period was also higher, a 16.5 percen, compared o bond volailiy of 9 percen. (Asse volailiy is convenionally measured by he sandard deviaion of hisorical reurns around he mean). hese daa illusrae he so-called equiy premium ha is, because socks (equiies) are seen by he marke as more volaile and hence riskier han bonds, purchasers of socks require an addiional risk premium or reurn in order o hold hem. f 9

13 Figure 2 here While all would agree ha higher volailiy means more risk for shor-erm holding periods, here is more conroversy over reurns on asses over longer period. Figure 3 illusraes he volailiy of sock reurns for longer invesmen horizons, using he same underlying daa as Figure 2, bu now expressing he volailiy of oal reurns over periods beween one and 30 years. Wha becomes clear is ha he annualized sock reurns become less volaile over ime, bu he opposie is rue for compounded sock reurns. 17 Applied o he guaranee conex, hese findings imply ha he volailiy of IA accouns should increase over ime, because his volailiy is affeced by compounded, raher han annual, reurns. Consequenly, guaranee volailiy rises over ime, raher han being diversified away over longer invesmen periods. Figure 3 here A closer examinaion of Figure 3 reveals ha, for invesmen periods longer han 25 years, volailiy esimaes become unsable, due o he pauciy of reurn daa for long invesmen periods. Over he pos-wwii period, here are a bes wo independen observaions for he 30- year period reurns. 18 Clearly, daa limiaions weaken confidence regarding he claim ha socks ouperform bonds over long-erm invesmen periods. Expers using daa from oher counries also sugges ha he Unied Saes paern is an excepion, since oher counries exhibi much smaller long-erm equiy premiums. 19 Furher, pas daa may be a raher poor predicor of fuure performance, so exrapolaing he poenial coss of a guaranee from his daa can be decepive. Illusraing Guaranee Coss o provide a beer undersanding of he facors deermining guaranee coss, his secion presens and analyzes several examples. We show how pension guaranee coss depend on hree 10

14 key facors: he relaion beween he guaranee formula and he benefi srucure, he volailiy of he invesor s porfolio, and he ineracion beween hese wo elemens and he invesor s invesmen horizon. Five specific srucures for guaranee designs help illusrae he ineracions beween pension guaranee formulas and benefi srucures. he firs hree IA guaranee designs discussed are examples of a minimum rae of reurn guaranee, differeniaed according o he rae of reurn guaraneed. Example 1 illusraes he cos of providing a principal guaranee, one ha promises he paricipan he reurn of his conribuions a reiremen (equivalen o a zero nominal ineres rae). Example 2 offers a real principal guaranee, one ha promises he paricipan he reurn of his conribuions wih an adjusmen for purchasing power a reiremen (equivalen o a zero real ineres rae). Example 3 provides he paricipan a guaranee ha his individual accoun provides his principal plus a minimum ineres rae equal o a 10-year reasury bond reurn. wo addiional examples are aken from he minimum benefi family of guaranees. Examples 4 and 5 consider a mixed sysem of social securiy benefis such as he one described in general erms in he second secion. 20 In his conex, we refer o SS as presen law benefis, or he benefis projeced according o he formulas in effec under he radiional social securiy sysem. he social securiy benefi formula does no currenly incorporae any minimum or floor benefi on is own. Hence he guaranees provided in Examples 4 and 5 ensure ha he reiree receives a oal paymen equal o he larger of he presen law benefi or he povery line. 21 he annuiy I will be recalled ha in a mixed sysem, he reiremen benefi consiss of he sum of RED SS and a paymen from he Individual Accoun IA. In Example 4, as we have 11

15 consruced i, he plan paricipan may inves 2 percen of his earnings o an Individual Accoun, in lieu of paying social securiy axes in ha amoun. Example 5 considers a larger IA sysem, where he paricipan can conribue 6 percen of his earnings o an IA. For boh examples, in exchange for is paricipaion in he IA, he paricipan s annuiy is obained by subracing an offse from he presen law benefis, i.e. SS RED = SS Offse. his offse is equivalen o he paricipan s IA conribuions accumulaed a he 3-monh -bill rae of reurn. 22 he curren social securiy benefi formula is progressive, providing low earners a higher replacemen rae hough a lower dollar amoun, as compared o higher earners. he guaranee formulas examined here promise differen replacemen raes by income level, as compared o presen law. We illusrae his sensiiviy o earnings levels in Example 4 by conrasing he guaranee coss for wo hypoheical workers: one a medium earnings level corresponding o he Social Securiy sysem s Average Wage Index (AWI), and anoher a a low earnings level represening 45 percen of his amoun. Guaranee coss are also influenced by how he paricipan invess his IA accoun. o show his, we develop guaranee cos esimaes for hree alernaive IA porfolios: one fully invesed in equiies; a second one invesed half in equiies and half in bonds; and a hird held all in bonds. he role of he invesmen horizon is depiced hrough he use of four differen conribuion periods, wih IA conribuions occurring over, respecively 10, 20, 30, and 40 years. For each of he variaions jus lised, ables 1, 2, and 3 express he cos of providing he guaranee in quesion, for he specific invesmen mix, earnings level, and saving horizon illusraed. hese coss are compued using he valuaion mehod oulined in he second secion of his chaper, and presened in a variey of unis: as a percen of asses (able 1), in presen value dollars (able 2), and as a percenage of lifeime conribuions (able 3). (he Appendix 12

16 deails he assumpions underlying he calculaions.) hroughou his secion, we refer mainly o able 1 s coss expressed in basis poins (hundredhs of a percen of asses) because i is convenional o refer o coss associaed wih managing reiremen accouns in hose erms. However, his measure does no readily reflec changes in coss associaed wih varying he conribuion rae or he invesmen horizon. Hence, for some purposes, we explore presen value dollar coss from able 2. Guaranee Formula and Benefi Srucure. For ease of discussion, we ake as he base case a paricipan wih a 50/50 sock/bond porfolio and a 40-year invesmen horizon. For such an invesor, Line 8 of able 1 shows ha he cos of guaraneeing he 10-year reasury bond reurn (Example 3) would be 0.65 percen of asses annually, or 65 basis poins (bp). Alernaively, his is worh $3,406 in presen value dollars (able 2), or equivalenly, 16 percen of oal conribuions (able 3). o undersand why he guaranee is expensive, i is helpful o look a he anicipaed gap beween he value of he guaranee and he benefis provided by he IA. 23 In he base case, he expeced values of he Individual Accoun and he guaranee are equal. 24 herefore, guaranee paymens will be generaed as soon as he IA porfolio provides a belowmean reurn. In he cases of Examples 1 and 2, he principal and real principal guaranees, he guaraneed amouns represen, respecively, only 30 percen and 52 percen of he expeced IA value. Consequenly he IA s invesmen performance would have o be significanly worse han expeced before any guaranee would be paid; hose paymens will also be smaller in size as compared o Example 3. his ranslaes ino lower guaranee coss, as illusraed in Line 8 of able 1: he guaranee coss drop o 0 and 2 bp respecively. Of course guaranee coss his low indicaes ha such guaranees provide limied proecion agains invesmen risk. Alhough we 13

17 have ignored adminisraive coss associaed wih he guaranee, in his case i is ineresing o noe ha such fees could even exceed he guaranee paymens hemselves. Coninuing wih he base case and moving along Line 8, we nex consider he minimum benefi guaranees of Examples 4 and 5. Recall ha for hese examples, he minimum benefi is defined as he Unied Saes presen law benefi, plus a povery line minimum income. Here he expeced gap beween he guaranee and he reiree s benefis is influenced by he paricipan s lifeime earnings level. 25 For he low earner, he guaranee represens from 100 percen o 120 percen of expeced benefis under he mixed sysem, whereas his raio is always 100 percen for he medium income earner. I is worh noing ha he minimum benefi guaranee in his case inroduces benefi improvemens unrelaed o he provision of invesmen risk proecion. o see his, we noe ha he guaranee is cosly even when he low earner invess his IA enirely in a bond porfolio: as indicaed in able 1, providing a minimum benefi for he low earner invesing only in bonds sill coss from 6 bp o percen of asses. Finally, coss are also influenced by he size of he IA accoun. o illusrae his, Examples 4 and 5 compare wo differen sysems, one wih an IA conribuion rae of 2 percen and he oher wih a conribuion rae of 6 percen. A larger Individual Accoun inroduces more risk, which in urn resuls in higher coss for he guaranee. he guaranees cos he same amoun in basis poins (able 1) bu hese are based on higher conribuions and higher asses. o beer judge he magniude of he guaranee cos, dollar figures are presened in able 2. Line 8 shows ha as he conribuion rae is ripled from 2 o 6 percen, he presen value of guaranee coss is also ripled, rising from $3,401 o $10,204. his confirms ha a minimum benefi guaranee in he conex of a larger invesmen accoun is more cosly. 14

