Variable Payout Annuities with Downside Protection: How to Replace the Lost Longevity Insurance in DC Plans

Transcription

1 Varable Payout Annutes wth Downsde Protecton: How to Replace the Lost Longevty Insurance n DC Plans By: Moshe A. Mlevsky 1 and Anna Abamova 2 Summary Abstract Date: 12 October 2005 Motvated by the rapd declne of tradtonal defned beneft (DB) penson plans and ther mplct longevty nsurance, n ths report we quantfy the value of havng access to varable payout annutes wth downsde protecton nsde an ndvdually-controlled defned contrbuton (DC) plan. We delberately use the term varable payout annuty (VPA) to emphasze an nstrument whose sole purpose s to generate retrement ncome,.e. to eventually annutze and convert nto an mmedate varable annuty (IVA). VPAs are an mportant component of a well dversfed portfolo at all stages of the human lfe cycle, especally for those who lack a tradtonal DB penson. In addton -- for those who are concerned about the retrement ncome volatlty -- havng some form of downsde protecton durng the payout stage s worth payng for and hence mproves the rsk & return propertes of a payout annuty. Our smulatons ndcate that -- although over long perods of tme a balanced portfolo of equtes and bonds are lkely to apprecate -- the value of an mplct annutzaton put opton (APO) on such a portfolo can be substantal. In addton to developng some metrcs for explctly quantfyng ths value, we provde a varety of numercal examples and case studes under a partcular form of downsde protecton. 1 Moshe Mlevsky s an Assocate Professor of Fnance at the Schulch School of Busness, York Unversty and the Executve Drector of the Indvdual Fnance and Insurance Decsons (IFID) Centre n Toronto, Canada. He can be reached at x 3010 or va Emal: mlevsky@yorku.ca. 2 Anna Abamova s a Research Assocate at The IFID Centre. Ths report was funded by a research grant from Genworth Fnancal and the authors would lke to acknowledge helpful comments from Peter Wesnger. Page 1 of 51

2 1.) Introducton and Motvaton: The Slow Death of Longevty Insurance Durng the year 2002 a hstorcally unprecedented penson experment took place n the State of Florda. Every one of the State s more than 500,000 publc employees n addton to every new employee jonng the State s payroll -- was gven the opton of convertng ther tradtonal Defned Beneft (DB) penson plan nto an ndvdually managed Defned Contrbuton (DC) plan. The DC nvestment plan was very smlar to a corporate-style 401(k) plan, under whch the employee has full control over asset allocaton and nvestment decsons. The new Publc Employee Optonal Retrement Program (PEORP), as t has been called, was the focus of ntense scrutny by local and natonal meda. Ths s because t was the largest such penson converson n the hstory of the U.S. and was vewed by many observers as a potental laboratory for Socal Securty reform. It s estmated that over 50% of new employees of the State have decded to forgo the tradtonal DB penson and nstead enroll n the DC nvestment plan. Ths large-scale transton from DB to DC s not solated to the State of Florda alone. A number of other States -- ncludng a faled attempt by Calforna Governor Arnold Schwarzenegger -- have proposed convertng ther State s publc employee DB plan nto ether a mandatory or optonal DC plan. The mpetus for ths massve shft can be attrbuted to a wde varety of factors, but s prmarly due to the actuaral fundng crss that has been brewng for many years. The economc cost of fundng and mantanng DB pensons has reached unprecedented levels, drven by low nterest rates, poor performance of the equty markets and the uncertanty of ncreasng lfe spans. A recent cover story n Busness Week n June of 2005 brought ths crss to natonal promnence. Prvate sector corporate penson plans have not been mmune to ths trend ether. In aggregate, DB penson plans n the U.S. have a collectve fundng defct n the hundreds of bllons of dollars, dependng on whch assumptons are used to dscount labltes. They, too, have suffered from the same ncreasng longevty patterns, declnng nterest rates, poor equty returns and a cumbersome regulatory envronment. It s no surprse, then, that accordng to the U.S. Department of Labor, the number of prvate sector DB plans n the U.S. has fallen from 112,208 n the year 1980 to 29,512 n the year Lkewse, the number of prvate sector employees covered by a DB plan has fallen from 30.1 mllon n 1980 to 22.6 mllon n early More nterestngly, the percentage of prvate sector employees covered Page 2 of 51

3 by a DB plan has fallen from 28% n 1980 to 7% n early In sum, Defned Beneft penson plans are dyng. For the most part, the vacuum created by the demse of DB penson coverage has been taken-up by DC style accounts such as 401(k), 403(b), 457, etc. plans. Accordng to LIMRA Internatonal, the percent of U.S. ndvduals covered by a DC plan ncreased from 17% n 1980 to 58% n These DC plans dffer from ther DB cousns by provdng control over asset allocaton, moblty, flexblty and greater transparency. Indeed, many consumer advocates and free-market economsts have argued that ths trend from DB to DC s a movement n the rght drecton as the U.S. labor force transtons from tradtonal lfelong manufacturng jobs to servce-type employment. Ths report remans neutral as to whether DC plans are better (or worse) for the general workforce and we refran from ths contentous debate as t relates to transacton costs and consumer behavor. Moreover, we concede up-front that a DC-style plan offers a number of benefts especally for younger, professonal and moble employees -- that are smply unavalable under a DB arrangement. However, there s one aspect of DC plans as currently emboded n most 401(k), 403(b) and smlar structures -- that places them at a dsadvantage relatve to tradtonal DB plans. We beleve that ths problem can be remeded by expandng the set of menu optons avalable wthn DC plans together wth approprate educaton for plan partcpants and plan sponsors. The Achlles Heel of DC plans s that regardless of how much money plan partcpants manage to accumulate n ther accounts and despte how successful they mght be n managng ther fnancal affars, n the words of penson economsts, they have lost ther longevty nsurance. That s, they have lost the guarantee of lfetme ncome that s an ntegral part of a DB plan. Indeed, a retree wth a DC-style plan who decdes to ether roll-over nto an IRA or take a lump-sum settlement and create systematc wthdrawal plans to fnance ther retrement consumpton, loses the longevty nsurance aganst the cost of lvng far longer than they had antcpated. Ths, n fact, s the core message of ths report. No matter how large the menu of mutual funds, wrap accounts, ETFs or low-cost ndex funds the plan sponsors offer partcpants, most DC-style plans do not offer fnancal products that contan or have the ablty to create -- longevty nsurance. Accordng to a recent study by LIMRA Internatonal, Page 3 of 51

4 fewer than three n ten 401(k) plan sponsors offer any type of payout annuty as the normal form of dstrbuton. The number of plan partcpants who voluntarly annutze that s convert part or all of ther nest egg nto a lfetme ncome stream s even smaller. There are clearly two levels of decson makng that must take place when t comes to retrement ncome plannng. The frst ter revolves around whether to fnance wthdrawals and consumpton needs from a systematc wthdrawal plan (SWP) where the retree retans longevty rsk or whether to outsource or transfer ths rsk to an nsurance company who s better able to pool ths rsk amongst a large populaton. Ths s known as the annutzaton opton. Of course, these two optons are not mutually exclusve and a recommended possblty would be to dversfy across a SWP program and an ncome annuty. It s our belef that ths frst ter decson should not be delayed untl retrement and careful attenton must be devoted to longevty rsk well before retrement. The Mlevsky (2005) artcle, recently publshed n the North Amercan Actuaral Journal, further elaborates on and argues ths poston. Once ths frst ter decson has been made, and a commtment has be made to fund some porton of retrement ncome usng an annuty nstrument, a second ter decson revolves around the optmal tmng of annutzaton and the type of annuty to purchase. For example, some varable payout annutes provde fluctuatng ncome wth no guaranteed base, whle others protect a baselne level of ncome regardless of market performance. Some payout annutes protect the retree aganst nflaton rsk, whle others make payments n nomnal terms. Fnally, the second ter decson nvolves another dmenson, whch concerns guarantee perods and survvorshp benefts. We beleve that DC plan sponsors should gve serous consderaton to provdng a dversfed menu of asset classes and product classes to help partcpants prepare for a retrement n whch they must generate lfetme ncome. In fact, even those plan sponsors that do offer a lfe annuty as the prmary form of dstrbuton, only offer a fxed (nomnal) payment product that s unlkely to keep up wth the retrees cost of lvng. Longevty nsurance s a very pecular and odd-soundng form of nsurance and t takes some thnkng to understand how ths nsurance s embedded wthn DB penson plans, payout annutes, and other nsurance products. Most consumers understand the mechancs of lfe, car, home or health nsurance. A premum s pad upfront to protect one s famly and possessons aganst a catastrophc fnancal event, such as the death or dsablty of the prmary breadwnner. These commodty-type nsurance polces have few fnancal Page 4 of 51

5 characterstcs and one rarely thnks of them as provdng an nvestment rate of return. Tradtonal nsurance polces hedge the famly aganst catastrophc fnancal events. Yet, the same lne of thought can also be extended to nsurance protecton towards the end of the human lfe cycle, when the rsks a retree faces are of the exact opposte magntude. As one ages and transtons nto retrement, the value of human captal (future labor ncome) dwndles and all one has to support themselves durng ther extended retrement years s the fnancal captal they have amassed durng the workng years. At that pont n ther lfe, ther future consumpton labltes are uncertan and unpredctable. The retree may be fortunate enough and lve a very long lfe well nto ther 90s, or they may be unlucky and barely reach a typcal retree s lfe-expectancy of 80. Ths uncertanty can be hedged or dversfed away by beng a member of a DB penson plan or by voluntarly purchasng a lfe annuty, whch mplctly provdes a hgher rate of return, the longer one lves. So, although ther labltes mght ncrease beyond what was expected f they reach ther 90s, so too wll the nvestment return from a lfe annuty, or what we call longevty nsurance. Ths s why a number of publc commentators -- ncludng the prmary author of ths report -- have argued that varable payout annutes (VPAs), whch are converted nto mmedate varable annutes (IVA), should form the backbone of one s retrement ncome portfolo. In ths report we echo ths poston and take t one step further. We acknowledge that one of the prmary concerns wth lnkng retrement ncome to the performance of an nvestment portfolo, s the volatlty. Therefore, n addton to servng as an advocacy pece for VPAs, the techncal objectve of ths report s to examne the benefts and costs of havng access to a downsde-protected, or guaranteed VPA. From an economc pont of vew, a guaranteed VPA (GVPA) s a savngs & nsurance contract that provdes an opton to annutze the account at some pre-specfed prce, wth an addtonal guarantee that the lfetme ncome wll not fall below some baselne level. The GVPA becomes a GIVA, whch can be thought of as an IVA wth a put opton. We wll descrbe ths n greater detal, later n the analyss. The remander of ths report s organzed as follows. Secton 2 revews the mechancs of the pure longevty nsurance, whch s embedded wthn a varable (or fxed) payout annuty. It helps to translate the language of nsurance to the language of nvestments. Secton 3 dscusses the general structure of varable payout annutes that provde downsde Page 5 of 51

6 protecton and Secton 4 goes on to report on extensve smulaton results for the relatve value of havng ths downsde protecton for one partcular product desgn. Secton 5 concludes the report wth some fnal thoughts and a Techncal Appendx contans the bulk of the mathematcal detal. All smulaton results are dsplayed at the end of the document. 2.) Understandng the Benefts of an Immedate Annuty (wthout havng a Degree n Actuaral Scence) In ts most general form, purchasng an mmedate annuty (whether jont or sngle, for lfe or for a fxed-term) nvolves payng a non-refundable lump sum to an nsurance company n exchange for a guaranteed, constant monthly or quarterly ncome. Wth some products, the ncome ends after a pre-determned or fxed perod of tme; these are called fxed-term (or perod certan) annutes. Wth lfe annuty products, the ncome ends at death. Obvously, a retree cannot outlve the ncome from a lfe annuty; ths s one of the product s strong sellng ponts. No matter how long you lve, how markets perform, or what happens to nterest rates or the economy as a whole, you wll always get a monthly cheque. Annutes, n other words, are a type of longevty nsurance. Insurance companes can provde ths lfelong beneft by (a) poolng a large enough group of annutants and (b) makng a very careful and conservatve assumpton about the rate of return earned on ts assets. The poolng of annutants means that ndvduals who do not reach ther lfe expectancy, as calculated by actuaral mortalty tables, wll end up subsdzng those who exceed t. A smple example can help convert longevty nsurance embedded wthn annutes and DB penson plans nto the language of nvestments. Suppose, accordng to populaton mortalty tables, there s a 20 percent chance that a 95-year-old female wll de durng the next year, before she reaches her 96 th brthday. If 1,000 such females enter nto a one year term annuty (a.k.a. tontne) agreement by nvestng $100 each n a pool yeldng 5 percent, the funds wll grow to $105,000 by the end of the year. Of the ntal 1,000 females, 800 are expected to survve, wth a rather small varance around the expected value, leavng an average of $105,000/800 = $ per survvor. Ths leads to a total return of 31.25% and qute obvously far exceeds the nterest rate (or nvestment return) of 5% used to store the funds, because the annutants have ceded control of assets n the event of death. Page 6 of 51

7 The powerful algebra of longevty credts can be stated symbolcally as follows: f r denotes the effectve nterest rate per year and f p s the probablty of survval per year, then the return for the survvors from the one-year annuty s expected to be (1 + r)/p - 1 > r. The expectaton wll become realty as long as the group of annutants partcpatng n ths rskmtgatng scheme s large enough. The gap between the one-year returns to the survvors and the nterest rate are the so-called mortalty credts. Table #1a llustrates some numercal values for these credts at dfferent ages, usng a unsex annutant mortalty table. Table 1a The Investment Benefts from a One-Year Term Annuty Age Mortalty Credts (b.p.) Assumng 40/60 male/female splt for Annuty 2000 Table under 6% nterest To put these numbers n perspectve, a (unsex) 85 year-old that decdes not to buy the one-year term annuty and nstead take hs or her chances by nvestng n tradtonal (nonmortalty contngent) asset classes, would have to earn 725 bass ponts (whch s 7.25%) above the rsk-free rate of 6% durng the next year, n order to be as well-off as someone who decded to buy the one-year term annuty at age 85. Thnk of ths (6% % =) 13.25% number as a hurdle-rate that must be earned by the self-annutzer to keep up wth the annutzer. At age 90 ths hurdle rate ncreases to 18.56%, whch becomes vrtually unachevable usng any conventonal nvestment products. Of course, dfferent nterest rates and mortalty tables wll lead to dfferent numercal results, but the order of magntude s always the same. At advanced ages nothng beats the mpled yeld from an ncome annuty. Page 7 of 51

8 As many penson actuares understand and apprecate, the rsk-sharng prncple of tontne nsurance s n fact the concept underlyng all mmedate annutes, and all DB penson plans for that matter. In practce, however, the rsk-sharng agreement s made over a seres of years, as opposed to just one year. We wll elaborate on the dstncton n a moment. Consder what we descrbed as term longevty nsurance versus whole-lfe longevty nsurance. The mechancs reman the same, and the survvors derve a hgher return whch s then amortzed over one s lfe -- compared to placng the funds n a conventonal (nonmortalty-contngent) asset. More mportantly, whle the above example assumes that the nterest rate r s fxed, n theory, the exact same prncple apples wth a varable nvestment return as well. In fact, the ex post returns mght be even hgher. For example, the 1,000 females who are 95 years-old, can nvest ther $100 n a balanced mutual fund that earns the random return R. They do not know n advance what the fund/pool wll earn. At the end of the year the annutants wll learn (or realze) ther nvestment returns, and then splt the gans among the survvng pool. Moreover, n the event that the nvestment earns a negatve return and loses money the partcpants wll share n the losses as well, but the effect wll be mtgated by the mortalty credts. Algebracally, the expected return wll be the same (1 + R)/p - 1 > R. In fact, ths concept s the foundaton of an mmedate varable annuty. In practce, most nsurance companes go one step further than the above (partcpatng annuty) example and actually guarantee that the annutant wll receve the mortalty credt enhancements, even f the mortalty experence of the partcpants s better than expected. In other words, n the above-mentoned example for one-year fxed annutes, wth an expected 20% mortalty rate, the nsurance company would guarantee that all survvors receve 31.25% on ther money, regardless of whether or not 20% of the group ded durng the year. Next, we wll llustrate how rsk poolng and the resultng longevty nsurance works n practce, n the case of a lfe annuty rather than a tontne. Table #1b provdes a set of hypothetcal examples (snce these numbers can change on a weekly bass). It states that a 65 year-old sngle female wth $100,000 can purchase an annuty that wll provde her wth $630 per month for the rest of her lfe, no matter how long she lves. The same $100,000 wll buy an annuty that wll provde a 65 year-old male wth a greater ncome of $730 per month for lfe. The addtonal $100 per month, or 16%, that a male wll receve s a drect result of hs Page 8 of 51

9 lower lfe expectancy. That s, a group of 65 year-old men can expect to lve 14 more years, whle a group of 65 year-old females, on the other hand, can expect to lve 20 more years, on average. Thus, f the money must last longer, the payments must be smaller. Table 1b Sample Annuty Quotes $100,000 buys monthly payments for lfe Current Age Female Male 55 $533 $ $630 $ $712 $ $832 $1, $1,014 $1,250 Source: CANNEX Fnancal Exchanges, 2003 Wth that n mnd, f the 65-year-old exceeds the medan lfe span of approxmately 14 (20) more years, he (she) wll end up earnng a return that s greater than the average nterest rate that was appled at the tme of purchase. If he or she falls short of the medan lfe span, the return wll be nferor. Another mportant aspect of lfe annutes s that the monthly payments that retrees can receve ncrease the longer they wat before buyng the annuty. As noted prevously, a 65-year-old male (female) can get $730 ($630) per month from a $100,000 annuty. But f they wated another 10 years to make the purchase, untl age 75, the male (female) would get $1,008 ($832), for lfe. That s an ncrease of approxmately 35%, smply for deferrng the purchase for 10 years. Once agan, the medan lfe span s the key. At age 75, a male s medan lfe span s approxmately 83.5 years (86.5 for women). Ths translates nto an average of 9 (12) more years of payments, as opposed to 14 (20) more years when they annutze at age 65. The fewer years the age cohort s lkely to lve, the larger the monthly payments wll be. So the lesson s: the longer you wat to annutze, the more you wll get per month. The natural alternatve to buyng a lfe annuty s the do-t-yourself annuty usng a systematc wthdrawal plan (SWP). A retree can create and manage hs or her own annuty stream. For example, the retrng 65-year-old male (female) can keep the $100,000 nvested n an IRA for the next few years and then start wthdrawng a fxed monthly ncome of exactly Page 9 of 51

10 $730 ($630). That, you wll remember, s the hypothetcal annuty amount that the nsurance company would have provded at age 65. But what f they lve too long? Wll ther money last? Indeed, ths do-t-yourself strategy runs a serous fnancal rsk: under-fundng retrement n the event of long-run nferor nvestment returns n conjuncton wth unexpected human longevty. Ths s exactly how and why a lfe annuty provdes longevty nsurance. Here s an addtonal explanaton of how age mpacts the return from a fxed lfe annuty. Table #1c shows the nternal rate of return (IRR) a measure of proftablty from purchasng a lfe annuty wth $100,000 at varous ages, assumng that you wll lve and receve payments untl age 95. Table 1c You purchase a lfe annuty wth $100,000. What s your IRR, assumng you lve to age 95? Purchase Age Female Male % 8.24% % 11.17% % 13.54% % 19.62% Table #1c states that f an 80 year-old male purchases a lfe annuty, and survves to age 95 thus recevng $1,250 per month for 15 years he wll earn an mplct annual return of 13.54% on hs ntal nvestment. It s mplct because when you dscount 15 years of $1,250 monthly payments, at a rate of 13.54% per year, you obtan the orgnal $100,000. Conceptually, ths s equvalent to a $100,000 home mortgage, amortzed at 13.54% over a 15-year perod, wth monthly payments of $1,250. The same purchase at age 85 provdes an even better yeld an mplct 19.62% annual return. A 19.62% return s very hgh and would clearly be dffcult to beat usng alternatve nvestment classes. However, at age 65, the nternal rate of return s much lower (8.24%), even wth the assumpton that you lve to age 95. In sum, we hope the above llustratons help the reader understand the benefts of longevty nsurance and how these benefts can be translated nto nvestment terms. A retree who s recevng ncome from an mmedate annuty earns a return on the order of magntude Page 10 of 51

11 dsplayed n Table #1c. Ths s why we advocate (eventual) annutzaton n order to sustan and mantan a reasonable standard of lvng durng retrement. Moreover and once agan, only nsurance companes can offer ths form of rsk poolng mechansm. 3.) The Mechancs of a Guaranteed VPA: Protectng the Downsde There are many ways n whch to construct or desgn a payout annuty nstrument that offers downsde protecton to annutants. The common denomnator of all (possble) desgns s that they offer an mplct put opton on ether: () actuaral mortalty rates, () nterest rates or () portfolo nvestment returns. Collectvely we label them annutzaton put optons (APOs). For example, a $10,000 premum deposted nto an underlyng fund by a 40 year-old can be attached to an explct guarantee that f the contract s annutzed at age 65, the annuty wll provde at least $2,000 n annual ncome for the rest of the annutant s lfe. In ths case, the annuty payment (ncome) can fluctuate and be lnked to the performance of an underlyng fund. Ths guarantee would contan an explct put opton on nvestment returns and mortalty rates. Therefore, from our perspectve, under the most general condtons, all guaranteed VPA (GVPA) structures can be analyzed wthn the followng framework. Intal Retrement Income = MAX [( D + C) / A, B] (Formula.1) In ths fundamental formula, the letter D denotes the orgnal depost premum, the letter C denotes the cumulatve nvestment gans, the letter A denotes an annuty converson factor and the letter B denotes a base ncome. Any and all of the three letters A,B or C can be guaranteed, projected or completely random. For example, a contrbutor mght be guaranteed that ther depost premum wll earn (or be credted wth) at least 100% nterest, so that C = D n the above formula, but only gven an antcpaton of what A and B wll be. In ths case, there really s no guarantee beng provded snce nether the rght nor the left part of the MAX expresson s gven a lower bound n advance. On the other hand, the contrbutor mght be guaranteed that they wll receve annual retrement ncome of at least 20% of ther ntal depost, n whch case B = 0.2D n the above formula, and a frm guarantee s beng provded. On a slghtly more esoterc level, the partcpant mght be guaranteed that the annuty converson factor wll be A =10, so that each Page 11 of 51

12 and every $10 n the account (D+C) wll generate at least $1 of retrement ncome, etc. Note, also, that C tself can be zero or even negatve. The mportant pont s that n order to analyze any guarantees that are embedded wthn a VPA, one must carefully represent the payoff based on (formula.1) and then read-off the values of A, B and C to determne whether they are smply antcpated or absolutely guaranteed. Note that these three varables themselves mght contan ther own guarantees -- for example A could be at least 20, or B could be at least $1,000 but all VPAs can stll be expressed n the above manner. Then, n subsequent years, the retrement ncome can ncrease (or declne) based on the performance of a reference nvestment basket or fund. We can express subsequent payments usng a smlar formula: Subsequent Retrement Income = MAX [ I + C, B], (Formula.2) In ths case, the new letter I denotes the prevous year s retrement ncome and C denotes an aggregate nvestment return (net of fees and any adjustments) n the pror year, and B s the same guaranteed base. Note that C mght be negatve, whch mght reduce the subsequent year s ncome. In the next secton we conduct a number of smulaton experments to quantfy the value of a guaranteed VPA relatve to a non-guaranteed VPA assumng that there are no guarantees on the parameters C, that the parameter A s antcpated and that the parameter B s guaranteed. Note, once agan, the dstncton between a quantty that s random (nvestment returns), antcpated (mortalty table to be used n convertng the account nto ncome) or guaranteed (mnmum retrement ncome). For a more detaled understandng of the underlyng formulas, we encourage the reader to consult the techncal appendx. 4.) Numercal Examples and Analyss of One Possble Product Desgn Ths secton reports the results of extensve computer smulatons that we conducted n an attempt to quantfy the value of downsde protecton on an Immedate Varable Annuty (IVA). As mentoned earler, all of our smulatons were conducted wth an assumed guaranteed structure that randomzes C, antcpates A and guarantees B, as per (formula.1). We hypothesze two plan-partcpants or nvestors, one of whom deposts $10,000 n a regular VPA, whch wll be converted (a.k.a. annutzed) nto an IVA, the other nvests n a Page 12 of 51

13 guaranteed VPA, whch wll be converted to a GIVA. Both ndvduals are charged the exact same level of fees and nvest n the exact same underlyng securtes (or fund). The fees were dentcal for both types of accounts n order to solate the value of the downsde protecton, rather than nfluence the outcome of the analyss by chargng dfferent fees. Further, both partcpants are also exposed to the same random growth-rate of the underlyng fund, denoted by the letter C. They both convert (or exchange) ther VPA nto an IVA at the antcpated rate of A (for example, $17 dollars per each dollar of lfetme ncome). Fnally, the partcpant wth the guarantee s promsed the payment wll never fall beyond the base B. Note that the product desgn we are nvestgatng n ths secton assumes that the guaranteed base B wll be establshed at retrement. Specfcally, n the basc cases, B wll equal the maxmum of a specfed, age-dependent percentage of the ntal depost and 5% of the account value at retrement. Thus, the partcpant wll ratchet-up the value of ther ntal guarantee, but only at the tme of annutzaton. Ths means that f the account value of the underlyng fund ncreases substantally durng the savngs perod and the orgnal guaranteed base (whch we denote by g y ) s less than 5% appled to the retrement account value, t wll be ratonal to step-up ths guarantee. The techncal appendx elaborates on ths aspect of the guarantee. Table #3 whch s n the last secton of report -- lsts the precse nput varables that were used for each of the 25 case smulatons we conducted. Gven the scalable nature of the analyss, n all cases we assumed that $10,000 was deposted nto both accounts: the VPA (whch upon annutzaton becomes an IVA) and the GVPA (whch upon annutzaton becomes a GIVA). The subsequent tables lst the nput parameters (on top) and the output results (on the bottom) of each smulaton. A number of nput parameters are hghlghted to emphasze the man focus of each smulaton. In Smulatons #1-4, we assumed that the growth rate (denoted by h) s equal to 8%, and that the volatlty (denoted by σ) s equal to 15%. Asset-based fees were held constant at 50 bass ponts for the asset management fees (denoted by f A ) and 80 bass ponts for the nsurance expense fees (denoted by f G ). Based on our smulaton results, we fnd that there s a sgnfcant probablty that the ntal ncome provded by the IVA wll be less than that of the GIVA at the pont of retrement, after deferral perods of 30, 20 and 10 years. Ths s what we mean by the probablty of relatve loss. Page 13 of 51

14 In Smulatons #1-4, the ndvdual who nvests $10,000 at age 45 and annutzes the accumulated value at age 65 faces the hghest relatve rsk of loss. In ths case, accordng to the smulaton results, the probablty IVA 65 <GIVA 65 s 31.09%. If the same $10,000 s nvested at age 35 and annutzaton takes place at age 65, the probablty of relatve loss s 25.22%. The ntuton for ths result s as follows. Although the ncome base that s guaranteed at the tme of the orgnal nvestment s hgher at age 35, the ncreased tme span between nvestment and annutzaton allows the ntal depost of $10,000 to grow to a hgher value. Ths, n turn, partally offsets the level of the hgher guaranteed ncome factor. Smulaton #3 ndcates that nvestng at age 55 and annutzng at age 65 (after a 10 year deferral perod) results n a probablty of relatve loss of 27.53%. The tables wth Smulatons #1-4 also provde loss probabltes for the later years of retrement. The relatonshp between the nvestment age and the probablty of relatve loss remans the same. The 35 year-old nvestor faces a chance of approxmately 32.48% that the ncome provded by an IVA s less than that of the GIVA at age 70 (note that the opposte s not true,.e., that 67.52% of the tme the IVA > GIVA; n theory, the upsde would be the same snce they both use the same underlyng fund); the 45 year-old faces a 34.24% chance and the 55 year-old a 30.53% chance. We can also examne the probabltes of relatve loss for a 65 year-old nvestor who annutzes mmedately and there s an 18.75% chance that the IVA ncome wll be less than the GIVA ncome at age 70. At age 75, the probablty equals 15.95%, at age %, at age %, at age %, and fnally at age %. Smulatons # 5a-5e were conducted usng the growth rate and volatlty parameters, based upon the hstorcal returns of a generc dversfed fund. In ths partcular case, the combnaton of a hgh return and a low volatlty resulted n lower relatve probabltes of loss. Ths s because the (better) performance of the fund s expected to trgger the ncome guarantee less frequently. In the subset contanng Smulatons #5a-5c we vared the fees for the contract of an nvestor assumed to annutze mmedately. In Smulatons # 5d-5e, we assumed a 20 year deferral perod that s, an nvestment that s made at age 45 and annutzed at age 65 - and also vared the fees. As would be expected ntutvely, hgher combned fees resulted n margnally hgher probabltes of relatve loss. We also conducted a set of smulatons (#6-9) n whch we examne the mpact of ncreasng the rsk of the underlyng nvestment portfolo by changng the expected growth Page 14 of 51

15 and volatlty parameters to 10% and 20%, respectvely. In makng ths change, we dscovered a reduced probablty of relatve loss durng retrement years across all nvestment ages. Ths effect, not surprsngly, was most pronounced at younger nvestment ages. For example, as can be seen n Smulatons #1 and 6, the rsk of loss at retrement decreases by 10.27%. For a 45 year-old nvestor the rsk at retrement drops by 9.56% and for a 55 year old nvestor by 4.93%. However, f the nvestor annutzes mmedately upon nvestng at age 65, the probablty that the ncome from the IVA s less than that of the GIVA at age 70 drops by only 0.2%. Conversely, when we reduce the expected growth rate from 8% to 6% and reduce the volatlty from 15% to 10%, we notce that the probablty that the IVA<GIVA throughout the retrement years ncreases for all nvestment perods. Ths effect, agan, s most notceable when the ntal depost s made at age 35. Here, the loss of probablty at retrement at age 65 - rses from 25.22% (n Smulaton #1) to 53.90% (n Smulaton # 10). Durng the later retrement ages, for example age 70, the probablty of loss rses from 32.48% to 53.79%. The alternatve parameters do not have such a drastc mpact when the nvestor mmedately annutzes hs or her nvestment at age 65. For example, 5 years after retrement, at age 70, there s an 18.75% chance (Smulaton #4) that the ncome from the IVA s less than the ncome from the GIVA under the ntal parameters, whereas the probablty ncreases by only 0.20% to 18.94% (Smulaton #13) when the return and volatlty are lowered. The second metrc that we focused on to assess the value of downsde protecton was the Opton s Worth. The Opton s Worth s a valuaton procedure that attempts to estmate what t would cost an ntermedary to hedge a partcular guarantee usng the market for dervatve securtes. Ths valuaton procedure s at the heart of the famed Black-Scholes equaton and s frequently used by nvestment banks and hedge funds to mark-to-market ther tradng poston on a daly bass. Ths valuaton procedure s also used for accountng purposes, for example, to estmate the cost of ncentve stock optons, whch must be treated as expenses. Thus, the Opton s Worth valuaton algorthm s ubqutous n fnancal markets and for ths reason s qute approprate n our context. For example, an Opton s Worth of 140% means that the buyer s gettng a value whch s 40% more than what they are payng. Lkewse, an Opton s Worth of 95% mples that the buyer s losng 5% by acqurng ths nstrument. One can thnk of the Opton s Worth as the generalzed money s worth, except that the random nature of the underlyng varables s taken nto account explctly. Page 15 of 51

16 Mathematcally, the Opton s Worth s computed by projectng future cash flow benefts net of any fees pad -- at a rsk-adjusted rate and then dscountng those cash flows at a rsk-free rate. The precse mechancs of ths calculaton are dscussed n greater detal n the techncal appendx. Note that n a properly functonng captal market, one would expect that the Opton s Worth of any traded fnancal nstrument s very close to 100%. Of course, when these nstruments can not be sold short or are n the presence of transacton costs and other market restrctons, t s possble to see large dscounts or premums, whch are represented by the Opton s Worth. However, lke any valuaton methodology that s based on future assumptons, cauton s warranted n nterpretng the results. Ths s especally true wthn the context of long-term projectons. At best, an Opton s Worth greater than 100% mples that the product adds relatve economc value. And, an Opton s Worth that s much smaller than 100% mples that economc value s beng destroyed, both on a present value bass. The set of smulatons pertanng to the Opton s Worth was comprsed of Smulatons # The (rsk neutral) expected benefts mnus fees quantty can be vewed as a proxy for the market value of the guarantee offered by the GIVA. A separate smulaton was conducted n order to confrm that the value of the IVA s equal to the ntal nvestment, when all fees are equal to zero. And ndeed, the smulated expected value of the generc annuty s wthn $15 of the orgnal $10,000 nvestment. The results of Smulatons #19-22, where the nsurance fee of 0.80% s charged, lead to the concluson that the value of the downsde protecton s hghest when the ntal nvestment s made at age 35 and annutzed at age 65. Ths s compared to nvestng at ages 45, 55 and 65 whle mantanng the same annutzaton age. Specfcally, the value of the GIVA at age 35 s approxmately $14,145, or 141% of the orgnal nvestment for a 35 year old, $12,664 or 127% of the ntal nvestment for a 45 year old, $10,403 or 104% for a 55 year old, but s only $9,673 or 97% for a 65 year old. Table #2 provdes a summary of the relatonshp between the varous nputs to the GIVA n relaton to the () probablty of relatve loss and () Opton s Worth of the contract. Page 16 of 51

17 Input Factor Table 2 Is It Better or Worse? What nfluences the Value of a GIVA Probablty of Relatve Loss (GIVA better than IVA) Optons Worth Hgher Investment Volatlty Increases Increase Better Investment Returns Decrease No Impact Purchase at Younger Age Depends on Age & Horzon Increases 5% Ratchet at Retrement Increases Increases Projectng Mortalty Table Increases Decreases Hgher Asset-Based Fees Increases Decreases Note: In the GIVA vs. IVA comparson we are assumng that both products are dentcal n all aspects, except for the guaranteed base downsde protecton. 5.) Conclusons and Fnal Remarks: There appears to be unversal agreement amongst fnancal economsts and penson actuares about the substantal socal welfare benefts from payout (or mmedate) annuty contracts. But the publc and meda have yet to embrace ths rsk-management nstrument as beng equally mportant as a well dversfed retrement portfolo of stocks and bonds. Indeed, the global trend away from Defned Beneft (DB) and towards Defned Contrbuton (DC) plans, n conjuncton wth exceptonally low levels of voluntary annutzaton, cry out for a new way or revstng old ways of thnkng about the provson of lfetme retrement ncome. Ths paper promotes, advocates and explores the fnancal rsk-and-return propertes of a guaranteed varable payout annuty (GVPA). The GVPA would be acqured at a young age and small premums would be pad over a long perod of tme but would begn payng at retrement. The GVPA s a close relatve of a DB penson and s ntended for those who have an nsuffcent or no DB plan, as an opton wthn a DC (or 401k) style plan. The GVPA would enttle the holder to nsure aganst the rsk of outlvng assets. Page 17 of 51

18 We have provded a number of dfferent metrcs for quantfyng the value and beneft of a GVPA compared to a generc VPA that does not offer any downsde protecton. We conclude by argung that over long tme horzons the mplct nsurance beneft offered by such a structure can be substantal. References and Addtonal Ctatons: Amerks, J., M. Veres and M. Warshawsky (2003), Retrement ncome that lasts a lfetme, Journal of Fnancal Plannng, pg Brown, J. R. and M. Warshawsky (2001), Longevty-nsured retrement dstrbutons from penson plans: Market and regulatory ssues, Natonal Bureau of Economc Research (NBER), Workng Paper # Chen, P. and M.A. Mlevsky (2003), Mergng asset allocaton and longevty nsurance: an optmal perspectve on payout annutes, Journal of Fnancal Plannng, Vol. 16(6): Drnkwater, M., M.W. Swanson and N.M. Byrne (2005), Payout Optons n 401(k) Plans, LIMRA Internatonal, Wndsor Connectcut. Ibbotson Assocates (2004). Stocks, Bonds, Blls and Inflaton 2004 Yearbook. Chcago: Ibbotson Assocates. Mlevsky, M.A. (2005), Real Longevty Insurance wth a Deductble: Introducton to Advanced Lfe Delayed Annutes (ALDA), North Amercan Actuaral Journal, October/November Mlevsky, M.A. (2006) The Calculus of Retrement Income: Fnancal Models for Pensons and Insurance, Cambrdge Unversty Press, forthcomng. Page 18 of 51

19 Techncal Appendx: In the body of the report we conducted fnancal smulatons to compute two dstnct metrcs for valung the protecton embedded wthn a Guaranteed Immedate Varable Annuty (GIVA), compared to a non-guaranteed or generc Immedate Varable Annuty (IVA). The frst metrc focused on the Probablty of Relatve Loss forecast that an IVA wll generate less ncome compared to a GIVA, when both annutes are lnked to the same underlyng nvestment account. The second metrc focused on the Opton s Worth, whch serves as a proxy for the amount captal markets would charge to re-nsure the downsde protecton embedded wthn a GIVA, compared to an IVA whch does not offer ths protecton. Computng the above-mentoned probablty of relatve loss and the Opton s Worth requres dstnct smulaton nputs and outputs, although the underlyng data generatng models are smlar. In ths appendx we descrbe the precse methodology and assumptons behnd these two metrcs. Our analyss starts at tme t=0, when the partcpant/nvestor deposts a lump-sum W 0 nto a varable annuty account at age y. The value of the account (depost) wll grow at a stochastc annualzed rate denoted by η (Greek letter eta), between the date of depost and retrement age x>y at t = T. Ths annualzed rate s gross of any fees. For convenence, we assume that η s expressed usng contnuous compoundng, whch means that the random value of the varable annuty account (a.k.a. the orgnal depost) at tme T, wll be equal to and denoted by the symbol W T ηt := W0e, before any asset management (AM) or mortalty fees (ME) are deducted. Once we subtract these fees, the stochastc value of the varable annuty account at retrement wll be equal to W T : = W e 0 ( η f f ) T A G, where f A denotes the annual AM fee and f G denotes the annual ME fee, both expressed usng contnuous compoundng. For all ntents and purposes we wll assume that the monthly compoundng of fees s akn to contnuous compoundng snce qute close to f e. Page 19 of 51 ( 1 f /12) 12 + s In all the smulatons, we assumed that the random growth rate η was Normally dstrbuted wth a (geometrc) mean value of h = E[η ] and a standard devaton (volatlty) of σ / T t, where T t denotes the calendar tme that elapses between the depost t, and retrement T. Ths obvously mples zero seral correlatons between successve returns snce

20 the returns are assumed ndependent. We are cognzant that our (smple) model mght poorly descrbe the performance of a bond-heavy fund, but are reasonably confdent that our results wll not be meanngfully mpacted when dealng wth an equty-heavy fund. Stated dfferently, we beleve that the uncertanty regardng the nput parameters from long-term growth rates are more mportant from a probablstc perspectve compared to the dfference between a 0% and 10% seral correlaton. In the probablty of relatve loss smulatons we used values of h = 6%,8%,10% and volatlty values of σ = 10%,15%,20%. Note, also, that although: h = E[η ], the expected account value of W T at retrement, s actually E[ W ] T 2 ( h+ 0.5σ ) T = W0e. Ths s why the quantty.5 2 h + 0 σ s often labeled the arthmetc mean return and h s the geometrc mean return. For example, f h = 8% and σ = 15%, then (0.15) 2 = s the arthmetc mean return. We reported both numbers n all smulaton results. Now, let s move on to retrement, once the (guaranteed) varable payout annuty has been converted nto a (guaranteed) mmedate varable annuty. Let the symbol IVA denote the annual ncome the annutant receves from a generc IVA durng the th year of retrement. Ths quantty s stochastc and depends on the performance of the underlyng fund n the (-1) th year of retrement. Lkewse, let the symbol GIVA denote the annual ncome the annutant receves from the guaranteed IVA durng the th year of retrement. Ths quantty s also stochastc, but wll have a lower bound denoted by G, where G s determned and known at the pont of retrement. The quantty G wll automatcally be set equal to the greater of tmes the orgnal depost W 0, and g 65 = tmes the account value at retrement W T, where g y ths new symbol g y denotes the guaranteed ncome factor stpulated at the tme of the depost. For example, for the year 2005 baselne smulatons, we used the followng guaranteed ncome factor values: g =.2464, g = , g = The G = max[ g W,0.05W ] structure whch s the essence of the downsde protecton y 0 T we are nvestgatng n ths report -- allows us to capture the opton of the partcpant to stepup the guaranteed beneft just pror to annutzaton. We also ran some cases wth 0.04 and 0.06 nstead of 0.05 to measure the senstvty of the results to ths so-called opton. Page 20 of 51

21 To understand the relatonshp between IVA and recursve way n whch the generc payment GIVA, we must frst understand the IVA s determned. Note that f UF denotes the gross return from the underlyng fund (UF) durng the th year of retrement, pror to any management fees, then: where the new factor IVA (1 ) + 1 = + M IVA, (eq.1) M s defned va: ( f A + f ) UF + e G M = 1, (eq.2) 1 + R The UF value s stochastc, and generated usng the same dstrbuton as n the accumulaton phase; UF = η e 1. Note that M s obvously ncreasng wth UF, but decreasng wth the fees ( f A + fg ) and the assumed nterest rate R. The value of M can be negatve and next year s ncome wll declne -- f the gross returns from the underlyng fund s not enough to overcome the fees and the hurdle rate R. For example, f n the 5 th year of retrement the ncome from the generc IVA was $10,000 per annum and durng the same year the underlyng fund earned UF = 11% before 5 asset management fees of f = 0.5% and mortalty expense fees of f = 0.8%, then under an A R = 3% assumed nterest rate (AIR), the ncome from the generc IVA n the 6 th year of retrement would be IVA = (1 6.51%). 6 + Now, movng on to compute the perodc payment under the guaranteed IVA, we must perform a two-step recursve procedure. Frst, at retrement, we compute the ntal ncome from the GIVA usng the followng formula: GIVA = max[ G, W T / a ], (eq.3) 1 x where G s the guaranteed base and a x s the annuty factor, whch s appled to the account value at retrement, tme T. For example, under the Annuty 2000 (female) mortalty table, the value of a 65 at age 65 s 1000 / = per dollar of lfetme ncome, wth a 20-year payment certan. Thus, f the account value at retrement was W = n one of the smulaton outcomes, then the ntal GIVA ncome would be the greater of G and / = dollars per year. T G Page 21 of 51

22 In the second and subsequent years of retrement, the annuty ncome from the GIVA wll satsfy the followng recursve equaton: [(1 + M ) IVA L G] GIVA = max,, (eq.4) + 1 where M s the same ncome adjustment factor defned n equaton (eq.2), but the new varable L s defned by: L j = 1 = max[ ( GIVA IVA ),0] (eq.5) j j Intutvely, one can thnk of L as a shadow account (or nterest free loan), whch keeps track of any excess payments that have been made to the GIVA annutant, above and beyond payments made to the IVA annutant. If ths shadow account and the value of M are postve, then the GIVA annutant wll not receve the full ncrease n annuty payment relatve to the prevous year, untl the shadow account balance s elmnated. Of course, there s always a floor n place, denoted by G, whch creates a lower bound on payments. To understand the mechancs of GIVA versus IVA, here s a smple three-perod example. The assumed nterest rate s R = 3%, the asset management fee s f = 0.5% and the mortalty expense fee s f = 0.8%. Assume that G = 3000 dollars, W = dollars G and that a 65 = at age 65, as per the Annuty 2000 (female) table. The non-guaranteed IVA payment wll be equal to IVA 2789 dollars, whle the ntal guaranteed payment wll be 1 = GIVA = dollars. Thus, the shadow account starts off at a value of L = dollars, snce there has been an extra payment made to the protected annutant. Assume further that T A UF = 15% n the frst year of retrement. Thus, M = 18.73% accordng to equaton (eq.2), 1 1 and the IVA payment for the second year of retrement shrnks to IVA 2267 dollars. The GIVA payment stays the same, at the mnmally guaranteed GIVA 3000 dollars. The 2 = shadow account value has now ncreased to L 944 dollars. Now, for the last part of ths 2 = 2 = example, assume that UF = +30% n the second year of retrement. In ths case, 2 { M = % } and the IVA ncreases to IVA = However, the GIVA payment wll stay at 2 3 $3000, and the shadow account wll ncrease to L 3 = 1112 dollars. Wth a numercal example behnd us, and all the mportant symbols n place, we can put ths all together to arrve at precse expressons for our two metrcs of nterest. The frst s: Page 22 of 51

23 Probablty of Relatve Loss = Pr[ IVA z GIVAz y] (eq.6) Ths s the probablty that IVA ncome wll be lower than the GIVA ncome and hence the protecton was worthwhle vewed from the perspectve of someone aged y. The varable y can be age 35, 45, 55 or even 65 and the probablty forecast wll obvously depend on ths condtonng age. The closer we are to the age z n queston, the more nformaton we have regardng whether Pr[ IVAz GIVAz y]. For example, Pr[ IVA GIVA75 ] denotes the probablty assumng the partcpant s currently 45 years old that hs/her IVA payment would be lower than the promsed GIVA payment, at age 75. Lkewse, the quantty Pr[ IVA75 GIVA75 55] s the same probablty, but now we are condtonng on age 55. Of course, one s never certan whether they wll actually be alve at age 75, whch s why all our results report the probablty of survval adjacent to the actual Pr[ IVA GIVA y] values. We wll denote ths quantty by ( p y ). Ths s the probablty that a y-year old wll survve years. For consstency, we used IAM 2000 values for ths quantty as well. Thus, by smulatng values of UF and hence values of GIVA and z z IVA, we are able to count the number of tmes IVA GIVA and dvde ths by the total number of smulatons to z z arrve at an estmate for Pr[ IVA GIVA y]. We used N = 10,000 smulaton for all of our z z results. Movng on, the second quantty of nterest the expected Opton s Worth -- s computed n three stages. Frst, we quantfy the dscounted payoff va: B = 120 t ( + T t) ( 1+ R) ( T t+ p y ) GIVA (eq.7) = 1 The varable B s stochastc snce we don t know the outcome of any of the values untl after the returns GIVA payment UF have been observed. Ths s the present value of the benefts that one obtans from the guaranteed IVA, where the dscountng takes place at the assumed nterest rate R. We then subtract-off any fees charged for ths guaranteed IVA. Ths s calculated va the formula: F T t 120 x j ( T t+ ) = f G ( j p y ) W j (1 + R) + ( T t+ p y ) GIVA ( ax+ )(1 + R), (eq.8) j= 1 = 1 Page 23 of 51