Lifecycle Funds. T. Rowe Price Target Retirement Fund. Lifecycle Asset Allocation

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1 Lifecycle Funds Towards a Dynamic Asse Allocaion Framework for Targe Reiremen Funds: Geing Rid of he Dogma in Lifecycle Invesing Anup K. Basu Queensland Universiy of Technology The findings of he Mercer 2000 survey of DC plans in UK (as cied in Blake, 2006 show ha hese funds were he mos common defaul opions covering 55% of funds. As repored by Vanguard (2006, one of he larges pension plan managers in USA, wo hirds of heir plans offered lifecycle opions in 2005, up from one-hird in Asses under lifecycle fund amouned o $160 billion in 2005 compared o below $10 billion in The US Presiden s plan o reform Social Securiy is modelled on a lifecycle porfolio sraegy (Shiller, Lifecycle Asse Allocaion T. Rowe Price Targe Reiremen Fund Age based asse swiching (100 age% in socks Malkiel (1996 Oher rules like your age in bonds (Bogle, 1994; Viceira, 2007 Invesmen Objecives Growh in early years Preservaion in laer years 3 4 1

2 Fideliy Targe Reiremen Fund A lifecycle plan ha makes he percen allocaed o socks somehing akin o he privaely- offered lifecycle plans may do much worse han a 100% socks porfolio since young people have relaively lile income when compared o older workers... The lifecycle porfolio would be heavily in he sock marke (in he early years only for a relaively small amoun of money, and would pull mos of he porfolio ou of he sock marke in he very years when earnings are highes. Rober Shiller (The Economiss Voice, Tesing he Efficacy of Lifecycle Funds: Earlier Paper Porfolio Size Effec in Reiremen Accouns: Wha Does I Imply for Lifecycle Asse Allocaion Funds (Basu and Drew, 2007 Lifecycle Porfolios We use four differen lifecycle porfolios o simulae wealh oucomes. Iniially all of hem are 100% sock porfolios. They sar swiching o a porfolio of bonds and cash a differen poins of he invesmen horizon. The swiching is linear such ha he allocaion o socks is nil a he poin of reiremen. Lifecycle (20 20 Swich asses 20 years before reiremen Lifecycle (25,15 Swich asses 15 years before reiremen Lifecycle (30,10 Swich asses 10 years before reiremen Lifecycle (35, 5 Swich asses 5 years before reiremen 7 8 2

3 Conrarian Porfolios As Benchmarks Lifecycle & Conrarian Pairs We design CONTRARIAN porfolios as MIRROR IMAGES of lifecycle porfolios. Iniially all of hem are 100% bonds and cash porfolios. They, hen, swich o socks over differen periods in he invesmen horizon. The swiching is linear such ha he allocaion o socks is nil a he poin of reiremen. A Conrarian(20,20 Swiches o socks over firs 20 years. Conrarian (15,25 Swiches o socks over firs 15 years. Conrarian (10,30 Swiches o socks over firs 10 years. Conrarian (5,35 Swiches o socks over firs 5 years. B 9 10 Lifecycle & Conrarian Pairs TERMINAL VALUES OF RETIREMENT PORTFOLIO (in nominal dollars Sraegy Mean Median 1s Quarile 3 rd Quarile Pair A C Lifecycle (20,20 Conrarian (20,20 CONT - LCYL (% Pair B Lifecycle (25, Conrarian (15, CONT - LCYL (% Pair C D Lifecycle (30,10 Conrarian (10, 30 CONT - LCYL (% Pair D 11 Lifecycle (35,5 Conrarian (5, CONT - LCYL (%

4 TERMINAL VALUES FOR MOST ADVERSE OUTCOMES (in nominal dollars Accumulaion Pahs ASSET ALLOCATION Perceniles of Disribuion STRATEGY PAIR A Lifecycle (20, A Converse (20, LCYL CONT (% 43.08% 18.85% 8.41% 2.36% -1.35% PAIR B Lifecycle (25, Converse (15, LCYL CONT (% 32.24% 9.93% 2.50% -1.62% -4.46% PAIR C Lifecycle (30,10 Converse (10,30 LCYL CONT (% % % % % % B PAIR D Lifecycle (35, Converse (5,35 LCYL CONT (% % % % % % Accumulaion Pahs Cond. Accumulaion Pahs (2-D View C A D B

5 Accumulaion Pahs (2-D View cond. Summary of Resuls C D 17 The growing porfolio size in laer years is imporan from he asse allocaion perspecive. Due o his porfolio size effec, final invesmen oucomes of plan paricipans become more sensiive o choice of asse allocaion in laer years relaive o early years. By invesing conservaively in laer years, lifecycle sraegies dampen growh poenial of reiremen plan porfolio i.e. he cos o reduce volailiy is significan in erms of foregone upside poenial. Swiching o less volaile asses before reiremen can lessen he impac of severe sock marke downurns. Bu his move o preserve accumulaed wealh can only be jusified when he accumulaion a he poin of swich exceeds he arge se by he paricipans. 18 Curren Paper: A Dynamic Framework for Lifecycle Asse Allocaion Lifecycle Sraegies In he previous sudy, we exposed he limiaions of lifecycle sraegies. Convenional lifecycle funds follow a pre-deermined and performance-blind asse allocaion sraegy where no only he swiching of asses is always unidirecional from socks o fixed income bu i is also done in proporions ha are prespecified during he incepion of he fund. In his sudy, we propose a dynamic asse allocaion framework which is based on performance feedback. Blake e al. (2001 and Ars & Vigna (2003 examine a feedback based allocaion rule in UK bu his differs significanly from he sraegy we formulae. We consider wo variaions of he convenional lifecycle sraegy: LC 20,20 Invess in a 100% socks porfolio for 20 years and hen linearly swiches o bonds and cash over he remaining 20 years. A he poin of reiremen all asses are held in bonds and cash. LC 30,10 Invess in a 100% socks porfolio for 20 years and hen linearly swiches o bonds and cash over he remaining 20 years. A he poin of reiremen all asses are held in bonds and cash

6 Dynamic Lifecycle Sraegy Dynamic Lifecycle Sraegy..Con d We consruc wo dynamic lifecycle sraegies where he swiching of asses is based on how he porfolio has performed relaive o he invesors wealh accumulaion arge (annual reurn of 9% on invesmens DLC 20,20 Invess in a 100% socks porfolio for firs 20 years and hereafer, for he nex 10 years, if he acual accumulaion exceeds he arge, he asses are swiched o a relaively conservaive porfolio comprising 80% socks and 20% fixed income (equally spli beween bonds and cash. However, if he acual accumulaion in he accoun is found o fall below he arge, he porfolio remains invesed in 100% socks. In he final 10 years if he value of he porfolio in any year maches or exceeds he invesor s arge accumulaion a ha poin, 60% of asses are invesed in equiies and 40% in fixed income (equally spli beween bonds and cash. Failing o achieve 21 he arge reurn for he holding period, resuls in all asses being invesed in a 100% socks porfolio. DLC 30,10 Invess in a 100% socks porfolio for firs 30 years and hereafer, for he nex 5 years, if he acual accumulaion exceeds he arge, he asses are swiched o a relaively conservaive porfolio comprising 80% socks and 20% fixed income (equally spli beween bonds and cash. However, if he acual accumulaion in he accoun is found o fall below he arge, he porfolio remains invesed in 100% socks. In he final 5 years if he value of he porfolio in any year maches or exceeds he invesor s arge accumulaion a ha poin, 60% of asses are invesed in equiies and 40% in fixed income (equally spli beween bonds and cash. Failing o achieve he arge reurn for he holding period, resuls in all asses being invesed in a 100% socks porfolio. 22 Accumulaion Model Reurn Generaion Model where W = value of plan asses accumulaed a he poin of reiremen k = plan conribuion rae p = probabiliy of unemploymen in year S = annual salary in year r rae of invesmen reurn earned in year = R = number of years in he plan before reiremen where = S 0 g = W = k S = S R 1 = 0 (1 p S (1 + r 1 0 (1 + g saring salary of he plan paricipan annual salary growh rae R 1 u= + 1 (1 + r u 23 Porfolio Reurns are dependen on reurns for individual asse classes and weighs assigned o hem h where w weigh assigned o he asse class in year i, = i reurn on he h = i asse class in year r i, w is given by he asse allocaion sraegy under consideraion i, r i, is derived by resampling hisorical reurn daa for nominal reurns on socks, bonds, and bills. This is used o generae porfolio reurns every period. r p, = wi, ri, 24 6

7 Daa & Mehodology Boosrap Resampling We use updaed version of nominal reurn daa for US socks, bonds, and cash beween 1900 and 2004 (105 years compiled by Dimson, Marsh, and Saunon and commercially available hrough Ibboson Associaes, Chicago. We use boosrap resampling o generae simulaed annual reurns for each lifecycle and dynamic lifecycle sraegies. These reurns are used o compue he final accoun balance of he paricipan a he poin of reiremen. For he purpose of comparison, we also simulae erminal wealh oucomes under a balanced sraegy and a 100% socks sraegy. 25 We randomly draw wih replacemen from he empirical disribuion of asse class reurns o generae asse class reurn vecors for each year of he 40 year invesmen horizon of he DC plan paricipan. Thus we reain he crosscorrelaion beween he asse class reurns as given by he hisorical daa series while assuming ha reurns for individual asse classes are independenly disribued over ime. The asse class reurn vecors are hen combined wih he weighs accorded o he asse classes in he porfolio under each of he lifecycle and dynamic lifecycle sraegy pairs (as well as he balanced and 100% socks sraegies o generae porfolio reurns for each year in he 40 year horizon. The simulaed invesmen reurns are applied o he reiremen accoun balance a he end of every year o arrive a he erminal wealh in he accoun. For each sraegy he simulaion is repeaed 10,000 imes. Thus, for each of he sraegies, we have 10,000 invesmen reurn pahs ha resul in 10,000 wealh oucomes a he end of he 40-year horizon. 26 TERMINAL VALUES OF RETIREMENT PORTFOLIO (in nominal dollars CDF Plos for LC20,20 and DLC 20, 20 Sraegy Mean Median 25 h Percenile 75 h Percenile Panel A Dynamic( DLC 20, 20 Lifecycle( LC 20, % Socks Balanced Panel B Dynamic( DLC 30, 10 Lifecycle( LC 30, % Socks Balanced

8 CDF Plos for LC and 30,10 DLC 30, 10 Shorfall Measures of Dynamic Sraegies Asse Allocaion Sraegy Shorfall Probabiliy ( LPM 0, DLC DLC 20,20 Average Shorfall ($ ( LPM 1, DLC Lifecycle ( LC 20, % Socks Balanced DLC 30,10 Lifecycle ( LC 30, % Socks Balanced Exreme Adverse Oucomes for Differen Asse Allocaion Sraegies Asse Allocaion Sraegy Panel A Dynamic ( DLC 20, 20 Lifecycle ( LC 20, 20 VaR a Differen Confidence Levels ETL a 95% Confidence Level 99% 95% 90% % Socks Balanced Panel B Dynamic ( DLC 30, 10 Lifecycle ( LC 30, % Socks Balanced Summary of Resuls Wihou giving up he basic ene of lifecycle invesing - seeking reduced volailiy in he value of he accumulaion fund as one ges closer o reiremen he dynamic sraegies overcome he limiaions of convenional lifecycle sraegies o produce superior wealh oucomes. Our resuls conradic he findings of Blake e al. (2001 bu his is no unexpeced. The dynamic sraegies have slighly higher chance of achieving he accumulaion arge compared o 100% socks sraegy. In our sudy, he dynamic sraegies have an almos even or higher chance of ouperforming 100% socks sraegy. The below 5 h percenile oucomes for he dynamic sraegies are slighly inferior o hose of convenional lifecycle sraegies. A saic balanced diversified fund produce he bes oucomes in his range. 32 8