18 Volailiy of he Invesmen Porfolio. he illusraions also reveal ha meeing a guaranee hreshold is more likely if he Individual Accoun is invesed in more volaile asses; hus boosing he allocaion in equiies always resuls in greaer guaranee coss. For insance, when we move from he base case wih a 50/50 sock/bond mix o a porfolio invesed all in equiies, he cos of he guaranee doubles from 65 o 127 bp (able 1, Example 3, Lines 4 versus 8). Reducing he fracion in equiies o zero eliminaes guaranee coss in he Example 3 case, of course, because he IA porfolio canno do worse han he guaraneed benefi. his implies ha giving IA paricipans a choice over invesmen mix could be cosly, in ha hey migh boos he guaranee cos by selecing a riskier invesmen porfolio. In general, i would be dangerous o provide paricipans wih an IA guaranee wihou placing resricions on heir porfolio mix. However, able 1 reveals ha, for some guaranee designs, he impac of he invesmen porfolio on coss is less han in he base case. When guaranees are eiher very likely or very unlikely o be exercised, heir coss are less sensiive o he porfolio allocaion. Ineracion wih Invesmen Horizon. As menioned in above, some observers conend ha lenghening he invesmen horizon migh resul in lower guaranee coss, because hey believe ha invesmen risk decreases over ime. Neverheless, Bodie (1995) showed ha a pu opion guaraneeing he risk-free rae becomes more expensive as he invesmen horizon widens. In pracice, he relaion beween guaranee coss and invesmen horizon proves o be fairly complex, as able 2 reveals. his relaion is deermined by he evoluion over ime of he wo facors defined in his secion: he relaion beween he guaranee formula vs. he benefi srucure, and he IA volailiy. I will be recalled ha, in he base case, he expeced value of he guaranee formula and he IA are equal, which implies ha he guaranee coss are only driven by volailiy. As he 15

19 invesmen horizon lenghens, so oo does he size of he IA and is volailiy. Since guaranee coss increase wih volailiy, he cos of he guaranee would be expeced o rise wih he invesmen horizon. Comparing Lines 5 and 8 of able 2, we see ha lenghening he invesmen horizon from 10 o 40 years in Example 3 resuls in coss rising more han proporionally, from $570 o $3,406. On he oher hand, he cos of he principal guaranees (Examples 1 and 2) falls wih ime, raher han rising. his is because under he principal guaranee, he guaranee cos falls as a percen of he IA from 71 o 30 percen as he ime period is exended from 10 o 40 years. he fac ha he guaranee becomes less generous over ime dominaes he volailiy effec and explains why he principal guaranee coss fall over ime. Similarly, for he low earner in Example 4, he social securiy annuiy grows over ime a a faser rae han does he povery line, which makes i less likely ha he guaranee will pay off for he longer holding period. Financing Pension Accumulaion Guaranees Proposals o include guaranees in an Individual Accoun model mus specify no only heir coss, as oulined above, bu also how hey could be financed. Financing decisions include several aspecs: Who will bear he guaranee coss? (e.g. paricipans, axpayers) Who will manage he guaranee and how? (e.g. privae secor, governmen agency) Wha will he price srucure be? (e.g. one price for all, prices differeniaed by earnings level, porfolio mix, ime horizon, ec) his secion examines several issues relaed o hese hree quesions. Guaranee Financing: Pay-as-you-go vs. Self-Financed. Feldsein and Liebman (2001) have suggesed ha he risk associaed wih guaranees could eiher be shifed o fuure axpayers or ransferred o privae markes. 26 One way o pay for an IA guaranee is o allow paricipans o 16

