On the Timing Ability of Mutual Fund Managers. Nicolas P.B. Bollen and Jeffrey A. Busse *

Transcription

1 On he Timing Abiliy of Muual Fund Managers Nicolas P.B. Bollen and Jeffrey A. Busse * January 2000 * Bollen is Assisan Professor of Finance a he David Eccles School of Business, Universiy of Uah. finnb@business.uah.edu. Busse is Assisan Professor of Finance a he Goizuea Business School, Emory Universiy. Jeff_Busse@bus.emory.edu. The auhors hank René Sulz, an anonymous referee, Uri Loewensein, Tom Smih, Liz Tashjian and seminar aendees a he Universiy of Uah and he Ausralian Graduae School of Managemen for heir useful commens.

2 On he Timing Abiliy of Muual Fund Managers ABSTRACT Exising sudies of muual fund marke iming analyze monhly reurns and find lile evidence of iming abiliy. We show hrough simulaion ha daily observaions subsanially increase he power of iming ess. When we esimae he iming abiliy of muual funds using boh daily and monhly reurns, he daily ess generae more significan iming coefficiens han he monhly ess. We consruc a se of synheic fund reurns in order o conrol for spurious measuremens, and rejec he hypohesis ha muual fund iming coefficiens equal heir synheic counerpars. These resuls sugges ha muual funds may possess more iming abiliy han previously documened. The performance of muual funds receives a grea deal of aenion from boh praciioners and academics. Almos 50% of U.S. households inves in muual funds, wih an aggregae invesmen of over $5 rillion dollars (Invesmen Company Insiue, 1999). Given he size of heir sake, he invesing public s ineres in idenifying successful fund managers is undersandable, especially in ligh of mouning evidence ha he reurns of mos acively managed funds are lower han index fund reurns. 1 From an academic perspecive, he goal of idenifying superior fund managers is ineresing because i challenges he efficien marke hypohesis. In his paper we examine he abiliy of muual fund managers o ime he marke, ha is, o increase a fund s exposure o he marke index prior o marke advances and o decrease exposure prior o marke declines. Mos exising sudies find lile evidence ha fund managers possess marke iming abiliy. Treynor and Mazuy (1966, TM), for example, develop a es of marke iming and find significan abiliy in only one fund ou 1

3 of 57 in heir sample. Henriksson (1984) uses he marke iming es of Henriksson and Meron (1981, HM) and finds ha only hree funds ou of 116 exhibi significan posiive marke iming abiliy. Graham and Harvey (1996) analyze invesmen newsleers suggesed allocaions beween equiy and cash, hereby measuring explicily he ex-pos performance of iming sraegies. Again, hey find no evidence of iming abiliy. In he sudies menioned hus far, observaions of muual fund reurns are recorded monhly or annually. As discussed by Goezmann, Ingersoll, and Ivkovic (1999, GII), a monhly frequency migh fail o capure he conribuion of a manager s iming aciviies o fund reurns, because decisions regarding marke exposure are likely made more frequenly han monhly for mos funds. 2 GII show ha he HM measure of iming abiliy is srongly biased agains finding iming skill when decisions are made daily bu observaions are recorded monhly. The auhors sugges ha when daily fund reurns are unavailable, he impac of iming aciviy can be esimaed in a regression framework by including a monhly iming facor consruced from daily index reurns. We have daily observaions of muual fund reurns. This allows us o direcly overcome he problem invesigaed by GII. To deermine wheher observaion frequency maers, we generae daily and monhly daa under he null of no iming abiliy and under various alernaives and, a boh observaion frequencies, es he size and power of sandard iming regressions, including he monhly es suggesed by GII. Boh daily and monhly ess falsely rejec he null a abou he righ rae for a given significance level. In all cases, however, he ess using daily daa exhibi superior power han he monhly ess. Furhermore, he power of daily ess is robus o differen frequencies a which managers migh deploy iming sraegies. The monhly ess are much less reliable. 2

