Research. Michigan. Center. Retirement. Understanding Trading Behavior in 401(k) Plans Takeshi Yamaguchi. Working Paper MR RC WP

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1 Mchgan Unversty of Retrement Research Center Workng Paper WP Understandng Tradng Behavor n 401(k) Plans Takesh Yamaguch MR RC Project #: UM05-S2

2 Understandng Tradng Behavor n 401(k) Tradng Plans Takesh Yamaguch The Wharton School September 2006 Mchgan Retrement Research Center Unversty of Mchgan P.O. Box 1248 Ann Arbor, MI (734) Acknowledgements Ths work was supported by a grant from the Socal Securty Admnstraton through the Mchgan Retrement Research Center (Grant # 10-P ). The fndngs and conclusons expressed are solely those of the author and do not represent the vews of the Socal Securty Admnstraton, any agency of the Federal government, or the Mchgan Retrement Research Center. Regents of the Unversty of Mchgan Davd A. Brandon, Ann Arbor; Laurence B. Detch, Bngham Farms; Olva P. Maynard, Goodrch; Rebecca McGowan, Ann Arbor; Andrea Fscher Newman, Ann Arbor; Andrew C. Rchner, Grosse Ponte Park; S. Martn Taylor, Gross Ponte Farms; Katherne E. Whte, Ann Arbor; Mary Sue Coleman, ex offco

3 Understandng Tradng Behavor n 401(k) Plans Takesh Yamaguch Abstract We use a new database coverng 1.2 mllon actve partcpants to study tradng actvtes n 1,530 defned contrbuton retrement plans. Descrptve statstcs and regresson analyss ndcate some nterestng tradng patterns. Frst, we show that tradng actvty n 401(k) accounts s very lmted: only 20% of partcpants ever reshuffled ther portfolos n two years. Second, demographc characterstcs are strongly assocated wth tradng actvtes: traders are older, wealther, more hghly pad, male employees wth longer plan tenure. Fnally, we fnd that plan desgn factors, such as the number of funds offered, loan avalablty, and specfc fund-famles offered have sgnfcant mpacts on 401(k) plan partcpants tradng behavor. Moreover, on-lne access channels stmulate partcpants to trade more frequently, although they do not ncrease turnover rato as much. We conclude that plan desgn features are crucal n sharng tradng patterns n 401(k) plans. Authors Acknowledgements I thank Olva S. Mtchell for her support and gudance durng the research process. I thank Stephen Utkus and Gary R. Mottola from the Vanguard Group for provdng excellent data and suggestons. I am also grateful for comments from Prof. Terrance Odean, Tongxuan Yang, Sojong Park, Qngy Song. Any error s my own.

4 1. Introducton Indvdually-managed 401(k) accounts are now the most wdespread nvestment form for retrement savng n the U.S. Currently, about one-thrd of all workers are enrolled n 401(k) plans, managng near $1.9 trllon n assets 2 worth about 20% of the U.S nomnal GDP. Defned contrbuton schemes are also becomng more popular n other countres ncludng Australa, Chle, Sngapore, and Sweden where nvestment choces are offered to partcpants. Japan passed ts Defned contrbuton penson Act n Oct 2001, and Korea also started a DC plan scheme n December Although some theoretcal fnancal research papers suggest that the ndvdual tradng behavor can nfluence the returns and volatlty of the fnancal market (e.g. Bertola and Fores 1995, Odean 1998), lttle s known about how people actually nvest ther 401(k) plan assets. Further, there s nothng known about how ther tradng patterns mght nfluence retrement outcomes. Recent emprcal research by Odean and hs colleagues (Odean 1999; Barber and Odean 2000, 2001) provdes evdence on tradng actvtes and portfolo performance of ndvdual nvestors, but these papers focus on the dscount brokerage accounts, representng only a narrow and probably non representatve subset of the unverse of ndvdual nvestors. In addton, because dscount brokerage account holders are those who presumably lke to trade, t s necessary to pay attenton to self-selecton bas to nterpret ther results. For defned contrbuton accounts, as far as we know, Agnew (2003) s the only emprcal analyss focusng on the relatonshp between ndvdual tradng actvtes and ther demographc characterstcs n 401(k) plans. Consequently, nevertheless that t s necessary to confrm whatever prevous results can be extended to other broader databases. We also need to nvestgate whether other factors beyond demographcs also drve partcpants to trade ther penson portfolos. In ths paper, we use an nvaluable new dataset, provded by the Vanguard Group on more than 3 mllon 401(k) partcpants n over 2,000 plans, to llustrate how partcpant and plan characterstcs shape tradng behavor n ndvdually-held voluntary retrement accounts. We examne the patterns of tradng n 401(k) plans, focusng on who trades, how often, what ther 2 The latest estmate about 401(k) plans by Department of Labor s for plan year 1999, whch was released n Summer In 1999, there are 335, (k) type plans coverng 38.6 mllon actve partcpants wth $1,790 bllon n assets. EBRI/ICI (Employee Beneft Research Insttute/Investment Company Insttute) estmates 401(k) plan unverse held $1,885 bllon n asset at year-end

5 turnover patterns are, as well as how plan desgn and other plan features nfluence ther tradng actvtes. The rest of ths paper s organzed as follows. In Secton 2, we revew prevous lterature on ndvdual nvestor tradng patterns. Secton 3 descrbes the dataset. Secton 4 presents descrptve statstcs regardng tradng behavor. In Secton 5, we present our multvarate analyss methodology, hypotheses, and regresson results. Conclusons appear n Secton Prevous Lterature Although there s a substantal theoretcal lterature regardng ndvdual portfolo tradng behavor, most of t has not focused on nvestment patterns n defned contrbuton retrement accounts. For nstance, the conventonal fnancal theory suggests that nvestors wll trade when the margnal beneft of tradng equals or exceeds the margnal cost (Grossman and Stgltz, 1980). By contrast, overconfdence theory predcts that nvestors wll trade to ther detrment (Gervas and Odean, 2001). Recently, Mtchell, Muermann, and Volkman (2004) have found that antcpated regret regardng nvestment outcomes prevents a regret-prone nvestor from makng extreme portfolo allocatons, whch would make hm more lkely to rebalance hs account as compared to a more conventonal ratonal nvestor. To date, lttle emprcal lterature has explored tradng patterns n retrement accounts, though there has been much research on nterestng and unexpected patterns of tradng n dscount brokerage accounts. A set of studes by Odean and hs co-authors (Odean 1999; Barber and Odean 2000, 2001) supports the overconfdence theory more than ratonal expectatons framework wth the exstence of transacton cost. Usng data on tradng actvtes of 78,000 dscount brokerage accounts, they computed the transacton cost, defned as the sum of bd-ask spread and commsson fees. Comparng realzed returns and the transacton costs, they provde evdence on tradng behavor and nvestment performance of ndvdual nvestors. For an nstance, they conclude that people tend to trade too much; tradng behavor appears hazardous to nvestors portfolo performance (Barber and Odean, 2000); men appear to trade more than women because they are more overconfdent (Barber and Odean, 2001). In addton, Kng and Leape (1987) examne the changes n portfolo composton over the lfe cycle from the transacton cost approach. Usng 1,978 Survey of Consumer Fnancal Decsons conducted by SRI (Stanford Research Insttute), they studed the portfolo selecton 3