20 elec self-financed guaraneed choices from a menu of invesmen opions. Financial insiuions could offer guaraneed reurn accouns in he se of invesmen choices for people willing o pay for hem. In his case, paricipans desirous of a guaraneed invesmen produc would pay he premium, irrespecive of wheher he governmen or he privae secor managed he accouns. (In Germany and Japan, privae financial services firms are slaed o provide he guaraneed accouns.) An advanage of he self-financing approach o guaranees is ha hose who mos value he enhanced securiy would also be hose who would pay for i. Less risk-averse people would no have o subsidize he more risk-averse. In addiion, since guaranee coss rise wih he size of he porfolio being guaraneed in his conex, financing would be more expensive for higher earners wih larger accouns. Having hose who value guaranees mos pay for hem avoids he poor poenially having o subsidize he risk-averse rich. A poenial disadvanage of self-financing guaranees is ha some low-wage earners migh value a guaranee more highly, ye hey would be leas able o afford i. Financing guaranee coss for he poor, in his case, migh require subsidizing low-income savers ou of general revenue. his migh be feasible, bu i also migh derac from he appeal of guaraneed accouns o he exen ha addiional revenue would have o be idenified o pay for hem. Even in his case, however, i is criical o noe ha guaranee coss do no disappear jus because he federal governmen shoulders hem. Failing o repor economic coss and benefis of guaranees canno avoid he realiy ha economic resources are sill a risk under he guaranee, and value is being ransferred o paricipans. If guaranee coss were passed on o fuure axpayers insead of having paricipans selffinance hem, i would mean ha fuure axes would have o be devoed o he sysem when 17

21 guaranees were in he money. A major problem wih his acic is ha he guaranor could be asked o pay ou precisely when economic condiions imes were bleak. his could occur if he sock marke and he economy collapsed a he same ime, for insance. In such a circumsance, axpayers migh be unable or unwilling o raise axes on hemselves o cover he guaranees, even if promises had been made in he pas. In oher words, i is incorrec o assume ha he federal governmen has deep pockes and can simply raise axes on fuure workers o cover shorfalls whenever Individual Accoun invesmens perform poorly. Indeed, one migh ask wheher such guaranees could be any more reliable han presen social securiy promises. he law has esablished ha radiional social securiy benefi promises are payable only when revenues are sufficien o cover hem (Fleming v. Nesor, 1960). A similar poin could be made abou any form of guaranee: in a massive economic downurn, he promises would be worh no more han could be paid. A relaed issue is ha supporers of Individual Accouns ofen sae ha hese accouns are useful in building wealh and reducing unfunded ax claims on our children and grandchildren. Insiuing guaranees wihou making hem self-financed represens a new enilemen likely inconsisen wih he reform philosophy. he Choice of a Guaranee Provider. Alhough a guaranee resembles an insurance conrac, is underlying risk is no diversifiable; hence, i canno be managed wih radiional insurance pooling echniques. Figure 1 shows ha he guaranee paymens are asymmeric and his shape is preserved even when guaranee paymens of all IA paricipans are aggregaed. his shape canno be replicaed by simply deposiing he premiums ino an insurance fund. However if hese premiums were used o purchase he appropriae financial insrumens, i would be possible o obain he desired srucure of payoffs. As an example, Bodie (2001) discusses how invesmen accumulaion producs could be guaraneed wih he use of a combinaion of capial 18

22 marke insrumens. 27 In he evenualiy ha hese producs are no available in he capial markes, 28 heir payoffs could be replicaed by applying opion-pricing echniques o a porfolio of appropriae securiies. When he guaranee payoffs can be replicaed by he derivaive sraegy jus described, eiher he governmen (or one of is agencies) or privae providers would be able o offer he guaranee. 29 In pracice, several elemens of he guaranee conrac canno be hedged in capial markes (e.g. lifeime earnings, reiremen age, ec.) o deal wih his issue, one migh imagine financial services firms offering conracs ha are sandardized in erms of earnings, porfolio mix, reiremen age, and so forh. his approach has he advanage of reducing moral hazard, bu i also subjecs he paricipan o more risk due o he difference beween his idiosyncraic siuaion and he sandardized case (he basis risk, in he opions lieraure). If guaranees were no sandardized, i would become more difficul for privae providers o manage hese conracs and i becomes more likely ha he governmen would provide he guaranee. his is because he governmen may be beer able o ransfer losses o fuure generaions, as compared o financial insiuions. Such consrains could be miigaed if he privae providers had access o reinsurance. Finally, if he guaranees feaured some elemen of subsidy, privae providers would be unable o manage he enire program wihou addiional suppor. Price Srucure. he illusraions in he hird secion showed ha he price of a guaranee is sensiive o he individual invesor s characerisics and o his porfolio allocaion. Consequenly, a well-designed pricing sraegy should avoid he creaion of opporuniies for adverse selecion and moral hazard. In his conex we have already menioned he need o have he guaranee linked o a specific IA porfolio mix. Depending on he guaranee srucure, providers oo can be subjec o moral hazard. Making he guaranee provider responsible for 19

23 asse allocaion provides an incenive o inves in safer asses (Jensen and Sorensen, 2000). In Colombia, for insance, he guaranee premium under he IA program is no adjused for risk; parly as a resul, only 0.3 percen of he funds were invesed in shares (as of December 1996; Fischer, 1999)). Discussion and Conclusions Opponens of Individual Accouns end o undersae he problems facing underfunded naional pay-as-you-go social securiy sysems, overlooking he fac ha reducions in oulays and increases in revenues will be required o close he fuure financing gap. I is precisely he social securiy sysem s looming insolvency ha makes curren sysems poliically risky. Including Individual Accouns in a naional social securiy reform plan can srenghen old-age economic securiy. hese accouns can reduce he poliical risk confroning aging Americans when hey assess he chances of acually receiving promised benefis under he insolven social securiy sysem. hese accouns also afford paricipans he opporuniy o save in a coseffecive manner, and o diversify heir invesmens in ways ha hey may no be able o a presen. Noneheless, here may be concern among policymakers ha Individual Accoun paricipans will face capial marke risk, paricularly if hey concenrae heir accouns in sock marke invesmens in he pursui of higher reurns. One approach o his problem is o resric he exen of equiies allowed in workers accouns; anoher is o offer guaranees. his chaper has explored several guaranee designs and assessed heir likely coss. I shows ha offering guaranees on defined conribuion pension accouns could be cosly, even when paricipans are resriced o holding no more han half heir porfolio in sock and he res in bonds. For insance, in his framework our model suggess ha a 10-year reasury bond 20

24 reurn guaranee would sill require increasing annual conribuions by 65 basis poins, or 16 percen of conribuions, for he long-erm saver. his would likely be perceived as a subsanial cos increase over and above he basic conribuion by mos plan paricipans. If hese coss were no self-financed, subsanial subsidies would be required. Subsidies of his sor mus be measured, recognized, and heir financing implicaions spelled ou in deail for a full accouning of he economic coss and benefis of guaranees. hese cos esimaes migh seem high o people accusomed o he argumen ha sock reurns are expeced o ouperform bond reurns over ime. We argue, however, ha because of he pauciy of independen observaions in hisorical daa on long holding periods, pas reurns are noisy predicors of fuure reurns. In addiion, guaranee coss are driven by sock and bond volailiy raher han heir expeced reurns. 21

25 able 1 Cos Esimaes of Alernaive Guaranees: Annual Charge as a % of IA Asses (in basis poins) Source: Auhors calculaions. Line Years wih Individual Accoun Example 1 Principal (i.e. 0%) Minimum Rae of Reurn Minimum Benefi (wih a Mixed 1 sysem) Example 2 Real Principal (i.e. inflaion) Example 3 10-yr reasury Bond Reurn Example 4 Presen Law Benefi w/ Povery Line Minimum 2 (Conribuion Rae = 2%) Example 5 Presen Law Benefi w/ Povery Line Minimum 2 (Conribuion Rae = 6%) Any Earnings Low Earnings 3 Medium Earnings 3 Medium Earnings 3 I. Porfolio invesed 100% in Equiies 1 10 years 60 bp 136 bp 267 bp 2946 bp 265 bp 265 bp 2 20 years years years II. Porfolio invesed 50% in Equiies, 50 % in reasury 10-yr Bonds 5 10 years years years years III. Porfolio invesed 100% in reasury 10-yr Bonds 9 10 years years years years In his example, a paricipan in a mixed sysem would be allowed o diver par of his social securiy conribuion o an IA and his firs-pillar benefi (social securiy annuiy) would be reduced by an offse in reurn. 2 his design guaranees ha he combinaion of he firs pillar benefis (annuiy) and he IA is as leas as much as he presen law social securiy benefi. In addiion, his benefi is subjec o a minimum se equal o he povery line for hose who conribue o he firs pillar benefis for a leas 30 years. 3 he income of he low and medium earners represen respecively 45% and 100% of he Average Wage Index (AWI). In 2000, hey would have earned respecively $14,470 and $32,

26 able 2 Cos Esimaes of Alernaive Guaranees (in presen value dollars) Source: Auhors calculaions. Minimum Rae of Reurn Minimum Benefi (wih a Mixed 1 sysem) Line Years wih Individual Accoun Example 1 Principal Example 2 Real Principal Example 3 10-yr reasury Bond Reurn Example 4 Presen Law Benefi w/ Povery Line Minimum 2 Example 5 Presen Law Benefi w/ Povery Line Minimum 2 Conribuion Rae = 2% Conribuion Rae = 2% Conribuion Rae = 6% Medium Earnings 3 Low Earnings 3 Medium Earnings 3 Medium Earnings 3 I. Porfolio invesed 100% in Equiies 1 10 years $252 $576 $1,127 $16,781 $1,120 $3, years ,782 10,656 2,776 8, years 214 1,173 4,681 4,150 4,677 14, years 163 1,240 6,613 2,971 6,602 19,087 II. Porfolio invesed 50% in Equiies, 50 % in reasury 10-yr Bonds 5 10 years , , years ,408 10,557 1,406 4, years ,390 3,144 2,390 7, years ,406 1,531 3,401 10,204 III. Porfolio invesed 100% in reasury 10-yr Bonds 9 10 years , years , years , years In his example, a paricipan in a mixed sysem would be allowed o diver par of his social securiy conribuion o an IA and his firs-pillar benefi (social securiy annuiy) would be reduced by an offse in reurn. 2 his design guaranees ha he combinaion of he firs pillar benefis (annuiy) and he IA is as leas as much as he presen law social securiy benefi. In addiion, his benefi is subjec o a minimum se equal o he povery line for hose who conribue o he firs pillar benefis for a leas 30 years. 3 he income of he low and medium earners represen respecively 45% and 100% of he Average Wage Index (AWI). In 2000, hey would have earned respecively $14,470 and $32,

27 able 3 Cos Esimaes of Alernaive Guaranees: as a % of Lifeime Conribuions Source: Auhors calculaions. Line Years wih Individual Accoun Example 1 Principal (i.e. 0%) Minimum Rae of Reurn Minimum Benefi (wih a Mixed 1 sysem) Example 2 Real Principal (i.e. inflaion) Example 3 10-yr reasury Bond Reurn Example 4 Presen Law Benefi w/ Povery Line Minimum 2 (Conribuion Rae = 2%) Example 5 Presen Law Benefi w/ Povery Line Minimum 2 (Conribuion Rae = 6%) Any Earnings Low Earnings 3 Medium Earnings 3 Medium Earnings 3 I. Porfolio invesed 100% in Equiies 1 10 years 3.6% 8.2% 16.1% 531.9% 16.0% 16.0% 2 20 years 2.0% 7.6% 21.9% 186.2% 21.8% 21.8% 3 30 years 1.2% 6.7% 27.0% 53.2% 27.0% 27.0% 4 40 years 0.8% 5.9% 31.3% 31.3% 31.3% 31.3% II. Porfolio invesed 50% in Equiies, 50% in reasury 10-yr Bonds 5 10 years 0.2% 2.0% 8.1% 531.7% 8.1% 8.1% 6 20 years 0.0% 1.2% 11.1% 184.5% 11.1% 11.1% 7 30 years 0.0% 0.8% 13.8% 40.3% 13.8% 13.8% 8 40 years 0.0% 0.5% 16.1% 16.1% 16.1% 16.1% III. Porfolio invesed 100% in reasury 10-yr Bonds 9 10 years 0.0% 0.0% 0.0% 531.6% 0.7% 0.7% years 0.0% 0.0% 0.0% 184.5% 1.0% 1.0% years 0.0% 0.0% 0.0% 35.9% 1.3% 1.3% years 0.0% 0.0% 0.0% 1.6% 1.6% 1.6% 1 In his example, a paricipan in a mixed sysem would be allowed o diver par of his social securiy conribuion o an IA and his firs-pillar benefi (social securiy annuiy) would be reduced by an offse in reurn. 2 his design guaranees ha he combinaion of he firs pillar benefis (annuiy) and he IA is as leas as much as he presen law social securiy benefi. In addiion, his benefi is subjec o a minimum se equal o he povery line for hose who conribue o he firs pillar benefis for a leas 30 years. 3 he income of he low and medium earners represen respecively 45% and 100% of he Average Wage Index (AWI). In 2000, hey would have earned respecively $14,470 and $32,

28 Figure 1. Guaranee Paymens as a Funcion of he Individual Accoun Value Source: Auhors calculaions. IA<Guaranee Guaranee in-he-money Guaranee Paymens IA>Guaranee Guaranee ou-of-he-money Individual Accoun Value Guaraneed Individual Accoun Balance a Reiremen 25

29 Figure 2: Annual Reurns for Unied Saes Sock and Bond Markes, Source: Auhors compuaions, daa from CRSP; hisorical annual sock reurns from S&P 500 index including dividends; bond reurns from an index of 10-year reasuries. 60% 50% Line = Sock Reurn 40% Annual Reurns 30% 20% 10% 0% -10% -20% Column = Bond Reurn -30% Year Figure 3: he Effec of Longer ime Horizons on he Volailiy of Sock Reurns Source: Auhors compuaions using daa described in Figure % Volailiy of oal Reurns oal Reurns Average Reurns 16% 14% 12% 10% 8% 6% 4% 2% Volailiy of Average Reurns 0 0% Invesmen Horizon (Years) 26

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32 Appendix: An Illusraion of Opion-Pricing echniques Applied o Individual Accouns his Appendix deails he modeling assumpions used o derive cos esimaes for he illusraive examples discussed in he ex. We summarize guaranee coss for four workers who paricipae in he Individual Accouns (IA) program for, respecively, = 10, 20, 30, and 40 years. I is assumed ha he IA sars in 2004 and economic variables are projeced accordingly. Secions A and B of his Appendix describe he economic and demographic assumpions. he sochasic processes followed by he bills, bonds, and socks are modeled separaely in Secion C. Secion D deails he elemens necessary o compue he IA values as well as he social securiy annuiy. Secion E derives he cos of each guaranee formula while Secion F shows how o generae numerical values for he guaranee coss using a Mone Carlo simulaion. A. Economic Assumpions All projecions are expressed in nominal values, wih he inflaion and real processes modeled separaely. Assumpions for inflaion growh, real wage growh, and real ineres raes are aken from he OASDI Annual Repor (2001). In ha repor, he inermediae scenario assumes ha real wage growh is g = 1.0%, while inflaion grows a i = 3.3%. By combining hese wo assumpions, he resul is a 4.3% nominal wage growh assumpion. According o he REAL inermediae scenario, he real ineres rae assumpion is r = 3%. his fixed ineres rae assumpion is used for he annuiy calculaion in Secion B, while he remaining calculaions use he sochasic model of Secion C. A he incepion of he IAs, earnings levels are denoed by W 0. In subsequen years, earnings W are obained by projecing hese iniial earnings wih a fixed rae of 4.3%. wo caegories of wages are used in he simulaions: he medium earner correspond o he Social Securiy Acuary s Average Wage Index (AWI) while a low earner represens 45% of his amoun. For insance, he low and medium earners would have received respecively $17,785 and $32,155 in Finally, according o he Unied Saes Census Bureau, he povery line for singles over 65 years old was $8,494 in 2001, a level assumed o grow wih he Consumer Price Index (CPI) over ime. B. Demographic Assumpions he four illusraive cases are assumed o be, respecively, 22, 32, 42, and 52 years old a he incepion of he IA sysem. Each paricipan is assumed o reire a he early reiremen age of 62 years old. A his age, he value of a $1 annuiy wih paymens indexed o inflaion is denoed by he annuiy facor a 62. o compue his annuiy facor, i is necessary o define survival probabiliies afer reiremen. he sandard noaion p62 is used o denoe he probabiliy ha an individual reiring a age 62 would sill be alive a age 62+. Pos-reiremen survival probabiliies are derived from he Social Securiy 1997 period life able 31 (pre-reiremen moraliy is no included in he model). As for he real ineres rae used o discoun he annuiy paymens, i is aken from he OASDI inermediae scenario. Leing he las age (radix) of he moraliy able be represened by ω, he value of he annuiy facor is given by: ω = 1 = 0 REAL ( + r ) a p. (7) 62 29