4 We analyze a se of muual fund reurns a boh he daily and monhly frequencies o deermine wheher he use of daily daa changes inference regarding managerial abiliy. The daily ess resul in a larger number of significan esimaes of iming abiliy, boh posiive and negaive. Jagannahan and Korajczyk (1986, JK) show ha sandard iming ess spuriously rejec he null hypohesis of no abiliy if fund reurns are more or less opion-like han he marke proxy. To conrol for his, we generae a synheic mached sample of funds ha mimic he holdings of he acual funds bu have no iming abiliy by consrucion. The synheic funds also exhibi iming abiliy. However, approximaely one-hird of he muual funds have significanly greaer iming coefficiens han heir synheic counerpars. These resuls indicae ha a subsanial number of he funds in our sample possess significan iming abiliy. This paper makes wo main conribuions o he muual fund performance lieraure. Firs, we demonsrae ha daily daa provide differen inference han monhly daa regarding iming abiliy. Using boh simulaed and acual fund reurns, we find more significan iming abiliy using he daily daa. Second, we provide evidence ha he iming resuls canno be explained simply as a spurious saisical phenomenon. In summary, our resuls moivae he use of daily daa in fuure ess of muual fund performance, and sugges ha more fund managers possess marke iming abiliy han previously documened. The res of he paper is organized as follows. Secion I discusses he ess of iming abiliy used in he sudy. Secion II describes he daa. Secion III examines he size and power of iming ess. Secion IV presens he empirical analysis. Secion V offers concluding remarks. 3

5 I. Tess of Marke Timing Abiliy Marke iming refers o he dynamic allocaion of capial among broad classes of invesmens, ofen resriced o equiies and shor-erm governmen deb. The successful marke imer increases he porfolio weigh on equiies prior o a rise in he marke, and decreases he weigh on equiies prior o a fall in he marke. 3 This secion discusses he models we use o es for marke iming abiliy. TM use he following regression o es for marke iming: r 2 = α + β r + γ r + ε, (1) p, p p m, p m, p, where r p, is he excess reurn on a porfolio a ime, r m, is he excess reurn on he marke, and γ p measures iming abiliy. If a muual fund manager increases (decreases) he porfolio s marke exposure prior o a marke increase (decrease) hen he porfolio s reurn will be a convex funcion of he marke s reurn, and γ p will be posiive. HM develop a differen es of marke iming. In heir model, he muual fund manager allocaes capial beween cash and equiies based on forecass of he fuure marke reurn, as before, excep now he manager decides beween a small number of marke exposure levels. We es a model wih wo arge beas via he following regression: * r p, α p + β prm, + γ prm, + ε p, =, (2) where { r m, } r m * r m, I > 0, = (3) and I{} is he indicaor funcion. The magniude of γ p in equaion (2) measures he difference beween he arge beas, and is posiive for a manager ha successfully imes 4

6 he marke. We use boh iming models o measure iming abiliy in our sample of muual funds. Grinbla and Timan (1994) show ha ess of performance are quie sensiive o he chosen benchmark. For his reason, we run four-facor analogs of equaions (1) and (2) in which he hree addiional facors are he Fama and French (1993) size and booko-marke facors and Carhar s (1997) momenum facor. The addiional facors have been shown o capure he major anomalies of Sharpe s (1964) single-facor CAPM, and are included so as no o reward managers for simply exploiing hese anomalies. 4 We explain in he appendix how we consruc he daily version of hese facors. The hree addiional facors appear only as linear erms; we do no esimae facor iming excep for he marke facor. We express he four-facor TM regression as: 4 2 p, = α p + β p, iri, + γ prm, + ε p, i= 1 r, (4) and he four-facor HM regression as: 4 * p, = α p + β p, iri, + γ prm, + ε p, i= 1 r. (5) We esimae parameers of he wo models using boh daily and monhly daa o deermine wheher observaion frequency affecs inference regarding marke iming abiliy. Scholes and Williams (1977) poin ou ha when esimaing he parameers of a facor model of daily sock reurns, infrequen rading can resul in biased esimaes of variance, serial correlaion, and conemporaneous correlaion beween asses. This holds for porfolios of infrequenly raded asses as well, since he variance of a porfolio is largely deermined by he average covariance of he individual asses in he porfolio. 5

7 When using daily daa, we include lagged values of he facors as addiional independen variables in he regressions o accommodae infrequen rading. II. Daa We sudy daily reurns on 230 muual funds. The sample, aken from Busse (1999), is consruced as follows. A lis of all domesic equiy funds wih a common sock invesmen policy and a maximum capial gains, growh, or growh and income invesmen objecive and more han $15 million in oal ne asses is creaed from he December 1984 version of Wiesenberger s Muual Funds Panorama. Secor (e.g., echnology or healh care), balanced, and index funds are no included, nor are funds ha changed ino one of hese ypes of funds in subsequen years during he sample period. Daily per share ne asse values and dividends from January 2, 1985 hrough December 29, 1995 are aken from Ineracive Daa Corp, which acquires is ne asse value daa from he Naional Associaion of Securiy Dealers. Moody s Dividend Record: Annual Cumulaive Issue and Sandard & Poor s Annual Dividend Record are used o verify he dividends and dividend daes and o deermine spli daes. The ne asse values and dividends are combined o form a daily reurn series for each fund as follows: where NAV p, + D p, R p, = 1, (6) NAV p, 1 NAV p, is he ne asse value of fund p on day, and of fund p on day. D p, are he ex-div dividends Of he 244 funds in he December 1984 version of Panorama ha mee he specified crieria, 230 funds are racked hrough he end of he sample period or unil 6

8 merger or liquidaion and are included in he sample. The reurns of 14 funds could no be reconciled wih Morningsar s monhly reurns, and hese funds are no included. This sample does no suffer from survivorship bias of he sor discussed in Brown, Goezmann, Ibboson, and Ross (1992) and Brown and Goezmann (1995), wherein only funds in exisence a he end of he sample period are included. However, funds ha come ino exisence a some poin beween he end of 1984 and he end of he sample period are no included. To deermine wheher daily daa generaes differen inference han monhly daa, monhly reurns are consruced from he daily reurns as follows. Suppose here are N rading days in a paricular monh and le T denoe he firs day of he monh. The monhly reurn M R based on daily reurns D R is D ( + R ) 1 T 1 = + N M R 1. (7) = T Panel A of able I liss summary saisics of he fund reurn disribuions. We es he hypohesis ha fund reurns are normally disribued using he Jarque-Bera (1980) saisic, which is disribued χ 2 2 under he null. For he daily daa, only one of he funds fails o rejec normaliy a he 1% level. The average es saisic is 342,958, whereas a value of 9.21 or higher rejecs he null. For he monhly daa, four funds fail o rejec normaliy, and he average es saisic is 217. These resuls should come as no surprise, since he non-normaliy of sock reurns has been documened as early as Mandelbro (1963) and Fama (1965) and has spurred he sudy of alernaive disribuional assumpions as well as he developmen of sochasic volailiy models of reurns. Evidence of non-normaliy in our muual fund sample is relevan because of he JK 7

9 suggesion ha opion-like payoffs can generae spurious evidence of marke iming. We will reurn o his issue when inerpreing he resuls of our iming ess. Panel A of able I also liss summary saisics for our marke proxy, he CRSP value-weighed index including NYSE, Amex, and Nasdaq socks. The marke index rejecs normaliy a he daily and monhly frequency. Furhermore, he index exhibis higher excess kurosis and larger negaive skewness han he average of he muual funds. The negaive skewness is probably due o he crash of 1987 and oher smaller crashes in he sample. Again, he relaive degree of non-normaliy in he muual funds and he marke index may explain some of he marke iming resuls, as we discuss in secion IV. Panel B of able I shows he number of funds in he sample each year, as well as he average fund mean reurn and sandard deviaion of reurn. Noe ha he sample includes years of high and low reurns, as well as a range of sandard deviaions, suggesing ha he sample is rich enough o capure marke iming aciviy. In an effor o conrol for possible spurious resuls, we generae for each fund in he sample a synheic fund ha maches fund characerisics bu has no iming abiliy by consrucion. The synheic funds are creaed as in Busse (1999). For each fund in he acual sample, we solve a quadraic programming problem o deermine he fund s exposure o eigh asse classes: he six inersecions of he wo equally weighed size and he hree equally weighed book-o-marke indices, he equally weighed momenum index, and he equally weighed conrarian index. If we express fund p s reurn on dae as 8 r = b r + ε (8) p, i= 1 pi i, p, 8

10 where r i, is he reurn on asse class i on dae, hen he b s are seleced by minimizing he variance of ε p, subjec o a non-negaiviy consrain on he b s. Given hese weighs on he asse classes, a synheic fund is consruced by randomly selecing 100 socks chosen from he differen asse classes in proporions o mach he fund s vecor of b s. The socks are iniially equally-weighed. We replace socks by oher socks in he same asse class a random, wih an average holding period of one year. When a sock is replaced, weighs are rese o equal weigh. Beween replacemens, weighs evolve according o a buy and hold sraegy. This procedure is similar in spiri o he way Daniel, Grinbla, Timan, and Wermers (1997) creae characerisic-based benchmarks in order o es for managerial abiliy, excep ha Daniel e al. use heir funds quarerly holdings raher han a quadraic program o deermine asse class exposures. We consruc monhly and daily versions of he size and book-o-marke facors similar o he monhly facors of Fama and French (1993). We consruc monhly and daily versions of he momenum facor similar o he monhly facor of Carhar (1997) excep value weighed. The appendix explains how we consruc he daily versions of hese facors. We use he 90-day U.S. Treasury-bill index on Daasream (code TBILL90) o esimae he reurn on he riskless asse. In addiion, o compare our daily ess o he GII monhly ess, we reconsruc GII s monhly facor ha proxies for he monhly payoffs of a successful marke imer. The value of he monhly facor is compued each monh as: P { 1+ R,1 + R } 1 R, N = max m, τ f, τ m, (9) τ = 1 m, 9

11 where here are N days in monh, R m, τ is he marke reurn on day τ, and f, τ R is he riskless reurn. This facor is hen used in he following regression using monhly reurns o capure correlaion beween a fund s monhly reurn and he monhly value of daily iming: r 4 = α + β r + γ P + ε p, p p, i i, p m, p, i= 1, (10) where he four facors are hose used in he HM and TM models. This regression corresponds o he hree-facor model ha GII label he adjused-ff3 es. III. Saisical Properies of Tess of Timing Abiliy In his secion we simulae muual fund reurns under he null hypohesis of no iming abiliy and under various alernaives in order o gauge he size and power of he iming ess. We find ha sandard ess applied o daily daa are subsanially more powerful han monhly ess. This provides moivaion for he nex secion, in which we esimae he iming abiliy of acual muual funds using daily daa. We examine he size of he ess by simulaing fund reurns under he null hypohesis of no iming abiliy. Firs, we esimae parameers of a four-facor model of sock reurns applied o he daily se of acual muual fund reurns using OLS and save he residuals. The four-facor model is similar o he iming models described in secion I excep wihou he iming erms: r 4 = α + β r + ε p, p p, i i, p, i= 1. (11) Second, we generae 1,000 ses of simulaed reurns by randomly drawing residuals wih replacemen on each dae and adding o he fied reurns from he esimaed non-iming 10

12 models. We generae simulaed monhly daa by compounding he simulaed daily daa. Third, we esimae parameers of he wo iming models on he simulaed daily and monhly daa and assess individual fund iming significance a he 5% level using sandard OLS -saisics. The resampling procedure ensures ha residuals from his las sep are free of serial correlaion and heeroskedasiciy, and ha he simulaed reurns do no reflec iming sraegies. Panel A of able II shows he resuls of he size ess. The able liss he fracion of simulaions ha resul in posiive and negaive iming coefficiens, and he fracion ha resul in significan posiive and significan negaive iming coefficiens. The size of he daily ess appears correc for boh models, wih half of he coefficiens posiive and 5% significan. The significan coefficiens are equally spli beween posiive and negaive. The monhly ess appear somewha biased, however, wih beween 56.2% and 59.0% posiive, and wih abou wice as many posiive significan coefficiens as negaive significan coefficiens. We examine he power of he ess by simulaing fund reurns under he alernaive hypohesis of iming abiliy. We examine alernaives in which iming decisions are made each day, every wo days, once a week, every wo weeks, and once a monh; and for wo alernaive ypes of iming one ha mimics a TM sraegy, and one ha mimics an HM sraegy. GII conduc similar power ess o show ha he HM es suffers from low power when a manager imes he marke daily, bu reurns are recorded monhly. They consruc a monhly facor from daily index reurns, as in equaion (9), which proxies for he reurns from daily iming aciviy and improves he power of he 11

13 sandard HM es. Our goal is somewha differen; we inend o show ha increasing he frequency wih which reurns are recorded can increase power. To simulae he TM iming sraegy, for each simulaed fund, we se fund marke bea from day unil day + T o be β = β γ, (12) p, : + T p + r m, : + T where r m : + T, is he mean daily excess marke reurn from day unil day + T, and : + T represens he manager s iming inerval (one day, wo days, one week, wo weeks, or one monh). β p is he fund s bea from he non-iming model of equaion (11). Subsiuing he bea in equaion (12) ino he non-iming model and adding a randomly sampled residual (from he non-iming model regression) gives he simulaed fund reurn. We run he simulaions for γ = 5, 7.5, 10, 15, and 20. These values resul in mild o aggressive rading behavior. Consider, for example, a monhly iming inerval. A large monhly reurn for he marke is on he order of 5%. The lowes level of γ we consider, 5, corresponds in his case o an increase in fund β of.25; he highes level of γ we consider, 20, corresponds o an increase in fund β of 1.0. In he HM iming simulaions, we ake he marke bea of a perfec imer o be { r 0} β. β p, : + T = I m, : + T > p (13) Subsiuing he bea from equaion (13) ino he non-iming model and adding a randomly sampled residual (from he non-iming model regression) gives he simulaed fund reurn. We also run simulaions for imperfec iming abiliy by choosing bea according o equaion (13) for a fracion, 0.6 < p < 0.9, of he iming decisions. For he remaining 1 - p of he iming decisions, we chose bea incorrecly, 12

14 β { r 0} β. p, : T = I m, : + T p + (14) We run he alernaive iming models (TM, HM, and GII; all four-facor) on he simulaed daily daa and monhly daa and assess individual fund iming significance a he 5% level using sandard -saisics. Panels B and C of able II show he resuls of our power ess. Panel B shows he resuls for daa generaed under he TM alernaive. The ess resul in a posiive iming coefficien in mos cases, bu he daily ess resul in significan posiive iming coefficiens much more ofen han he monhly ess for all bu he mos exreme marke imer. For example, wih a iming coefficien of γ = 5, he daily ess generae significan posiive coefficiens abou 92% of he ime using he TM model and abou 83% of he ime using he HM model. The monhly ess resul in a significan posiive coefficien in only 34% of he simulaions using he TM model, and for only 25% of he simulaions using he HM model. The addiional facor suggesed by GII, which is designed o improve he HM es, increases he frequency of significan coefficiens, bu only o abou 33% of he ime. As he magniude of he iming abiliy increases, he monhly ess improve. Panel C shows he resuls for daa generaed under he HM alernaive. A similar paern emerges: he daily ess resul in significan iming coefficiens much more ofen han he monhly ess. Figure 1 displays hese power resuls graphically for several frequencies of iming aciviy. When we generae daa under he TM specificaion, he daily daa do no provide an advanage over he monhly daa when marke iming occurs daily or every wo days. However, as he iming frequency decreases, he relaive power of he daily ess increases, likely he resul of higher precision from an increased number 13

15 of observaions. When we generae daa under he HM specificaion, he correcly specified daily es dominaes he monhly ess a all iming frequencies. The GII es ouperforms he incorrecly specified TM daily es a high frequency iming, bu he TM daily es ouperforms he GII es when iming occurs weekly or less. In summary, he power ess show ha daily ess rejec he null of no iming abiliy more ofen han monhly ess if significan abiliy exiss. We urn nex o an analysis of he muual fund sample o measure acual iming abiliy. IV. Empirical Analysis A. Boosrap sandard errors Assessing he significance of iming regression coefficiens is complicaed by he possibiliy of misspecificaion of he iming funcion or of iming sraegies ha change over ime. For example, if a fund manager imes he marke according o he TM model, bu we measure iming abiliy using he HM specificaion, we will likely induce emporary serial correlaion in he residuals while he sraegy is being execued. Furhermore, here is evidence ha fund managers execue iming sraegies dynamically. For example, Brown, Harlow, and Sarks (1996) sugges ha fund managers may change invesing sraegies over he calendar year depending on year-o-dae performance in an effor o game compensaion schemes. Also, Busse (1999) provides evidence ha fund managers ime exposure o he marke o coincide wih low levels of marke volailiy. Misspecifying he iming funcion may cause violaions of regression assumpions in unknown and possibly ime-varying ways, so ha sandard correcions for 14

16 heeroskedasiciy and serial correlaion may no fully capure he effec of hese violaions on he sandard errors of regression coefficiens. To overcome his saisical problem, we consruc boosrap sandard errors for he iming coefficiens following he procedure described by Freedman and Peers (1984). There are hree seps in his procedure. Firs, for each fund, we esimae parameers of he TM and HM iming models using daily and monhly daa over he sample period. We arrange he residuals from he regressions ino a marix of N rows and 230 columns, where he rows represen he ime series of observaions wih N = 2780 for he daily daa and N = 132 for he monhly daa, and he 230 columns represen he funds in he sample. Second, we generae simulaed fund reurns as follows. For each dae, where = 1,..., N, we randomly choose wih replacemen one of he rows of residuals and add i o he h row of he marix of daily fied reurns from he original regressions. We repea he process 1,000 imes, resuling in 1,000 ses of random daa of lengh N. The hird sep is o esimae parameers of he iming models on each se of simulaed daa. For each fund, hen, we have 1,000 iming coefficiens for boh iming models and boh observaion frequencies. The sandard error of a fund s disribuion of iming coefficiens is he boosrap sandard error of he original iming coefficien, which we use o compue empirical -saisics of he form p, original =. (15) σ γ ( γ ) p, boosrap We assess significance a he 5% level and so compare he empirical -saisic o ±1.96, he criical value under he assumpion of normaliy. 5 15

17 B. Empirical Resuls Table III liss he fracion of funds ha have posiive and negaive iming coefficiens and he number of funds ha have significan posiive and negaive iming coefficiens. Displayed are he resuls from daily and monhly daa. Panel A shows he resuls for he muual fund sample. In all cases, he fracion of funds wih significan iming abiliy is higher when daily daa are used insead of monhly. For he TM model, for example, 42.8% of he funds generae significan posiive coefficiens and 26.2% produce significan negaive coefficiens using daily daa. The corresponding frequencies using monhly reurns are 33.7% and 7.7%. The HM model gives similar resuls. The daily daa s higher rejecion rae is consisen wih our power analysis and suggess ha here is a wide dispersion of abiliy over he sample of funds. A conservaive inerpreaion of he resuls requires he consideraion of wo poenial sources of spurious iming coefficiens. One possible source of spurious iming abiliy is he cash-flow hypohesis described in Warher (1995) and Ferson and Warher (1996). The hypohesis suggess we migh bias iming coefficiens downwards, even o negaive levels, because when marke reurns are high, invesors increase subscripions o muual funds, resuling in a emporarily larger cash posiion and a lower fund bea. Warher finds a srong relaion beween a fund s cash inflows and is porfolio weigh on cash. Ferson and Warher show direcly ha changes in condiional fund beas are negaively relaed o changes in fund cash flows. We do no have daily cash flow daa for our sample of funds, so we canno conrol for his possible effec, and leave his ask for fuure research. 16

18 Noe, hough, ha he cash-flow explanaion is asymmeric in he sense ha i can bias iming coefficiens downwards bu no upwards. For he HM specificaion, he iming coefficien is esimaed using reurns ha occur when he marke s excess reurn is posiive. If he cash posiion of he fund increases during hese imes, he iming coefficien will be biased downwards reflecing he decrease in bea. For he TM specificaion, he iming coefficien is esimaed in imes of boh marke rises, when subscripions o he fund likely increase, and marke declines, when we migh expec fund redempions o increase. In he former case, he iming coefficien will be biased downwards following he same argumen as in he HM specificaion. In he laer, we migh expec an increase in bea, since cash reserves become depleed, which serves o bias he iming coefficien downwards again. The reason for his is ha in he TM specificaion he iming coefficien weighs he squared marke reurn. In imes of negaive marke excess reurns we expec fund reurns o be lower han hey would be wihou he redempions, hence his forces he iming coefficien o be lower han i oherwise would. Since he cash flow explanaion posulaes ha iming coefficiens will be biased downwards, our resuls may underesimae he rue abiliy of fund managers in he sample. The oher possible source of spurious iming is provided by JK, who argue ha spurious iming abiliy can be generaed when porfolios hold socks wih payoffs ha are more or less opion-like han he marke proxy. In paricular, if he average sock in a muual fund is more opion-like ha he average sock in he marke proxy, a iming regression will resul in a posiive iming coefficien and a negaive inercep, which is usually inerpreed as measuring he sock-selecion abiliy of he fund manager. Recall 17

19 from able I ha he muual funds exhibi less negaive skewness han he marke proxy on average. We migh expec saes in which muual fund reurns and marke reurns are boh negaive, due o heir correlaion, and in which he marke reurn is more negaive han he muual fund reurns, due o is larger negaive skewness. These saes would generae a posiive iming coefficien even in he absence of marke iming aciviy. In panel A of able III, here does appear o be an inverse relaion beween he iming coefficiens and inerceps in he iming regressions as prediced by JK. In all cases he average inercep for he funds wih negaive iming coefficiens is much higher han he corresponding average for funds wih posiive iming coefficiens. Kon (1983) and Henriksson (1984) also documen a negaive correlaion beween regression inerceps and iming coefficiens. Boh find ha mos muual funds in heir respecive samples exhibi posiive inerceps and negaive iming coefficiens, he reverse of wha we find, perhaps due o differences in our sample periods. To es he relaion more formally, we regress inerceps on iming coefficiens cross-secionally for each iming model. Table IV liss he resuls. In all cases, he regression parameers are significan and he slopes are negaive, indicaing ha sock selecion and marke iming are significanly negaively relaed. Furhermore, for he daily daa, he regression R 2 s are.327 and.833, suggesing ha he wo measures are quie closely relaed. This resul suggess ha some of he posiive iming coefficiens in our sample could be spurious. In an effor o conrol for he JK source of spurious iming abiliy, we run he iming ess on a sample of synheic funds ha mach he acual funds characerisics bu have no iming abiliy by consrucion, as described in secion II. If he synheic funds 18

20 generae iming abiliy a he same frequency and magniude as he acual funds, hen he esimaed iming coefficiens are likely spurious raher han evidence of abiliy. Panel B of able III shows he resuls of our iming ess when applied o he synheic funds. Using boh monhly and daily daa, he synheic funds generae more significan iming coefficiens han expeced under he null of no iming aciviy. For he TM model, for example, 31.1% of he synheic funds generae a posiive significan iming coefficien and 13.6% produce a negaive significan coefficien using daily daa. This suggess ha some of he iming evidence for he acual funds is spurious, likely he resul of he JK phenomenon. However, noe ha in all cases he acual funds rejec he null more frequenly han he synheic funds. Furhermore, he magniude of he average posiive significan iming coefficiens using he acual fund reurns is roughly hree imes larger han he average using he synheic fund reurns. For he HM model, for example, he average posiive significan iming coefficien is.124 for he acual funds and.043 for he synheic funds. This indicaes ha alhough he synheic funds exhibi significan iming coefficiens, heir magniude is likely insufficien o fully explain he iming coefficiens of he acual funds. Table V invesigaes he relaion beween he iming abiliy of acual funds and heir synheic counerpars more sysemaically. For each fund, we measure he difference beween he iming coefficiens of he fund and is corresponding synheic conrol fund. We hen compue he fracion of funds for which his difference is posiive. Using monhly reurns, slighly less han half he funds have higher iming coefficiens han he synheic funds. Using daily reurns, slighly more han half he funds have higher iming coefficiens han he synheic funds. More imporan, hough, are he cases 19

21 where he differences are significan. We assess significance by consrucing a sandard error for he difference from he boosrap sandard errors of he iming coefficiens as follows: 2 2 ( difference ) σ ( γ ) σ ( γ ). σ = + (16) acual synheic Using monhly reurns and he TM model, 11.9% of he funds have iming coefficiens ha are significanly higher han heir synheic counerpars, bu 10.4% of he funds iming coefficiens are significanly smaller han he synheic funds. Using daily daa and he TM model, however, 37.7% of he funds have iming coefficiens ha are significanly higher han he synheic ones, and 27.6% of he funds have coefficiens ha are significanly smaller. The resuls are similar for he HM model. The cash-flow hypohesis can explain he significan negaive differences. To he exen ha he synheic funds conrol for spurious rejecions of he null, he significan posiive differences sugges ha a subsanial percenage of he funds have rue iming abiliy. We compue for boh iming models he Wilcoxon signed rank es (no repored) o es he hypohesis ha he disribuion of he acual funds iming coefficiens equals he disribuion of he synheic funds iming coefficiens. Using monhly daa, he Wilcoxon signed rank es fails o rejec he null hypohesis. Using daily daa, however, he Wilcoxon signed rank es does rejec he null hypohesis. This resul provides addiional evidence ha daily daa does maer when measuring iming abiliy. V. Conclusions In his paper we examine wheher he use of daily daa raher han monhly changes inference regarding he abiliy of muual fund managers o ime he marke porfolio. 20

22 Using simulaions, we documen ha sandard regression-based ess have more power o deec significan iming aciviy when daily daa are used. Nex we esimae iming coefficiens for a sample of 230 muual funds and find ha daily reurns increase he number of significan esimaes of iming abiliy. To es wheher he iming coefficiens are spurious, we consruc a se of synheic funds ha mach he characerisics of he acual funds bu have no iming abiliy by consrucion. Alhough he synheic funds also rejec he null of no iming aciviy more ofen han expeced, approximaely one-hird of he funds have daily iming coefficiens ha are significanly greaer han heir synheic counerpars. This indicaes ha he measured iming abiliy canno be explained as a spurious saisical phenomenon. In addiion, while we find no significan difference beween he disribuion of he acual funds monhly iming coefficiens and he disribuion of he synheic ones, we rejec he hypohesis ha he disribuions are equal using daily daa. Observaion frequency maers when judging fund performance. This resul suggess ha fuure research in muual fund performance and relaed opics, especially hose relaed o fund risk, may generae more precise esimaes and sharper inference if daily daa are used raher han daa colleced a a lower frequency. 21

23 Appendix A. Index Consrucion We consruc he SMB and HML indices following he procedure used by Fama and French (1993), excep wih daily reurns insead of monhly. We sor all firms lised on boh CRSP and Compusa and classified as having ordinary common shares (on CRSP) according o marke capializaion a he end of June each year beginning in June of As in Fama and French (1993), o miigae he problems associaed wih Compusa s pracice of back filling daa, firms mus exis on Compusa for wo years before we use hem. We ake marke capializaion o be he number of shares as of he end of June (per CRSP) muliplied by he end of June CRSP share price. We also sor hese same firms according o heir end of calendar year booko-marke raio, where we ake book value as he Compusa book value of shareholders equiy plus balance shee deferred axes and invesmen ax credi minus he book value of preferred sock. We ake he book value of preferred sock o be he redempion, liquidaion, or par value (in ha order) on Compusa. We use NYSE breakpoins o divide firms ino wo groups, big (B) and small (S), where he big group includes all firms (NYSE, Amex, and Nasdaq) greaer han or equal o he median marke capializaion of NYSE firms. We also use NYSE breakpoins o divide all firms ino hree groups, high book-o-marke (H), middle book-o-marke (M), and low book-o-marke (L), depending on each firm s book-o-marke relaive o he 70h and 30h perceniles of NYSE firms. Combining he wo marke capializaion groups wih he hree book-o-marke groups resuls in six groups of firms: one ha includes big firms wih high book-omarke raios, one wih big firms and medium book-o-marke raios, one wih big firms 22

24 and low book-o-marke raios, and an analogous se of hree groups of small capializaion firms. We compue a reurn index for each of he six groups by weighing he reurns by marke capializaion. We form he SMB index by aking he difference beween an equal weighed combinaion of he hree small marke capializaion indices and he hree big marke capializaion indices. We form he HML index by aking he difference beween an equal weighed combinaion of he wo high book-o-marke indices and he wo low book-omarke indices. We consruc he momenum index similar o ha of Carhar (1997), excep value weighed and a a daily frequency. For each monh, we rank all firms on CRSP (NYSE, Amex, and Nasdaq) classified as having ordinary common shares wih reurns for a monh -12 o -2 evaluaion period by oal reurn from -12 o -2. We ake he momenum index for monh as he difference beween he value weighed monh reurn index of he 30% of firms wih he highes reurns during he evaluaion period and he value weighed index of he 30% of firms wih he lowes reurns during he evaluaion period. We reallocae firms o he 30% highes reurns and 30% lowes reurns groupings monhly. 23

25 References Brown, S., W. Goezmann, R. Ibboson, and S. Ross, 1992, Survivorship bias in performance sudies, Review of Financial Sudies 4, Brown, S. and W. Goezmann, 1995, Performance persisence, Journal of Finance 50, Brown, K., W. Harlow and L. Sarks, 1996, Of ournamens and empaions: An analysis of managerial incenives in he muual fund indusry, Journal of Finance 51, Busse, J., 1999, