DNB W o r k i n g P a p e r. Stock market performance and pension fund investment policy: rebalancing, free f loat, or market timing?

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1 DNB Working Paper No. 154 / November 2007 Jacob Bikker, Dirk Broeders and Jan de Dreu DNB W o r k i n g P a p e r Sock marke performance and pension fund invesmen policy: rebalancing, free f loa, or marke iming?

2 Sock marke performance and pension fund invesmen policy: rebalancing, free floa, or marke iming? Jacob Bikker, Dirk Broeders and Jan de Dreu* * Views expressed are hose of he auhor and do no necessarily reflec official posiions of De Nederlandsche Bank. Working Paper No. 154/2007 November 2007 De Nederlandsche Bank NV P.O. Box AB AMSERDAM he Neherlands

3 Sock marke performance and pension fund invesmen policy: rebalancing, free floa, or marke iming? Jacob A. Bikker a,b, Dirk W.G.A. Broeders a and Jan de Dreu c November 6, 2007 Absrac his paper is he firs ha examines he impac of sock marke performance on he invesmen policy of pension funds. We find ha sock marke prices influence he asse allocaion of Duch pension funds in wo ways. In he shor erm, ouperformance of equiies over bonds and oher invesmen caegories auomaically resuls in a higher acual equiy allocaion (and vice versa), as pension funds do no coninuously rebalance heir invesmen porfolios. Each quarer, pension funds rebalance, on average, around 39 percen of excess equiy reurns, leaving 61 percen for free floaing. In he medium erm, ouperformance of equiies induces pension funds o increase heir sraegic equiy allocaion (and vice versa). hese findings sugges ha he invesmen policies of pension funds are parially driven by he cyclical performance of he sock marke. Pension funds respond asymmerically o sock marke shocks: rebalancing is much sronger afer negaive equiy reurns. On average, his sraegy led o negaive excess reurns over he period under consideraion. Invesmen policies of large funds deviae from ha of small funds: hey hold more equiy and heir equiy allocaion is much more srongly affeced by acual equiy reurns, reflecing less rebalancing. he larges funds reac highly asymmerically o posiive excess equiy reurns, adjusing heir porfolios by significanly more han 100%, reflecing overshooing of free floaing, or posiive feedback rading. Apparenly, managers of large funds demonsrae grea risk olerance, paricularly in bull markes. JEL Classificaion Codes: G11, G23; Keywords: Pension fund reurns, porfolio choice, excess reurns, sraegic equiy allocaion, size effecs, asymmerical behavior. a De Nederlandsche Bank (DNB), Supervisory Policy Division, Sraegy Deparmen, P.O. Box 98, NL-1000 AB Amserdam, he Neherlands, el: , b Urech School of Economics, Universiy of Urech, Janskerkhof 12, NL-3511 BL Urech, he Neherlands. c ABN AMRO, Risk Managemen Europe, Gusav Mahlerlaan 10, 1082 PP Amserdam, he Neherlands, el: , he auhors are graeful o Aerd Houben, heo Nijman and paricipans of he DNB research seminar for valuable commens and suggesions and o Jack Bekooij for his excellen suppor in consrucing he daase. he views expressed in his aricle are personal and do no necessarily reflec hose of DNB or ABN AMRO.

4 2 1 Inroducion he opimal equiy allocaion of pension funds is subjec o considerable debae. A high percenage of asses invesed in equiies resuls in significan exposure of pension wealh o flucuaions in sock marke prices. While nominal defined-benefi pension liabiliies are bes resembled by bond reurns, considerable equiy holdings may be opimal when indexaion of benefis is coningen on he funding raio of he pension fund. 1 During he nineies abundan equiy reurns led o premium reducions and even conribuion holidays for pension plan sponsors. However, he risks of equiy holdings surfaced afer he collapse of he sock marke in , which resuled in large losses for pension funds. In reacion, pension benefis were curailed and conribuions seeply increased. his episode raised a debae on he invesmen sraegies of Duch pension funds and, paricularly, on heir exposure o equiy markes. he invesmen sraegy of Duch pension funds is of key imporance o sociey, as i involves more han 600 billion in asses, or over 37,500 per inhabian. he way in which hese asses are invesed has a significan influence on he level of required premiums or final benefis. A one percen lower annual reurn over he lifecycle of a ypical worker ranslaes ino 27 percen lower accumulaed pension asses. 2 Consequenly, one of he mos imporan responsibiliies of pension funds rusees is o maximize he expeced reurn a an accepable level of risk, e.g. measured in erms of he probabiliy of underfunding. his sudy invesigaes wheher sock marke performance influences pension funds invesmen policies. In paricular, we examine wo ways in which sock marke performance impacs he equiy allocaion of pension funds: (i) in he shor erm, as a resul of marke iming or imperfec rebalancing, and (ii) in he medium erm, as a resul of adjusmens o sraegic asse allocaion. Consecuively, we examine he value added of acive marke iming decisions. his is paricularly relevan for indusrywide pension funds. In he Neherlands, paricipaion in hese secor funds is compulsory for companies operaing in ha specific secor. If he performance of such funds, measured as a five-year moving average, drops below a cerain hreshold, he affiliaed companies may apply for dispensaion from joining ha secor fund. 3 1 Nominal defined benefi pension liabiliies are bes resembled by nominal governmen bonds. Insead, defined benefi pension liabiliies ha are fully indexed o prices are bes resembled by inflaion linked bonds. In many Duch defined benefi pension deals, indexaion is coningen on he funding raio of he pension fund. he marke value of his coningen indexaion can be derived using opion pricing heory. In his case i migh be opimal o have considerable equiy exposure, see e.g. Broeders (2006). 2 he hree main componens deermining he coss of pensions are he qualiy of he pension scheme, he rae of reurn on invesmens and adminisraive and invesmen coss (see also Bikker and de Dreu, 2007). 3 his is known as he Sar-es which is based on he so-called z-score. he hreshold is based upon a reference porfolio, usually he sraegic asse allocaion of he pension fund.

5 3 able 1 presens he asse allocaion of Duch pension funds over he following five broad classes: Equiies, Bonds, Real Esae, Cash, and Oher Asses. Pension fund invesmen policy includes he sraegic asse allocaion decision, which refers o choosing he invesmen percenages in each asse class. Of he aforemenioned asse classes, equiies have he highes expeced reurn bu also he highes volailiy. For mos pension funds i is he larges asse caegory. Consequenly, equiy allocaion is one of he key policy variables deermining he risk-reurn profile of a given pension fund. able 1: Pension fund sraegic and acual asse allocaion 1999:I 2006:IV (in %) Asse classes Average sraegic asse allocaion Sandard deviaion Average acual asse allocaion Sandard deviaion Equiies Bonds Real Esae Cash Oher oal Noe: he asse shares are averages over de Duch pension funds and weighed by oal invesmens. Source: De Nederlandsche Bank. Pension funds generally deermine heir sraegic asse allocaion policies using asse and liabiliy managemen sudies, in which hey consider long-erm expeced reurns, reurn variances and covariances of broad asse classes, given he size and characerisics of heir pension liabiliies, see e.g. Campbell and Viceira (2002). 4 he sraegic asse allocaion is ypically se on a hree o five year horizon. For many pension funds, he sraegic asse allocaion includes bandwidhs for he acual asse allocaion o drif. hese bandwidhs are chosen in such a way ha he maximum ex ane racking error does no exceed a given hreshold. his racking error (E) is usually defined as E = w' Σw, where w is he vecor of acual porfolio weighs minus he vecor of sraegic porfolio allocaion and Σ is he variance-covariance marix. As invesmen opporuniies change over ime, deviaions in expeced reurns from heir long-erm averages may warran changes in he invesmen mix. 5 Choosing acual porfolio weighs ha deviae from he sraegic asse allocaion is known as acical asse allocaion or marke iming. Marke iming refers o aking shor-erm (informed) bes on he relaive asse class reurns. I can be implemened hrough acually buying and selling he underlying securiies, alhough in pracice, 4 Shefrin and Saman (1997) use behavioural finance heory o explain he asse allocaion of pension funds. hey argue ha invesors build porfolios as pyramids of asses, layer by layer. In conras o mean-variance heory, covariance beween asse classes are generally ignored resuling in subopimal porfolios. 5 Predicabiliy in expeced asse reurns may affec he opimal porfolio choice of invesors wih long horizons (see e.g. Barberis, 2000; Pasor and Sambaugh, 2001).

6 4 derivaives are also commonly used as an efficien manner o change a fund s asse allocaion. However, he poenial exra reurn hrough marke iming is limied, as indicaed also by he so-called fundamenal law of acive managemen, see Grinold and Kahn (1999). 6 his sudy examines he impac ha higher or lower reurns on socks compared o he oher asse caegories have on he equiy allocaion of pension funds. o he bes of our knowledge his is he firs sudy ha examines his relaionship. Figure 1 shows he various facors ha influence he equiy Figure 1: he impac of sock marke performance on equiy allocaion Sock Marke Performance Marke iming/ Free floaing Rebalancing Sraegic asse allocaion Equiy Allocaion allocaion of pension funds. Over he long erm equiy allocaion is deermined by a fund s sraegic asse allocaion. However, several facors influence asse allocaion in he shor o medium erm. We disinguish he following hree equiy invesmen sraegies ha pension funds may use o respond o posiive or negaive sock marke reurns: rebalancing, free floa, and marke iming. Rebalancing refers o he invesmen process applied o ensure ha a fund s acual equiy allocaion coninuously equals is sraegic equiy allocaion, which implies selling equiies afer relaive high sock marke reurns and buying afer relaive low equiy reurns. his migh also be indicaed as a form of negaive-feedback rading referring o buying pas losers and selling pas winners, see e.g. 6 his law saes ha he informaion raio equals he informaion coefficien imes he square roo of he number of independen invesmen decisions. he informaion raio is he risk-adjused excess reurn over a passive invesmen sraegy. An informaion raio of 0.5, which is considered high, requires ha asse managers earn a 50 basis poins excess reurn ( alpha ) per 1 percen of residual risk on a yearly basis. he informaion coefficien measures he skill of he asse manager, and is defined as he correlaion beween his forecass on invesmen reurns and he acual oucomes. he number of independen invesmen decisions is four, if he pension fund makes quarerly marke iming decisions. o generae a marke iming informaion raio of 0.5 requires, in ha case, an informaion coefficien of 0.25, which is considered exremely high. I would require he asse manager o forecas he direcion of he sock marke correcly 63 ou of 100 imes. herefore, he poenial added value of marke iming is limied.

7 5 Lakonishok e al. (1992a). his form of rading is commonly a par of he argumen ha insiuional invesors sabilize asse prices. By conras, we use free floa o indicae a passive invesmen sraegy, in which pension funds allow heir equiy allocaion o drif wih marke developmens. 7 Finally, as menioned above, marke iming refers o a emporary higher or lower weighing of equiies (or oher asse classes) relaive o he pension fund s sraegic asse allocaion, moivaed by shor-erm reurn expecaions. Noe ha where no equiy rades are made, i is difficul o disinguish beween free floa (passive managemen) and marke iming (acive managemen), as allowing he asse allocaion o drif could be seen as an acive invesmen decision. A number of sudies show ha sraegic asse allocaion dominaes porfolio performance. In paricular, sraegic asse allocaion is shown o explain more han 90 percen of he variabiliy in pension fund reurns over ime, while he addiional variaion explained by marke iming is less han 5 percen (Blake, Lehmann and immermann, 1999; Brinson e al., 1986, 1991; Ibboson and Kaplan, 2000). 8 Moreover, in line wih he efficien marke heory, evidence shows ha pension funds are unsuccessful in exploiing marke iming o generae excess reurns. In paricular, marke iming is shown o cause an average loss of basis poins per year (Blake e al., 1999; Brinson e al., 1986, 1991; Daniel e al., 1997). While a number of empirical sudies examine he impac of invesmen policy on reurns, 9 very few papers invesigae he impac of marke developmens on invesmen policy. Blake e al. (1999) and Kakes (2006) repor a negaive correlaion beween asse class reurns and ne cash flows o he corresponding asse class, which poins o rebalancing. However, Blake e al. (1999) also find ha he asse allocaion for UK pension funds drifs oward asse classes ha performed relaively well, in line wih a free-floa sraegy. Apparenly, UK pension funds only parly rebalanced heir invesmens in 7 Pension funds can rebalance coninuously, hereby ensuring ha heir asse allocaion always maches heir sraegic asse allocaion. However, pension funds are known o use rebalancing sraegies, which have some free floa componen. Examples include calendar rebalancing, whereby pension funds rebalance heir porfolio back o is sraegic weighs a regular inervals, and band rebalancing whereby pension funds creae bands around each asse class and rebalance heir porfolio as soon as one asse class breaches is band. 8 A shorcoming of hese sudies is ha he (average) difference beween acual and sraegic asse allocaion is no repored. his difference beween acual invesmens and invesmen policy is likely o be relaed o he percenage of reurn variabiliy ha can be aribued o marke iming. 9 he lieraure invesigaing he effeciveness of sock picking and marke iming in improving invesmen performance is exensive. Mos sudies focus on US muual funds and find ha fund managers are no able o exploi seleciviy and iming o generae excess reurns (e.g. Fama (1972), Henriksson and Meron (1981), Kon and Jen (1979) and Kon (1983)). Agnew e al. (2003) repor ha equiy allocaion of paricipans in 401(k) plans are posiively relaed o he previous day s equiy reurn (feedback rading). However, no significan correlaion is found beween changes in equiy allocaions and reurns over he following hree days suggesing he absence of marke-iming abiliies. he seminal paper by Lakonishok e al. (1992b) examines he US money managemen indusry and shows ha invesmens by pension funds have consisenly underperformed he marke. he auhors aribue his finding o exra layers of agency problems in he pension fund indusry. However, his finding is conesed in a recen paper by Bauer e al. (2007), who show ha pension funds perform close o heir benchmarks while muual funds underperform srongly. he laer auhors argue ha pension funds are less exposed o hidden agency coss han muual funds, since hey have beer negoiaing power and monioring capaciy and more efficienly pool heir funds.

8 6 response o differen reurns across asse caegories. Hence, he degree of rebalancing versus free floa in pension fund asse allocaion remains an open quesion. his paper uses quarerly daa from Duch pension funds over 1999:I 2006:IV. Alhough his period is relaively shor, i conains a significan sock marke bubble as well as burs. Figure 2 presens a preview of he empirical resuls, depicing he sraegic and he acual equiy allocaion for Duch pension funds, as well as he MSCI World Index. hree paerns sand ou from his figure. Firs, he acual equiy allocaion ends o have a paern similar o he MSCI World Index, bu wih some reversion o he sraegic asse allocaion. Generally, acual equiy allocaion increases when he sock marke goes up, and vice versa. he main explanaion for his paern is ha pension funds end o rebalance heir asse allocaion only parly in response o changes in he value of heir equiy porfolio. Figure 2: Sock marke reurns and equiy invesmens (1999:I 2006:IV) :Q1 1999:Q3 2000:Q1 2000:Q3 2001:Q1 2001:Q3 2002:Q1 2002:Q3 2003:Q1 2003:Q3 2004:Q1 Equiy allocaion (%). 2004:Q3 2005:Q1 2005:Q3 2006:Q1 2006:Q MSCI World index. 60 Sraegic allocaion (%) Acual allocaion (%) MSCI World index Second, Figure 2 poins o ineracion beween sock marke performance and sraegic asse allocaion. he sraegic equiy allocaion appears o follow he performance of he equiy marke, alhough wih a ime lag. Following he sock marke boom in he second half of he 1990s, he sraegic equiy allocaion increased unil he end of 2001, bu decreased from 2002 o 2003 in response o he fall of he sock marke, saring in Generally, funds adjus heir sraegic equiy allocaion gradually and wih a subsanial delay in response o sock marke movemens.

9 7 hird, he figure suggess ha pension funds may have los money from marke iming over he business cycle. hey seem o have gradually increased heir equiy allocaion unil he downurn of he sock marke was well under way, confroning hem wih relaively large losses. Conversely, pension funds did no significanly increase heir equiy allocaion porfolio invesmens o reap he full benefi of he subsequen upward sock marke rend. he srucure of his paper is as follows. Secion 2 presens he daa used in he analyses. Secion 3 invesigaes he influence of marke movemens on asse allocaion, whereas rebalancing is more closely examined in Secion 4. he nex secion analyses he relaionship beween sock marke reurns and sraegic asse allocaion. he quesion wheher pension funds are successful in adjusing heir equiy allocaion in anicipaion of expeced marke movemens is explored in Secion 6. Finally, he las secion summarizes and concludes. 2 Descripion of he daa We use a deailed daase wih quarerly informaion on 748 Duch pension funds for he 1999:I 2006:VI period. he daa is from De Nederlandsche Bank, responsible for he prudenial supervision of pension funds and heir regulaory compliance. For each pension fund daa is available on sraegic asse allocaion, asse sales and purchases, he marke value of invesmens in differen asse classes and heir ime-weighed reurns. 10 We use he MSCI World oal reurn index denominaed in euros as our principal benchmark o assess he impac of sock marke reurns on acual and sraegic equiy allocaion and o evaluae he performance of marke iming sraegies. 11 he sample is an unbalanced panel, as no all pension funds repored daa for he enire sample period due o new enrans, mergers, erminaions, and reporing failures. 12 Since our aim is o sudy asse allocaion over ime, we exclude pension funds wih less han wo years of daa. Finally, we exclude inconsisen observaions and observaions wih clear reporing errors. Our final sample includes daa on 748 pension funds from 1999:I 2006:IV, represening around 85% percen of oal pension fund asses in he Neherlands. able 2 presens summary saisics on he 10 For each pension fund, we calculae he average of is log reurns over ime, conver hese averages o simple reurns, and calculae he average of hese simple reurns across pension funds. his hree-seps procedure avoids a disorion in calculaing average reurns resuling from he fac ha he log of an average is no equal o he average of logs. 11 Alernaively, in some cases we use he AEX index as a benchmark for sock marke reurns in he Neherlands, alhough i should be noed ha pension funds generally have broader and more inernaional equiy porfolio allocaions han capured by he laer index. 12 We also ran regressions for a balanced sample of only 382 pension funds ha repored a leas seven years of daa. he regression resuls were similar o hose repored in ables 5-7, suggesing ha survivorship bias is no a significan issue.

10 8 invesmen porfolios of pension funds in our sample. he size of pension funds in he sample is hugely divergen: he smalles pension funds have asses worh less han 1 million, while he larges funds have asses of more han 200 billion. he average and median sizes of pension fund asses equal 799 million and 53 million, respecively. We disinguish beween size classes and ypes of pension funds and beween ypes of pension plans. Small funds end o inves relaively less in equiy compared o larger funds, and more in bonds, reflecing lower risk appeie. Alhough large in number (70% of he sample), small funds adminiser only a minor share (less han 3%) of all pension fund invesmens. able 2: Invesmens across size classes and pension fund ypes (1999:I 2006:IV) Number Average Max min Average acual equiy Max min Size classes based on of Average oal bond equiy invesmens sraegic equiy oal invesmens (mln euro) pension funds invesmens (mln euro) invesmens (%) invesmens (%) over ime (%) allocaion over Invesmen ime (%) gap (%) a (1) (2) (3) (4) (5) (6) (7) (Small) (Medium) >1000 (Large) 47 8, Average / oal ype of pension fund b Indusry (all) 95 3, Compulsory 76 4, Non-Compulsory 19 1, Company Professional group 10 2, Plan ype DB DC Noe: All saisics are averages weighed by oal invesmens excep for he firs and las column (Average oal invesmens and Number of pension funds). a Invesmen gap is he absolue difference beween he sraegic equiy allocaion and he acual percenage of equiy porfolio invesmens; b en pension funds belong o oher caegories. Our sample includes 631 company funds, 95 indusry-wide funds, and 10 professional group funds. 13 Compulsory indusry funds are larges in erms of invesmens. All funds inves beween 41 and 45 percen in equiy. Company funds and professional group funds inves relaively more in bonds han oher ypes of funds, reflecing heir sronger risk aversion. Indusry funds inves subsanially more in real esae. On average, defined benefi (DB) funds have higher equiy and lower bond invesmens han defined conribuion (DC) funds, suggesing ha DB funds may ake higher risks since hey can benefi from inergeneraional risk sharing. 13 Company funds provide pension plans o he employees of heir sponsor company. hey are separae legal eniies, bu are run by he sponsor company and employee represenaives. Indusry funds provide pension plans for employees working in an indusry. Such pension plans are based on a collecive labor agreemen beween an indusry s companies and he labor unions, represening he employees in his indusry. Finally, professional group funds offer pension schemes o specific professional groups (e.g. general praciioners, public noaries).

11 9 Columns 5 and 6 indicae how, respecively, he acual and sraegic equiy allocaion vary over ime. For he average pension fund, he range of he acual equiy allocaion is 16% and of he sraegic equiy allocaion is 13%. hus, boh acual and sraegic equiy allocaion move significanly over ime. he las column shows ha he difference beween sraegic and acual equiy allocaion is, on average, 0.8 percenage poin. able 3 shows ha he sraegic and acual equiy allocaion differs significanly across pension fund observaions. A small majoriy of funds inves percen of heir asses in equiies. A quarer of he funds inves more han 40 percen in equiies, while around one-fifh of he funds inves less han 20 percen in equiies. able 3: Disribuion of equiy allocaion across pension funds (1999:I 2006:IV; in %) Range* Equiy allocaion sraegy Acual equiy allocaion oal * he allocaion in each class is calculaed as a percenage of oal observaions. Pension funds use derivaives for hedging purposes and also o efficienly adjus heir acical asse allocaion, while avoiding he buying or selling (coss of) he underlying asses. able 4 presens he use of derivaives by pension funds of various size classes. he use of derivaives increases wih he size of pension funds, bu even he larges pension funds (i.e. wih oal invesmens larger han 1 billion) hold only 2 percen of heir equiy posiions hrough derivaives. For small pension funds (below 100 mln oal invesmens), he noional value of quarerly purchased fuures and forwards (Column 5) is small compared o he ne purchase of equiies (Column 4). However, for he larges pension funds, he noional value of ne purchased fuures and forwards is high and in fac exceeds he ne purchase of equiies. In conras, he ne premium paid or received for opions and warrans is relaively small for all funds, alhough again increasing wih fund size. Overall, we conclude ha only he larges pension funds make significan use of derivaives.

12 10 able 4: he use of derivaes across pension funds (1999:II 2006:IV) Number of Average equiy of which Ne purchase (in mln euro) of oal invesmens pension invesmens using Fuures and Opions and (mln euro) funds (mln euro) derivaives (%) Equiies forwards warrans (1) (2) (3) (4) (5) (6) (Small) ,000 (Medium) >1,000 (Large) Average / oal Noes: All saisics are simple averages. For ne purchases of fuures and forwards we repor noional amouns. For opions and warrans he premium is repored. 3 Relaive sock-marke reurns and shor-erm changes in equiy allocaion o sar our empirical analysis, his secion examines he shor-erm impac of sock marke performance on equiy allocaion. 14 Over ime, acual equiy allocaion may change eiher (i) due o excess reurns on equiies compared o oher asse classes (free floaing) or (ii) due o ne purchases or ne sales of equiies (rebalancing and marke iming). o invesigae he impac of relaive sock marke reurns on pension funds equiy allocaion, we esimae he following equaion: E ( r j ri, j ) + γ 1Policy 1 + δ1size 1 i k w = α 1 + Σ j 0β j + ε, = (1) he dependen variable w is he acual percenage of he porfolio invesed in equiies of pension fund i (i = 1,,N) a quarer ( = 1,,). he variable (r E r ) is used o measure excess sock marke reurns compared o oher invesmen caegories on a quarerly basis. For sock marke reurn (r E ) we use he reurn on he MSCI World index and for he reurn on he oal pension fund porfolio (r ) we muliply he sraegic asse allocaion of four key asse classes by represenaive broad marke indexes. 15 We consider wo varians of Equaion (1). he base model is wihou lagged sock marke reurns (k = 0), whereas alernaively, we include excess sock marke reurns wih ime lags (k = 5) o invesigae wheher pas reurns influence pension funds invesmens wih some delay. he sraegic equiy allocaion (Policy) also expressed as a percenage, is included o conrol for pension fund invesmen policy. Size, which is measured as he logarihm of he oal invesmen porfolio, conrols for he endency of larger funds o inves relaively more in equiies. he Policy and Size are included 14 For pracical reasons, we ignore ha equiy price changes may also affec (or go hand in hand wih) prices in real esae, hedge funds and privae equiy. 15 We consider five invesmen caegories: equiies, bonds, real esae, money marke insrumens and oher asses. For bonds we use he JP Morgan EMU bond index, for real esae we use he FSE EPRA Neherlands real esae index and for money-marke invesmens we use he 3-monh Euribor ineres rae. We assume ha he fifh caegory oher asses is proporionally invesed in he previous four invesmen caegories (or have a similar reurn). We calculae excess reurns as follows: excess reurn = reurn MSCI [(reurn on bonds * bond invesmens + reurn on real esae * real esae invesmens + 3-monhs Euribor * money marke invesmens) / (bond invesmens + real esae invesmens + money marke invesmens)].

13 11 wih one ime lag o avoid endogeneiy problems and since i may ake some ime before changes in hese variables lead o changes in he equiy porfolio invesmen. he panel is unbalanced, which implies ha he number of observaions varies across pension funds. 3.1 Empirical resuls of he impac of sock reurns on acual equiy allocaion able 5 presens esimaes of he impac of shor-erm relaive sock marke reurns on he percenage of equiy porfolio invesmens, using Equaion (1). A one percenage poin relaive ouperformance of he MSCI leads o an increase in equiy allocaion of percenage poin in he subsequen quarer (firs column). he second column shows ha excess equiy reurns also have a significan impac on equiy allocaion up o five quarers laer. he impac decreases over ime, indicaing ha pension funds rebalance gradually or infrequenly. able 5: Esimaes of he pension funds equiy invesmens model (1999:II 2006:IV) All funds Small funds Medium sized funds Large funds (1) (2) (3) (4) (5) Excess reurn MSCI 0.159*** 0.163*** *** *** 0.260*** Idem, lagged 1 quarer 0.114*** *** *** 0.139*** Idem, lagged 2 quarers 0.083*** *** *** 0.138*** Idem, lagged 3 quarers 0.060*** *** *** 0.079*** Idem, lagged 4 quarers 0.058*** *** *** 0.111*** Idem, lagged 5 quarers 0.047*** *** *** 0.060*** oal effec excess reurns Invesmen policy (-1) 0.927*** 0.918*** *** *** 0.869*** Size (-1) 0.003*** 0.002*** *** *** Inercep *** *** Number of observaions 17,290 14,216 8,601 4,330 1,285 R 2, adjused Noes: ***, **, and * denoe significance a he 1%, 5%, and 10% levels, respecively. he sandard errors have been correced for possible heeroskedasiciy or lack of normaliy using he Huber-Whie sandwich esimaors. Hence, sock marke ouperformance induces increases in he equiy allocaion in he following periods, alhough he impac decays over ime. able 5 reveals also ha a one percenage poin increase in he sraegic equiy allocaion causes a significan rise of around percenage poin in acual equiy porfolio invesmens in he nex period. Apparenly, pension fund invesmen managers adjus heir equiy porfolio invesmens almos solely in response o changes in he sraegic equiy allocaion. Finally, he posiive sign for he size of invesmens affirms ha larger funds inves relaively more in equiies, excep medium-sized funds. 16 A possible explanaion is ha large pension funds end o be less risk averse han small pension funds. 16 able 1 shows ha larger pension funds have relaively higher equiy invesmens han smaller ones.

14 12 If we consider he invesmen behavior across size classes (las hree columns), where size classes are defined as in able 4, we observe ha he impac of excess sock marke reurns on equiy allocaion increases wih he pension fund size, boh immediaely and in he long run. Apparenly, large funds allow more free floaing, whereas smaller funds rebalance more. In line wih his resul, larger funds reac less o changes in he invesmen policy, compared o smaller funds. As a robusness es we repea he esimaions of able 4 and laer ables wih balanced samples wih pension funds which have a leas 28 quarers wih all required daa, insead of 8 quarers as in he curren daa se. For all ables, he resuls are fairly similar. As a second es, we re-esimaed wih fixed effecs for pension funds and years. he Hausman es rejeced random effecs. he resuls are again fairly similar, excep for able hese resuls confirm ha our oucomes are quie robus. 3.2 Excess sock marke reurns and rebalancing he posiive impac of excess equiy reurns on equiy allocaion in he previous secion may be (parly) due o imperfec rebalancing by pension funds. Excess equiy performance will lead o changes in equiy allocaion if pension funds do no keep heir invesmen porfolios fully balanced a all imes. his secion presens an empirical rebalancing model, which is used o esimae o wha exen pension funds rebalance, ha is, adjus heir asse allocaion in response o excess equiy reurns. 18 his model is derived as follows, saring from he definiion of he acual equiy allocaion: w E / Ai, = (2) where E represens he equiy invesmens of pension fund i a ime, and A sands for oal asses. aking firs differences of Equaion (2), we obain: w w 1 E = A E A 1 1 E = A 1 1 (1 + r E (1 + r + NCF E + NCF ) E ) A 1 1 (1 + r + NCF ) wi ) (1 + r + NCF E E = w 1, 1 (1 + ri, + NCFi, (1 + ri, + NCF E E ( ri, ri, + NCFi, NCFi, ) = w 1, (3) (1 + r + NCF ) ) ) 17 In ha able, he coefficiens level of significance are subsanially lower. Apparenly, he pension funds fixed effecs picked up a par of he variaion in he explanaory variables. 18 An alernaive approach o measure rebalancing based on pension funds equiy sales and purchases is presened in he appendix.

15 13 where NCF is shor for new invesmens as a fracion of oal invesmens, NCF E for new equiy invesmens also as a fracion of equiy invesmens, r E for he reurn on equiies over he las quarer, and r for he reurn on oal asses (all for fund i and quarer ). Dividing boh sides by w -1 resuls in: w w w 1 1 E E ri, ri, NCFi, NCF = r + NCF 1+ r + NCF (4) his equaion explains he percenage change in equiy allocaion by: (i) excess equiy reurns, and (ii) ne cash flows o equiies, where boh variables are scaled by he change in he oal porfolio size. he firs righ-hand erm is exogenous, since excess reurns are deermined by marke developmens and ne cash flows ino he pension fund are based on decisions by employers and employees raher han on equiy allocaion. Given he small size of pension fund invesmens relaive o oal sock marke capializaion, we can safely assume ha changes in equiy allocaion do no affec sock marke reurns. he second righ-hand erm, however, is endogenous. While ne cash flows o equiy invesmens direcly influence he equiy allocaion of pension funds, he reverse can also be rue: changes in he equiy allocaion may sway pension funds o adjus heir ne cash flows o equiy invesmens. hus, here is muual causaliy beween changes in equiy allocaion and ne cash flows o equiy invesmens. o esimae he impac of excess equiy reurns on equiy allocaion, we apply he above decomposiion, ignoring he endogenous second righ hand erm. his resuls in he following empirical regression model: w w w 1 1 = r r Policy E 1 α 2 + β 2 γ ri, + NCF Policy 2 ε (5) he percenage change or growh in he sraegic equiy allocaion (Policy) is included o conrol for changes in invesmen policy. his variable is included wih a ime lag of one quarer, since i may ake some ime before changes in policy lead o adjusmens in he acual equiy porfolio invesmens. In Equaion (5), β 2 esimaes he degree of free floa or marke iming and 1-β 2 assesses he rebalancing percenage. As an alernaive model we spli he excess equiy reurn variable furher ino posiive and negaive equiy reurns. his allows us o observe possible asymmeric effecs in response o changes in excess equiy reurns. 3.3 Empirical resuls of rebalancing able 6 presens he esimaed impac of excess equiy reurns on equiy allocaion. he resuls show ha pension funds rebalance, on average, around 39 percen of excess equiy reurns, leaving 61 percen for free floaing. hus 61 percen of excess equiy reurns ranslae ino increases of he equiy

16 14 allocaion in he nex period. Column (2) shows ha pension funds rebalance differenly in response o posiive and negaive equiy reurns. Only 12 percen of posiive equiy reurns are rebalanced, agains 49 percen of negaive equiy reurns. Apparenly, whereas pension funds do no auomaically sell equiies in bull markes, hey do end o buy addiional equiies in bear markes. In line wih expecaions, changes in policy affec he acual allocaion posiively (significan a he 1% level), wih a lag of one quarer. able 6: Esimaes of he equiy allocaion model: rebalancing versus free floa (1999:II 2006:IV) All funds Small funds Medium sized Large funds funds (1) (2) (3) (4) (5) (6) (7) (8) Excess equiy reurns Posiive excess equiy reurns Negaive excess equiy reurns Change in policy (-1) Inercep Number of observaions 11,867 11,867 5,817 5,817 4,653 4,653 1,397 1,397 R 2, adjused Noes: All symmeric and asymmeric excess equiy reurns effecs are significan a he 1% level. he sandard errors have been correced for possible heeroskedasiciy or lack of normaliy using he Huber-Whie sandwich esimaors. Columns (3) o (8) presen he model esimaes for he various size classes. In line wih he resuls of Secion 3.1, we observe ha, in he symmeric model varian, large funds, a 30 percen, rebalance less han he small and medium-sized funds (around 40 percen), leaving 70 percen for free floaing. Changes in he one quarer lagged sraegic equiy allocaion (Policy) affec acual allocaion significanly (a he 1% level) for he small funds only. 19 If we urn o he asymmeric effecs on excess equiy reurns, we observe ha he posiive effecs increase significanly wih pension fund size, while he negaive effecs are similar across he size classes. he posiive reurns coefficien for he larges funds is, a 1.21, even above 1, indicaing ha large funds inves addiional funds in equiies in response o excess reurns in he las monh. his suggess ha excess equiy reurns are perceived by large pension funds o provide a posiive signal for fuure reurns, leading pension funds o increase heir sakes. his is in line wih resuls in able 5, which indicae ha large funds respond more srongly o excess equiy reurns han small ones. A possible explanaion is ha managers of large funds have more freedom o use marke iming sraegies in response o marke developmens. Figure 3 presens he asymmeric relaion beween excess equiy reurns and rebalancing discussed above. 20 If pension funds used a free floa sraegy and did no rebalance a all, excess equiy reurns 19 We esimaed also an alernaive specificaion wih ineracion erm excess equiy reurn imes size insead of hree size classes. However, he coefficien of his ineracion erms was insignifican. 20 o esimae his figure we adjused Equaion 5 by adding hree addiional erms: squared excess equiy reurns and excess and squared equiy reurns muliplied wih 0-1 dummies indicaing posiive and negaive reurns.

17 15 would go in full o proporionae increases in equiy allocaion. his is represened by he diagonal line. Insead, wih full rebalancing, excess equiy reurns would have no impac on equiy allocaion, marked off on he x-axis. he curvaure dividing he free floa and rebalancing areas reflecs he acual rebalancing behavior of Duch pension funds. Srikingly, rebalancing by pension funds depends on boh he sign and size of excess equiy reurns. Small posiive equiy reurns (of around 0-5%) are no rebalanced a all, bu he degree of rebalancing increases wih he size of excess equiy reurns. Insead, small negaive reurns (of around 0 o -10%) are rebalanced for he larges par, bu he degree of rebalancing decreases wih he size of negaive excess reurns. Figure 3: Reacion of pension funds o excess equiy reurns: rebalancing and free floa Rebalancing Change in equiy allocaion (%) 10 Free floa Free floa -10 Rebalancing Excess equiy reurn (%) 4 Excess sock marke reurns and medium-erm changes in sraegic equiy allocaion he previous secion described he effecs of excess equiy reurns on acual equiy allocaion. his secion invesigaes he impac of (annual) sock marke performance (ar E - ar ) on pension funds sraegic equiy allocaion (Policy). herefore, we esimae he following equaion: E ( ari, ari, ) + γ 3Policy 1 + δ 3Size 1 i Policy = α 3 + β 3 + ε, (6)

18 16 he excess sock marke performance has been aken on an annual basis, indicaed by (ar E ar ), where a refers o annual. 21 We assume ha he pension fund rusees base heir policy on longer-erm measures of performance, as also refleced by he empirical resuls. 22 As above, Size conrols for he endency of larger funds o inves relaively more in equiy porfolios. We also include a lag of he dependen variable Policy, as we expec only gradual changes in policy over ime. Hence, he equaion describes he quarerly adjusmens in policy Empirical resuls of he impac of sock marke reurns on sraegic equiy allocaion able 7 shows he impac of excess sock marke reurns on sraegic equiy allocaion. he invesmen policy is adjused significanly o changes in equiy reurns, irrespecive of wheher hey are measured by he MSCI or by he acual invesmen reurns earned by pension funds. his shows ha invesmen policy is no consan over ime bu, o some exen, follows marke developmens. he coefficien of he lagged dependen variable, 0.97, indicaes how slowly he sraegic equiy allocaion reacs o changes in he quarerly reurns. On average, 97 percen of he equiy invesmen policy is deermined by he previous quarer s invesmen policy, whereas marke developmens accoun for he remaining 3 percen. hese marke developmens, capured by he yearly excess reurn, have a small bu very significan impac, boh based on he MSCI and on he acual equiy reurn of he pension fund. heir final impac on equiy invesmen policy over ime is 0.28 (= /( )). he size effec is also small bu significan. 24 While his equaion shows how invesmen policy is influenced by marke able 7: Esimaes of he sraegic equiy allocaion model (1999:II 2006:IV) All funds Small funds Medium sized funds Large funds (1) (2) (3) (4) (5) Equiy invesmen policy (-1) *** *** *** *** *** Yearly excess reurn MSCI *** *** *** ** Yearly excess pension fund s equiy reurn *** Size (-1) *** ** ** Inercep *** Number of observaions 16,340 11,273 10,118 4,822 1,400 R 2, adjused Noes: ***, **, and * denoe significance a he 1%, 5%, and 10% levels, respecively. he sandard errors have been correced for heeroskedasiciy using he Huber-Whie sandwich esimaors. 21 Excess equiy reurn compares he MSCI World index o oher invesmen caegories, as above. 22 Annual reurns provide beer resuls han quarerly reurns. 23 An alernaive model, wih firs differences of Policy as he dependen variable, insead of gradual adjusmen, leads o similar esimaion resuls (no repored here). 24 We esimae also an alernaive specificaion of Equaion (6), wih as dependen variable he firs difference of equiy invesmen insead of is level, so ha we drop he lagged equiy invesmen policy erm. In ha specificaion, he various yearly excess reurn coefficiens are all a fracion higher and equally significan. he variable size is no longer significan. Where equiy levels are higher for large pension funds compared o small funds, he adjusmen of he sraegic equiy allocaion does no deviae significanly beween large and small funds.

19 17 developmens, i does no provide a model of he underlying invesmen policy decisions, which are generally based on asse liabiliy managemen sudies. he resuls across pension fund size classes seem similar. However, he sligh increases in he coefficiens of he lagged dependen variable and he yearly excess reurn for he larger funds imply an increase in he long-run effec of he yearly excess reurn from 27% (small funds) o 47% (large funds). 5 he impac of marke iming on pension fund reurns Secions 3 and 4 show ha boh acual and sraegic asse allocaion of pension funds are influenced by he relaive performance of equiy markes. Here we invesigae wheher he variaions of acual and sraegic asse allocaion have generaed excess reurns. Pension fund invesmen managers may profi from marke iming in heir decisions on he acual equiy allocaion, provided hey have some abiliy in forecasing sock marke rends. o earn higher risk-adjused porfolio reurns, skilled invesors can creae a posiive informaion raio hrough increasing equiy allocaion before he sar of a bull marke and conversely, decreasing hem ahead of a bear marke. Similarly, pension fund rusees may profi from marke iming in heir decisions on he sraegic equiy allocaion. his secion examines wheher pension funds indeed have profied from marke iming during he sample period. We use he following hree equaions o spli excess reurns ha can be aribued o marke iming (ER M ) ino hree sources: 25 = = 1, E ERM ( 1) ( Policyi Policyi )( r ri, ) / (7) = = 1, E ERM ( 2) ( wi wi ) ( r ri, ) / = = 1, E ERM ( 3) ( wi Policy ) ( r ri, ) / (8) (9) By approximaion (9) equals (2) minus (1) as, for each pension fund, he average Policy is in line wih he average w. he variable (r E r ) equals he quarerly excess reurn of pension fund i a ime as defined before. Policy and w are again, respecively, he sraegic and acual equiy weighs in he asse porfolio. Equaion (7) esimaes he average excess reurn from varying he sraegic equiy 25 Equaions (7) and (8) are adaped from Grinbla and iman (1993). he performance measure proposed by Grinbla and iman (1993) is differen from ours in wo ways. Firs, hey compare curren porfolio weighs o porfolio weighs in he previous period insead of average porfolio weighs. Second, hey do no specifically focus on marke iming bu insead sudy wheher acive sock picking generaed posiive risk-adjused reurns.

20 18 allocaion over ime, 26 Equaion (8) measures he added value of varying he acual equiy allocaion over ime, and Equaion (9) deermines he exra reurn from allowing he acual equiy allocaion o differ from he sraegic equiy allocaion. he equaions esimae he average quarerly reurn ha would have been realized by applying a marke iming sraegy o invesmens in broad marke indices. 27 Under he null hypohesis ha he porfolio manager has no abiliy in forecasing expeced sock marke reurns, he excess equiy reurns are uncorrelaed o over- or underweighing of equiy allocaions relaive o heir mean and excess equiy reurns would be close o zero. able 8: he average impac of marke iming on reurns (1999:II 2006:IV; in %) Average absolue weigh Average s.d. of weighs over ime Average excess equiy reurns Marke iming measure (1) Varying sraegic equiy allocaion over ime a) Small funds b) Medium sized funds c) Large funds d) Full sample (2) Varying acual equiy allocaion over ime a) Small funds b) Medium sized funds c) Large funds d) Full sample (3) Deviaing acual from sraegic equiy allocaion a) Small funds b) Medium sized funds c) Large funds d) Full sample Noes: All saisics are averages weighed by oal invesmens. he average absolue weighs are calculaed for he differen measures as follows: (1) he average of he absolue deviaion beween he sraegic equiy allocaion and he average sraegic allocaion calculaed over ime, (2) he same for acual equiy allocaion, and (3) he average of he absolue deviaion beween acual and sraegic equiy allocaion. able 8 presens he esimaion resuls of Equaions (7) o (9). he firs column shows ha he average absolue weigh, on which excess reurns from marke iming can be earned, is small. However, as he middle column indicaes, he variaion of he equiy allocaion is significan. 28 he las column presens boh he variaion of he sraegic and acual equiy allocaion over ime and shows ha he average negaive excess reurn is no less han beween 5 and 7 basis poins per euro invesed per quarer, ha is, bps annually. In conras, he effec from deviaing acual from sraegic equiy 26 he bars above Policy i and w i indicae he respecive averages over (ime). 27 We calculae he average reurns in hree seps. For each pension fund, we firs calculae he average of is log reurns over ime. Nex, we conver hese averages o simple reurns. Finally, we calculae he average of hese simple reurns across pension funds. his procedure avoids a disorion in calculaing average reurns resuling from he fac ha he log of an average is no equal o he average of logs. 28 Significance is based on he annualized sandard deviaion of he calculaed excess reurns, which is around 0.9%, well above he average excess reurns in able 8.

21 19 allocaion on excess reurns has been close o zero. Noe, however, ha none of he resuls are significanly differen from zero. Differences across size caegories appear o be small. he coss of marke iming are no fully inernalized ino he figures presened. he inclusion of ransacion and personnel coss would resul in even more negaive excess reurns from marke iming. Overall, hese resuls show ha for he average pension fund, marke iming led o negaive, nonsignifican excess reurns during he sample period. 6 Conclusions his paper is he firs o examine he ineracion beween sock marke performance and he invesmen policy of pension funds. We find ha sock marke performance influences he asse allocaion of pension funds in wo ways. In he shor erm, he ouperformance of equiies over bonds and oher invesmen caegories auomaically resuls in higher equiy allocaion (and vice versa), as pension funds do no coninuously rebalance heir asse allocaion. Each quarer, pension funds rebalance, on average, around 39 percen of excess equiy reurns. he remaining 61 percen leads o higher or lower equiy allocaion as a resul of free floaing, which are furher rebalanced in subsequen quarers. In he medium erm, ouperformance of equiies induces pension funds o increase heir sraegic equiy allocaion (and vice versa). Overall, our esimaes indicae ha he invesmen policy of pension funds is parially driven by he (cyclical) performance of he sock marke. Apparenly, pension funds suffer from myopic invesmen behavior: hey end o base invesmen decisions excessively on recen sock marke performance, raher han on long erm rends. We also find ha pension funds reac asymmerically o sock marke shocks. Equiy reallocaion is higher afer underperformance of equiy invesmens hen afer ouperformance. In paricular, only 16 percen of posiive excess equiy reurns is rebalanced, while 48 percen of negaive shocks resuls in rebalancing. hus, pension funds sricly limi any decline in equiy allocaion in response o underperformance bu hey allow higher exposures o equiies when hese ouperform oher invesmens. Apparenly, equiy porfolio managers have more funds available for invesmen, when hey gain excess reurns. We observe ha sraegic and acual equiy allocaion of pension funds vary significanly over ime. However, pension funds are no rewarded for marke iming. On average, boh he marke iming sraegy proposed by he pension fund adminisraion and acual marke iming execued by invesmen managers leads o negaive or zero excess reurns over he period under consideraion, depending on he measure used. In line wih mos empirical evidence, we find ha he marke iming sraegy of Duch pension funds does no generae excess reurns, indicaing ha Duch pension fund managers

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