6 problem of over 6,010 U.S. households. They classfy nvestment vehcles nto nformatonntensve assets such as ndvdual equty and other assets, and then they report that the ownershp of nformaton-ntensve assets ncreases even after controllng changes n wealth, margnal tax rate and household characterstcs. Therefore, the authors conclude that leanng and experence are mportant factors n lowerng transacton costs overtme, leadng to a postve relatonshp between nvestors ages and nformaton-ntensve portfolo selecton. Emprcal studes on tradng n 401(k) plans are few n number, manly because untl now, analysts have not had good qualty data on a wde varety of plan desgns and partcpant outcomes. To our knowledge, Agnew et al (2003) focusng on a sngle large 401(k) plan s the only emprcal work whch explores partcpants tradng patterns and ther portfolo selecton problem. That analyss studed about 6,500 retrement accounts durng Aprl 1994-August At frst, the authors examned the asset allocaton and tradng actvtes patterns usng tabulatons, and then they regressed equty allocaton, turnover rato and annual trade number on a set of demographc varables ncludng age, sex, salary, martal status, and tme n the plan. In addton, Agnew et al. also track partcpants over tme, whch makes t possble to nvestgate how equty allocaton and tradng behavor change as ndvduals age and gan senorty on the job. It also allows ther study to model the dependent varables as a functon of common tme effect. Fnally, they conclude that most asset allocatons are extreme (ether 100% or 0%), and there s nerta n asset re-allocatons; equty allocatons are hgher for males, marred nvestors and for nvestors wth hgher earnngs and more senorty on the job; equty allocatons are lower for the elder people. They fnd only lmted portfolo reshufflng, n sharp contrast to dscount brokerage accounts. Whether the results n Agnew et al. (2003) are generalzeable s n queston. For example, t would be useful to confrm whether ther fndng s specfc to that sngle plan, or rather whether t s a general phenomenon across plans. Moreover, when nterpretng the common tme-effect both on equty allocatons and tradng behavor, t s also necessary to take nto account that before Aprl 1994 (the begnnng pont of ther database), partcpants were only able to nvest n Guaranteed Investment Contracts (GICs). In addton, we also need to nvestgate whether other factors beyond demographcs can also nfluence ndvdual tradng 4

7 actvtes. 3 In partcular, we seek to learn whether plan desgn s sharng partcpants tradng behavor. As far as we know, our current nvestgaton s the frst comprehensve study on 401(k) tradng actvtes across multple plans. It s dstngushed from prevous studes n 2 ways: Frst, we study a database of over 3 mllon DC retrement accounts across above 2,000 plans, whch wll enable us to examne a larger subset of the 401(k) unverse. Second, we can study tradng patterns at the partcpant-level as a functon of both partcpant and plan-level varables. 3. Database and Descrptve Statstcs In ths secton, we descrbe our new database. In Part A, we ntroduce the raw data and dscuss ts reprensentatveness. Part B summarzes nvestment optons, ndustry, and plan-level nformaton. Part C presents partcpant-level characterstcs. A. The Vanguard Database Ths study uses a new database provded by the Vanguard Group (VG), contaned nformaton on more than 3 mllon DC plan accounts across 2, (k) plans. Those plans ncluded 984 funds n the nvestment menu 4 over the perod Jan Dec Ths s herarchcal database that conssts of 5 levels: tme, ndustry, plan, partcpant and trade. At the ndustry level, the database codes every plan sponsor based on 4-dgt NAIC 5 crtera, whch have been aggregated nto ten ndustres. 6 At the plan level, the plan fles record the major plan desgn features such as the number of funds offered, employer company stock as an nvestment opton, and loan avalablty. In partcular, ths fle enables us to fgure out changes n nvestment menu for each plan, so we can evaluate the mpact on partcpant level tradng behavor. 3 An analyss of just two 401(k) plans by Cho, Labson and Metrck (2002) evaluates only the mpact of nternet access to tradng behavor at plan-level, but does not look at tradng patterns and the mpact on partcpant-level. Benartz and Rchard Thaler (2001) consder a cross-secton of plans, rather than a cross-secton of ndvduals and nvestgates how allocatons at the plan-level change as a functon of the nvestment menu n the plans. 4 Actually, company stocks and cash are also for part of p lans, for convenence, we just call every avalable nvestment choce as fund. 5 North Amercan Industry Classfcaton. 6 1) Agrcultural, Mnng, or Constructon, 2) Transportaton, Communcatons or Utltes, 3) Manufacturng, 4) Meda, Entertanment, Lesure, 5) Wholesale & Retal Trade, 6) FIRE - Fnance, Insurance, Real Estate, 7) Busness, Professonal and Non-Proft Servces, 8) Educaton & Health, 9) Government, 10) Unknown. 5

8 The partcpant level fles gve us each partcpant s demographc characterstcs and monthly balance amount as well as hs portfolo allocatons. The trade level fle records trade drectons (e.g. sell company stock to buy Money Market Fund) and trade amounts. In addton, we also obtaned a separate fle descrbng fund features such as fund classfcaton (e.g. U.S equty, nternatonal equty or MMF). Compared to prevous emprcal studes, ths database s far more representatve of the 401(k) covered populaton. For example, f we take the EBRI/ICI database 7 as a proxy of the 401(k) unverse, we can compare some plan and partcpant-level features avalable both for EBRI/ICI and the VG database (nsert Table1). At the plan level, the total assets under management n the VG are over $146 bllon at the end of 2003, around 20% of the EBRI/ICI amount. But the EBRI/ICI database represents only about 41% of the total 401(k) plan assets, so we conclude the VG database represents about 7% assets of the partcpant populaton. For the account number, 2.5 mllon partcpants hold 401(k) accounts n VG, one-sxth of EBRI/ICI data. Almost of the plans n EBRI/ICI data have a few partcpants, wherever the average plan scale n the VG dataset s about 4 tmes larger for both total balances and accounts per plan. It s nterestng that at the partcpant level, the two datasets are very close n the terms of medan n age, plan tenure and portfolo allocatons. For the tradng analyss, we elmnate some observatons wth. At the plan level, we exclude three plan types of IRA, Deferred Compensaton, and ESOP that do not ft nto our 401(k) focus. At the partcpant level, we focus only on the accounts wth contnuous balance hstory (25 monthly balance records ncludng Dec 2002) and contnuous actve plan status. 8 We exclude non-actve accounts because the tradng actvtes of retred partcpants maybe dffer from those of actve workers; further, we need 25 monthly balance records to compute turnover ratos. We also exclude some nose observatons n the trade fle such as the trades wth only one-sde record (only sale or only buy) or zero trade amounts. 7 Employee Benefts Research Insttute / Investment Company Insttute. For further nformaton about EBRI/ICI database, refer to Perspectve Vol. 11 / No. 4A September For a dscusson of plan status, refer to Appendx 1. 6

9 B. Investment Menu, Industry-level, and Plan Level Factors After excludng napproprate observatons, our fnal sample sze for the tradng analyss s 1,186,554 accounts across 1,530 dstnct 401(k) plans. Ths subsecton reports the characterstcs of the plans nvestment menu, ndustry and plan desgn features. Over the sample perod (Jan 2003 Dec 2004), there are 691 unque funds ever selected as an nvestment opton. The Vanguard Group has classfes those funds nto seven prmary types as: 1) Balanced Funds, 2) Bond Funds, 3) Equty Funds, 4) Money Market Funds, 5) Other Funds, 6) Unfunded Funds, and 7) VG Brokerage Opton, of whch 5) and 6) are stable-value funds. In addton, Equty Funds are categorzed nto fve secondary types, whch are 1) Aggressve Growth funds 2) Company Stock Funds, 3) Growth & Income Funds, 4) Growth Funds and 5) Internatonal Equty. Money Market Funds are also dvded nto two types as Investment Contract Funds and Money Market Funds. For convenence, we re-arrange all funds nto three broader famles defned as Equty, Fxed Income and Balanced Funds (the latter are hybrd nvestment vehcles wth pre-determned target allocatons n Equty and Fxed Income). Across the offered menu, almost 80% are equty funds and the other 20% are Fxed Income and Balanced Funds (nsert Table 2). Gven the nvestment choce avalable n each plan, partcpants are allowed to alter ther asset allocaton patterns wthout any commsson fees on a daly bass. It s worth nothng that all partcpants n a gven plan wll be requred to reallocate ther assets from one specfc fund to the other avalable optons, f ther plan sponsor decdes to drop a gven fund from the menu. In ths case, we call ths type of trade as Plan-wde trade. 9 On the other hand, partcpants are never requred to allocate any asset to newly-added funds. In Table 3 (nsert Table 3), we summarze the ndustry level and plan-level characterstcs of our sample. On average, plans offered about 17 funds as of Jan 2003, of whch 10 were equty funds, 4 fxed ncome funds, and 3 balanced funds. There was a very wde range of plan desgn wth 86 funds for maxmum and one fund as mnmum. It s also nterestng to document that the average partcpant only holds a postve balance n 3.5 funds. In order to check whether menu change affects partcpants tradng actvtes, we also check whether plans have ever changed ther nvestment opton. Of the 1,530 plans, there were 513 plans whch ever added new funds 9 For further defnton of plan-wde trade, refer to Appendx 2. 7

10 and 121 plans ever dropped at least one fund, and the rest 896 never changed ther nvestment optons. Turnng to the nvestment menus offered, most plans offered ndexed equty funds, and nternatonal equty funds were avalable for over 90% plans. Although only n 15% plans (229) the employer company stock was a possble choce, because those plans are large, half of the partcpants could nvest n ther employer s share. In January 2003, about three quarters of the plans allowed partcpants to borrow from ther DC retrement account, whch covers 85% sampled partcpants. We also revew the dstrbuton of lfe-cycle fund offerng dummy. Lfe-cycle funds, also called as lfe-stage or target-date funds provde a mechansm to automatcally reduce the proporton of the portfolo held n equtes as an nvestor ages. In our sample, the Vanguard Group offers a set of Target Retrement Funds, each of whch has a target retrement year (2005, 2015,, 2045). As the target year approaches, the nvestment management wll gradually shft the funds from equtes to bonds or MMF. In practce, the allocaton changes are not drectly lnked to any partcular nvestor s age, but those funds are marketed to those who plan to retre n tme close to the target date of the fund. The dea s that nvestors who do not want to or are unable to spend money and tme to take care of ther asset allocaton, wll more easly manage ther retrement assets. In our sample, there are 744 plans (49%) provdng ths knd of nvestment vehcle. C. Partcpant Characterstcs Next, we present descrptve statstcs of partcpant level data. Demographc characterstcs of partcpants are shown n Panel A of Table 4 (nsert Table 4). The majorty of our sample s male (47.5%), 26.7% of the accounts are held by females, and the remnder (25.8%) s coded as mssng. Compared wth Agnew s sample, our sample accounts show an older mean age (43.5 vs years old) wth a wder range (our maxmum s 83 years old and the mnmum s 16). Household ncome class (coded as 1, 2,,11) s mputed by Clartas 10 for 2003 usng partcpants ZIP code. We converted these ncome classes nto ncome levels usng a lognormal dstrbuton. In 2003, the average household ncome s $88,000, somewhat hgher 10 Clartas s a marketng nformaton resources company whch provdes nome by ZIP code, for detal refer to 8

11 than Agnew et al. (2003) s sample mean ($69,000). For fnancal wealth, we use IXI Wealth class varables provded by IXI Corporaton. 11 and we convert t nto mean dollars of each class. The sample mean value n 2003 was $75,000. Panel B of Table 2 presents some nterestng partcpant-level varables. Employee Contrbuton Rato, defned as the Employee-contrbuted Balance dvded by the Total Balance, s mportant not only because t reflects the plan-match rato, but also t expresses partcpants atttude towards contrbuton to ther retrement accounts. 12 In addton, t s also possble that atttudes toward own money and house money are dfferent, whch could affect partcpants tradng behavor. In January 2003, the mean of Employee Contrbuton Rato s 57.5%, meanng that only 57.5% of the total balance of the average 401(k) account s contrbuted by the employee hmself, hs employer contrbutes the other 42.5%. On-lne tradng has been proposed as a cause of excessve tradng, Metrck et al. (2002) and several prevous studes show that nternet tradng channels ncrease ndvdual nvestors tradng frequency n dscount brokerage accounts and 401(k) plans. 13 We generate a web-access dummy varable, defned as equal to1 f a partcpant holds a web access to hs account, and 0 otherwse. Some 37.4% of our sample accounts are able to do web tradng. 4. Evdence of Tradng Actvtes In ths secton, we provde the defntons regardng tradng actvtes, present descrptve statstcs, and then summarze some tradng patterns. A. Measurng Tradng Actvtes All trade orders ssued by a 401(k) plan partcpant wthn the same day wll be executed at the end prce (3:00pm) for each fund. Accordngly, we defne a Trade as an asset allocaton change n a day, whch conssts of both a sell record and a buy record of at least one fund and a postve trade amount become recorded. For each trade, we compute the total sale/buy allocaton 11 IXI s a prvate company whch provdes wealth measures by ZIP code, for detal, refer to 12 Ths rato mght be dfferent across accounts n a gven plan. e.g, gven 15% as the upper lmt for total compensaton, 6% as upper lmt as employer contrbuton wth 100% match rato, a partcpant wth 6% employee contrbuton has dfferent Employee Contrbuton Rato wth a person wth 9% employee contrbuton. 13 As the example of emprcal studes based on dscount brokerage accounts, refer to Barber and Odean (2001), as a example of 401(k) plan studes, refer to Cho, Labson and Metrck (2002). 9

12 change amount across all funds regardng ths trade, and then we defne the average of the sale and buy amount as Trade Amount. Ths calculaton can be wrtten as below: trdmt _ out = n = 1 trdmt _ out _ fnd trdmt_ n = m j= 1 trdmt_ n _ fnd j trdmt _ out + trdmt _ n trdmt = 2 trdmt_out: total sale amount across all sold funds; trdmt_out_fnd : sale amount of fund ; n: number of sold funds; trdmt_n: total buy amount across all bought funds; trdmt_n_fnd j : buy amount of fund j; m: number of bought funds; trdmt: trade amount If an ndvdual nvestor ever exchanged hs asset allocaton at least once from January 2003 to December 2004, then we defne ths partcpant as Trader, otherwse, we consdered hm as a Non-trader. Each partcpant s total trade tmes s defned as hs Trade Number. Because plan-wde trades are not due to nvestors choce but rather drven by the employer, we do not count those allocaton changes as trades; therefore, f a partcpant only has plan-wde trades coverng the sample perod, we nclude hm as a non-trader. To measure tradng magntude, we use the Turnover Rato. Ths s defned as the rato of total trades amount over partcpants sample average balance, defned as the average balance of sample begnnng (December 2002) and sample end (end of Dec 2004). Ths calculaton could also be re-wrtten as below: trdmt _ smpl = k l= 1 trdmt l fndtotasset t fndtotasse t _ avrg = Rato _ turnover_ smpl = + fndtotasset 2 trdmt _ smpl fndtotasset _ avrg ( t 1) trdmt_smpl: total trade amount across total trades n sample perod; 10

13 trdmt l : trade amount of trade l; k: total trade number n sample perod; fndtotassets t : total assets n the end of perod t; fndtotassets_avrg: average total assets; Rato_turnover_smpl: turnover rato. B. Plan-level Tradng Actvtes Prevous research suggests that offerng a large number of funds provdes dversfcaton opportuntes for knowledgeable partcpants. Thus can lead to ncrease tradng probabltes; on the other hand, too much varety n the nvestment menu may cause nformaton overload problem (Agnew and Szykman, 2004): a lot of choces also potentally lmt 401(k) partcpants tradng actvtes. It s also possble to examne how nvestment package affects partcpants tradng behavor from an effcency perspectve. Gven an effcent nvestment fronter, for example, maybe an ndexed equty fund, a ratonal nvestor maybe only need to put hs money n that fund, and he may not need to select ndvdual assets to create hs own effcent portfolo. As descrbed n secton 3, ndustral recommendaton of lfe-cycle funds suggests that ths type of nvestment vehcle makes asset management easer. Desgned for one-stop nvestment shoppng, lfe-cycle funds dstrbute nvestors money among varous other funds, changng ther asset allocaton as they enter dfferent lfe stages. Of course, ratonal and engaged nvestors may fnd such knd of nvestment vehcles redundant. However, for nvestors who may not know ther rsk tolerance, the overwhelmng number of optons may seem lke more of a curse than a blessng, therefore, lfe-cycle funds can make portfolo selecton problem easer: automatc adjustment mechansm makes them mantenance-free for nvestors. Another ndustral story suggests that offerng nternatonal funds provdes nternatonal arbtrage opportuntes, and thus, ncrease nvestors tradng probabltes. Ths may be partcularly appealng to speculatve transactons. For example, f one expected the value of Japanese Yen to ncrease enough to cover transactons cost tomorrow n the eastern U.S. tme zone, just buyng tonght n Tokyo money market, and then sellng tomorrow n N.Y. market, may the nvestor make money. 11

14 Table 5 presents our data on tradng actvtes sorted by plan-level varables. Clearly, plan desgn factors, as well as wth partcpants fnancal lteracy, are very mportant on 401(k) partcpants asset allocaton behavor (nsert Table 5). Our data shows evdence to support those theoretcal mplcatons. For example, the plan-level tradng propensty, whch s defned as the rato of trader to actve partcpants per plan, has a hump shape assocated wth the number of funds offered. It ncreases from 14.4% n plans offerng 1-5 funds to 17.7% and 21.5% n groups wth 6-10, and nvestment choce respectvely, and then hts ts peak of 23.6% n plans wth funds. Fnally, t starts to decrease to 19.6% as a plan offers more than 30 funds. Ths pattern may suggest that addng new funds to nvestment menu does ncrease partcpants tradng probablty due to more dversfcaton opportuntes, but ths effect decreases margnally and there exsts an upper bound. Tradng propensty n plans offerng nternatonal equty funds or employers company stock also s sgnfcantly hgher than those plans wthout those types of nvestment choce. More than 20% of partcpants n an nternatonal equty avalable plan have ever reallocated ther portfolos n our sample, whch s 3.5% ponts hgher than a plan lackng nternatonal equty funds. Company stock avalablty also contrbutes to actvate exchange actvtes: there s 3.9% pont spread of tradng propensty between plans offerng company stock and those not. There are no obvous dfferent tradng patterns between plans offerng lfe-cycle funds, ndexed equty funds, and loan avalablty wth those plans that do not have those optons. In order to nvestgate f these varables nfluence partcpants tradng actvtes sgnfcantly, we need to analyze our data usng a multvarable approach. C. Partcpant-level Tradng Actvtes Table 6 presents the partcpant level tradng actvtes, whch are measured as 1) tradng probablty, 2) trade number, and 3) turnover rato. Only 20.5% of the 401(k) accounts ever altered ther portfolo allocatons over two-year, whch ndcates tradng actvtes n ndvdualmanaged retrement accounts are very lmted. Ths result s also consstent whch the statstcs n Agnew et al. (2003) sngle plan study, whch showed about 88% partcpants have no trades. In our data, condtonal on tradng, the average sample turnover rato reached almost 90%, whch means on average a trader changed hs asset allocatons by 90% over two-year perod (nsert Table 6). 12

15 Transacton cost theory tells us that nvestors wll change ther asset mx f when the margnal benefts from tradng s no less than the margnal cost. Gven fxed transacton costs, t wll be optmal for nvestors to relocate ther assets nfrequently wth a dscrete amount. Transacton costs could be classfed nto explct and mplct costs. The explct costs are always expressed n a monetary form such as bd-ask spread, commsson fees n case of common stocks or trustee fees n the case of mutual funds. On the other hand, mplct costs may take the forms of opportunty costs such as tme spent on nformaton collecton and nformaton analyss. Because tradng s free for all of the sampled accounts, thus, n our case, mplct costs are supposed to be the only transacton cost. 14 The mplcatons of the transacton cost theory can also be captured by nvestors characterstcs. For nstance, as Kng and Leape (1987) have argued, learnng, experence and knowledge can lower the fxed transacton costs and thus lead to ncrease tradng probablty. Ths suggests that elder partcpants n knowledge-ntensve ndustres ( e,g, Fnance, Insurance and Real Estate) are lkely to reshuffle ther portfolo more frequently wth bgger magntude. Meanwhle, longer plan tenure not only capture nvestors degree of knowledge on ther plan and tradng experence, and also ndcate bgger balances, whch wll ncrease the lkelhood of tradng. Table 6 presents the tradng probablty for each group sorted by partcpants demographc features. We see that men are more lkely to trade ther assets sgnfcantly. Nearly one quarter (24.1%) partcpants have ever changed ther portfolo allocatons over the two- year perod, but only 17.9% among females. These unbalanced tradng probabltes are consstent wth the overconfdence hypothess and the emprcal results n Barber and Odean (2001): men are more overconfdent than women, so men are more lkely to trade. Of course, the sharp contrast between males and females could also be explaned by the transacton cost framework 15. That s females often have lower salary, smaller fnancal wealth and less nvestment lteracy compared to men. The tradng probablty ncreases as partcpants get older for almost all age ranges. For nvestors under 35, only 16.9% partcpants have tradng experence, n years old group, ths rato goes up to 18.9%, and then t clmbs 22.8% n group, and t fnally hts ts peak 14 Of course, there s no free lunch. Ultmately, the transacton costs must be shared by mutual fund companes, plan sponsors, and partcpants n other forms. 15 Refer to experment study by Agnew (2004). 13

16 of 25.1% n group. Ths ncreasng trend fts the transacton cost theory descrbed above, and the sharp decrease n tradng among the over 65 years old group can also be ratonalzed: the portfolo allocaton should have been exchanged to relatve safe assets, thus reduce the motvaton to rebalance ther assets to safer optons. Tradng probablty has a monotoncally ncreasng trend wth partcpants plan tenure. The tradng probablty jumps from 17.4% n the partcpant group wth less than 5 plan years, to 31.7% for nvestors who have already stayed n the same plan over 25 years. Obvously, ths pattern s consstent wth the theoretcal mplcaton as descrbed above: the longer an nvestor stays n the same plan, the better he understands the plan, and the more experence/knowledge he has, whch wll ncrease hs tradng lkelhood. On the other hand, presumably, longer plan tenure also usually mples a bgger plan balance, whch ndcates possble substantal benefts from tradng actvtes, thus motvates the nvestor to exchange hs asset allocatons. Wealther nvestors and partcpants wth hgher salares are also more lkely to trade. We categorzed our partcpant level observatons as low ncome/wealth group f household ncome/ixi wealth was under the sample medan, and those who were above medan as the hgh group. The probablty of nvestors n the hgh ncome group s 23.1% sgnfcantly, whch s nearly 6% ponts hgher than ther low ncome counterparts. People n the hgh wealth group are lkely to relocate ther assets wth a probablty near one-quarter, but the poor partcpants dd less than one-ffth of the hgher. Our fndng s consstent wth those results reported n prevous studes: traders are older, wealther, more hghly pad, male employees, who have hgher balance n ther accounts. People n the fnancal ndustry also trade more frequently than n other ndustres. Trade numbers are drawn from a very skewed dstrbuton. As shown n Table 7, 79.5% accounts have zero trade n two years. Even among the traders, over half had only 1 trade. Roughly speakng, our 401(k) sampled partcpants altered ther asset allocatons 0.3 tmes n one year; that s to say they only trade once every 3.33 years on average. However, there s another extreme group who are tradng more than 50 tmes over 2 years (nsert Table 7). Trade number patterns assocated wth partcpants demographc characterstcs are smlar to tradng probablty. Males (0.75 trade/2 years) traded twce as frequently as female (0.36 trade/2 years), trade numbers ncreased wth age untl 65 years old, stayed n the same plan longer, earned more salary, and became wealther. Another nterestng pattern s that the trade 14

17 numbers for partcpants wth on-lne accounts was 5.5 tmes (1.23 trades/ 2 years) hgher than those lackng web access (0.22 trades/2 years). Of course, partcpants mght open ther on-lne accounts because they want to trade. On the other hand, ths sharp contrast stll ndcates that nternet access avalablty does permt actual tradng. Turnover ratos correlate wth trade numbers. On average, partcpants changed the composton of only 18% of ther assets, but condtonal on tradng, the average turnover rato for sample traders clmbed to 89.7%. When we sort turnover ratos by partcpants demographc characterstcs, we confrm portfolo exchangers were lkely to be men, older, hgh-ncome, wealther, and had longer plan tenure nvestors compared ther female, younger, low-ncome, lower wealth and shorter plan tenure counterparts. However, on-lne access dd not ncrease the sample turnover rato as dramatcally as t dd on trade numbers, maybe because nternet channels only convnce people to trade more frequently but reduce the trade amount per exchange compared wth the case f they had traded wth a conventonal way. Ths s also consstent wth the emprcal study results n Cho, Labson and Metrck (2002), whch s based on two large 401(k) plans plan level tradng records. All of these statstcs are consstent wth the sngle plan examned by Agnew et al. (2003). We conclude that tradng actvty s extremely lmted n 401(k) accounts. 5. Regresson Analyss Ths secton summarzed hypotheses to test, descrbes our regresson methodology, presents regresson results and then compares them wth the conclusons from other emprcal studes. A. Hypotheses Table 8 presents ndependent varables assocated wth the hypotheses we seek to test, and shows the predcted sgns n the regresson analyss (nsert Table 8). We can summares t as follows: 1) Transacton Cost Hypotheses: Tradng wll be more prevalent among the people n fnancal lteracy ntensve ndustry lke Fnance, Insurance and Real Estate for ndustry level; older, hghly pad, longer-tenured, wealther, web-regstered partcpants are more 15

18 lkely to reshuffle ther assets. Offerng lfe-cycle funds can make portfolo selecton easer, thus, t would reduce tradng propensty. 2) Overconfdence hypothess: Because men are more confdent than women, tradng wll be more prevalent among males more than females. 3) Dversfcaton Hypothess: the more funds offered at the plan level, the more lkely people wll trade; as nternatonal funds provde arbtrage opportuntes, nternatonal funds may boost tradng lkelhood; offerng company stock dversfy the nvestment menu, thus ncreases the tradng probablty. 4) Effcent nvestment fronter hypothess: Assumng ndexed funds span the effcent nvestment fronter, offerng ndexed funds wll decrease nvestors tradng patterns. 5) Informaton Overload and Fnancal lteracy Hypothess: the nformaton overload hypothess proposes that more choce n the nvestment menu wll reduce people s tradng; females are often low salary, less fnancal knowledgeable, thus, females trade less. B. Regresson Methodology For the regresson analyss, we focus on three dependent varables: sample trader, trade number and turnover rato. They measure the tradng probabltes, tradng frequency and tradng magntude, respectvely. We categorze the ndependent varables nto three levels ncludng fve sub-classes: ndustry, plan, and partcpant levels. We do not control on tme because two year s not long enough to estmate tme effects. The specfc ndependent varables are shown as below: 1) Industry Level: Industry Dummy. We code nne dummy varables based on the VG classfcaton wth the reference ndustry beng manufacturng. 2) Plan Level: We dvde plan-level explanatory varables nto a) plan desgn features, and 2) other plan level varables a. Plan desgn varables: Number of funds offered, ts square, and the change durng sample perod. Lfe-cycle funds dummy, Internatonal equty funds dummy, Company stock dummy, Indexed equty or/and fxed ncome funds dummy and loan avalablty dummy. 16

19 b. Other plan level varables: we adopt the natural log of the total plan assets as a proxy to measure scale economes. 3) Partcpant level: Partcpant-level ndependent varables are splt nto two sub-classes. a. Demographc characterstcs: sex, age, plan tenure, household ncome and wealth as well as mssng dummes for each varable. b. Other account-level features: On-lne access dummy, employee-contrbuton rato. The regressons use a Generalzed Lnear Mxed Model (GLMM) framework. The reason for Generalzed Lnear Model (GLM) part results from the features of our dependent varables: Sample traders s a bnary varable (0,1), tradng number s a non-negatve nteger, and turnover rato s a non-negatve real number. The GLM relaxes the normalty assumpton requred for a conventonal regresson model, and only requres the underlyng dstrbutons for dependent varables belong to the exponental famly. 16 In addton, by mxng or compoundng two dstrbutons, GLM also enables us to handle models wth more complcate underlyng dstrbutons. 17 We also adopt a mxed error structure due to the herarchcal structure of our ndependent varables, whch would generate seral correlaton and heteroscadastcty problem. The multlevel regresson approach provdes extremely flexble varaton for the error term structure, whch enables us to test random effects, fxed effects and robust standard errors models. In our analyss, we use the followng regresson model: Lnear Regresson: * y, k, m = X, k, m ' β + Z k, m ' γ + W ' m δ + wm + υk, m + ε, k, m *, k, m W Lnear Predctor: µ = E( y X, Z, ) Lnk Functon: η = η( µ ) where *, k, m y s the latent varable for ndvdual n plan k whose sponsor belongs to ndustry m, X, Z,W ndcate partcpant level, plan level, and ndustry level explanatory varable vectors; β, γ, δ are parameter vectors assocated wth X, Z,W. The error term conssts of three parts: 1) a ndustry-varant term w m, 2) a plan-varant term υ k,m, and 3) a dsturbance term ε,k,m. Here, we control on ndustry-varant term w m by usng ndustry dummes; we also assume that the plan s the ndependent analyss unt, allow seral correlaton and heteroscadastty wthn the same plan, 16 Some usual examples are Gaussan, Inverse-Gaussan, Posson, Gamma, and Bnomal. 17 It s well known that Negatve Bnomal s the mxture dstrbuton of Posson and Gamma dstrbuton. 17

20 and then compute the cluster-robust standard error Thus, the new error term can be rearranged asξ, k = υk + ε, k, wth ε, k ~ N(0, σ 1 ) and υ ~ N(0, ), but the two terms are not necessary to be ndependent. Therefore the re-arranged error structure may be wrtten as 19 Error structure: Cov ξ, ξ ) 0 for k l (, k j, l = Cov ξ, ξ ) 0 for k = l (, k j, l k 2 σ 2 C. Regresson Results 1) Sample Trader Wth the GLMM approach, we can rewrte our regresson functon for Sample Trader accordng to a usual Probt regresson model: * y, k, m = X ' β + Zk ' γ + W' mδ + ξ, k, m µ = E( y, k, m X, Z, W ) ( µ ) * 1 η = Φ, where Φ 1 s the nverse CDF of Normal Dstrbuton Table 9 presents the regresson results. The estmator ndcates a very hgh jont sgnfcance of the ndependent varables. The pseudo-r 2 s 10.9% and the concordant percent s 72.7%, whch mples the specfcaton valdty of the whole model. Compared a model that nclude only demographc factors as n Agnew et al. (2003), our current model also shows a sgnfcant advantage. Ths evdent n the absolute dfference of the lkelhood rato between the two models, but t also appears n the mprovement of pseudo-r 2 and concordant percent, whch ncrease 8.4% ponts (10.9%-2.5%=8.4%) and 12.0% (72.7%-60.7%=12.0%) respectvely (nsert Table 9). Our most remarkable fndng s that most of the plan level varables affect nvestors tradng lkelhood sgnfcantly. Tradng probablty rses as the number of funds offered grows as well as the number of fund changes. However, the sgn of the square of number of funds offered s negatve. From the margnal effects regardng the number of funds and number of 18 Monte Carlo smulaton results suggest the bggest cluster should not larger than 5% of total observatons. In our case, 59,350 partcpants are enrolled n the largest plan, whch s just 5% (59350/ =5%). 19 Theoretcally, t s also possble to buld mult-level regresson wth multple random effects: ndustry and plan. However, those computaton tasks are beyond a usual computer capacty even usng the most tme-effcent optmzaton technque. 18

21 funds squared ( vs ), we can easly calculate the postve effects reach ts peak at the 54 th fund. Ths fact suggests that our results support the dversfcaton hypotheses: addng new funds to the nvestment menu does stmulate partcpants to alter ther portfolo allocatons, although ths effect dmnshes as the total number of funds offered grows. Offerng a loan makes nvestors less much to change ther asset mx wth margnal effect of 2.2%. On the other hand, company stock avalablty encourages partcpants to change ther portfolos. Meanwhle, nvestors do make ther tradng decsons dependng on whether ther plan sponsors offer an ndexed equty fund. Controllng on other factors, a 401(k) plan partcpant s 44% less lkely to trade f hs plan offers an ndexed equty fund, compared to a plan lackng such a fund. We also fnd that offerng Lfe-cycle funds reduces nvestors tradng probablty because of ts automatc rsk adjustment mechansm, and an nternatonal equty fund encourages partcpants to change ther asset allocatons by 3.7% due to the potental nternatonal arbtrage opportuntes. Partcpant level ndependent varables confrm to those regarded n prevous studes. Demographc characterstcs such as sex, age, and plan tenure postvely correlate wth nvestors tradng probablty wth consstent learnng and experence hypotheses. Ten more years of age boosts the tradng probablty by 2.1%; ten more years of plan tenure arses t by 3%. Men alter ther 401(k) portfolo composton 4.65% more than females. Household ncome and fnancal wealth also sgnfcantly affect nvestors tradng probablty. A 1% ncrease n household ncome rases people s tradng probablty by 2.9%, and the ncrease n the rato of fnancal assets over household ncome also correlates postvely wth tradng probablty. 2) Trade Number In the regresson functon for trade number, we assume the dependent varable s drawn from Posson dstrbuton, and the parameter of Posson dstrbuton s from a Gamma dstrbuton. As a result, the trade number s assumed to be dstrbuted as Negatve Bnomal, whch s the mxture of Posson and Gamma. In GLMM estmaton, we use a log lnk functon. In fact, we can nterpret those statstcal procedures as a method to capture ndvdual heterogenety n an econometrc model. 19

22 20 Suppose the trade number s dstrbuted as Posson wth the probablty densty functon ( )!,, Pr y m k y e W Z X y Y λ λ = =, n whch λ s the Posson dstrbuton parameter. For the mathematcal convenence, we also assume λ s dstrbuted as Gamma wth the densty functon ( ) ) 1 ( ) ( Pr Γ = θ θ θ θ θ u u e u, where Γ ndcates the Gamma functon wth parameter θ and u. If we add another ndvdual heterogenety term ζ nto the error, a usual Posson Regresson wth cross-ndvdual heterogenety could be wrtten as: ) log( ) ln( ) log( ' ' ) log( k u u Z X λ λ ζ γ β µ = + = + + = Mxng Posson and Gamma dstrbuton, we can obtan the densty functon uncondtonal on heterogenety as: ( ) Γ = = 0 1) ( ) (! ) (, Pr u y u k du u e y u e Z X y Y θ θ θ λ θ θ λ Integratng respect to u, t s easy to get the closed form as the followng, whch s the famlar format for Negatve Bnomal dstrbuton. ( ) y k y y Z X y Y + + Γ + Γ + Γ = = α α α θ θ θ ) ( 1) ( ) (, Pr, Where θ λ α = ( ) k Z X y E λ = θα =, ( ) + = + = k Z X y Var λ θ λ α θα 1 1 ) (1, In our regresson functon, we need to estmate parameter vectors, β,γ,δ n the Posson part, and θ, the parameter n the Gamma part, whch s also called overdsperson parameter. Table 10 presents the estmator results. As before wth the trade propensty functon, our ndependent varables work sgnfcantly well to explan the dependent varable (nsert Table 10). For the plan-level varables, offerng company stock and nternatonal equty funds are the man plan desgn features that stmulate partcpants to trade more frequently; these ncrease trade number by 23% and 17% respectvely. Offerng more funds sgnfcantly encourages nvestors to exchange more frequently, but the magntude of the effect s relatvely small (one more fund offered causes 1.1% rse n trade number).

23 Demographc characterstcs also return ther explanatory power to nterpret ndvdual nvestors tradng number as appeared n trade propensty functon. Agan, male, hgher pad, rcher, and longer plan tenured partcpants trade more frequently than ther counterparts. Another nterestng result s that ndvdual on-lne access motvates nvestors to exchange ther asset mxture sgnfcantly more and wth a very hgh magntude. In addton, the overdsperson parameter s estmated to be 4.78, whch s sgnfcantly not equal to zero and suggests ndvdual heterogenety can not be captured by demographc characterstcs alone. 3) Sample Turnover Rato Table 11 presents a Heckman second-stage OLS regresson results for the turnover rato. We adopt the Heckman second-stage regresson rather than a conventonal censored regresson method because we want to explctly decompose the explanatory power of ndependent varables nto two parts: the ndrect effects through tradng probablty, and the drect effects condtonal on tradng (nsert Table 11). The coeffcent regardng the nverse Mlls rato from the 1 st -stage Probt regresson, s estmated to be 0.75, whch suggests all of the ndependent varables jontly explan the turnover rato ndrectly through ncreasng tradng probablty. At the plan-level, offerng nternatonal equty funds and offerng ndexed equty funds are stll correlated the turnover rato as seen n the tradng propensty and the trade number functons. However, the number of funds offered and ts square changed ther sgns suggestng that traders tend to exchange ther 401(k) assets a subset of funds, and do not ntend to extend ther portfolo varety. D. Implcaton So far, we have followed the analyss framework of Agnew et al. (2003) by nvestgatng the tradng patterns n 401(k) retrement accounts. We confrm the fact that the tradng actvty n 401(k) retrement accounts s extremely lmted: only 20% partcpants ever altered ther portfolos wthn a two year perod. Demographcs hence can explan tradng patterns n the ways that supports the theoretcal mplcatons. However, our analyss s dstngushed wth prevous studes n several ponts. 21

24 Frst, we fnd that plan desgn can explan tradng behavor. Offerng ndexed funds and loans sgnfcantly reduces partcpants tradng, whle offerng nternatonal equty funds and employer company stock gves nvestors more motvaton to trade assets. The more funds the plan sponsor offers, the more actvely partcpants trade, but that effect ncreases at a decreasng rate. Second, nstead of conventonal Tobt regresson, we use Heckman 2-stage regresson method for sample turnover rato analyss. Therefore, we explctly show the drect and ndrect effect from the same ndependent varable. For example, even controllng on traders (.e. controllng on the ndrect effects through tradng probablty), plan desgn stll retan ts sgnfcant power to explan the traders turnover rato. It s easy to obtan the ntutve mplcatons for plan sponsors and partcpants from our fndng. Table 12 summarzes the margnal effects on 401(k) partcpants tradng behavor (nsert Table 12). As descrbed above, although there s no any explct transacton fee for tradng 401(k) portfolos, ultmately, the transacton costs must be shared by mutual fund companes, plan sponsors, and partcpants n other forms. Therefore, the nerta tradng actvty n 401(k) accounts drectly ndcates cost savng for the plan sponsor f t shares part of the transacton costs. However, t s not clear whether the lmt tradng behavor s postve or negatve for partcpants before examne the tradng performance: maybe lmt tradng make nvestors pass over some better nvestment opportuntes, t s also possble that lmt tradng protects nvestors from rather worse nvestment outcome. On the other hands, t may be necessary to take nto account the mpact on partcpants tradng actvty from the plan desgn factors when an employer desgns ts 401(k) plan. For example, the most effcent way to mnmze the tradng probablty, the number of tradng, and the turnover rato s to offer an ndexed equty fund. In fact, more than 95% of our sampled plans hold at least one such fund n the nvestment menu. Meanwhle, offerng nternatonal equty funds, employer company stock, and brokerage optons s the effectve way to dversfy the nvestment optons, and thus attract the partcpants. In order to control the tradng probablty to a pre-determned target, offerng lfe-cycle funds can offset the postve dversfcaton effects by addng 13 new funds to the nvestment menu. 22

25 Furthermore, sgnfcant explanatory power of partcpants characterstcs also requres the plan sponsors to pay attenton to the demographc structure of the partcpants. For example, n an extreme case, compared to a 100% female company, a 100% male company needs to offer loan avalablty and lfe-cycle funds to balance out the overconfdent effects of men. Overall, our analyss provdes the evdence that both partcpants and plan sponsors need to be aware of the behavor of opposte part. An employee seekng to maxmze hs net 401(k) savng needs to pay attenton to the plan desgn features, because they sgnfcantly affect partcpants tradng behavor, and then ther nvestment performance; an employer as fducary also need to take nto account the mpact on partcpants tradng behavor when t desgns ts 401(k) retrement plan. 6. Concluson Our analyss of 1.2 mllon 401(k) plan partcpants shows relatvely lttle overall tradng n DC retrement plans, wth substantal heterogenety. We fnd that only 20% partcpants ever reshuffled ther portfolos over a two-year perod, ndeed, most of the people never trade. Even when people do trade, t s rare and over half traders only trade once. Lke prevous studes, we fnd demographc characterstcs can sgnfcantly explan tradng actvty: traders are older, wealther, more hghly pad, male employees wth more money n ther accounts. We also fnd plan desgn factors do have sgnfcant mpact on 401(k) plan partcpants tradng behavor: partcpants trade more n plans wth more nvestment choce, company stock, and nternatonal equty funds, and offerng ndexed funds, lfe-cycle funds, and loan avalablty reduce people s portfolo turnover. Fnally, on-lne access stmulates partcpants to trade more frequently, although they do not ncrease turnover rato as much. Our analyss also shows that tradng actvtes n 401(k) plans dffers from those n dscount brokerage accounts. Compared to the results of Odean and hs co-authors, ndvdual nvestors seem lkely to trade ther asset through dscount brokerage account rather than retrement savng: nvestors trade 1.44 tmes annually n the dscount brokerage accounts but only trade 0.30 tme n the 401(k) accounts. Ths sharp contrast maybe comes from 1) self-selecton problem n dscount brokerage accounts, and 2) lmted choce n nvestment menu. 23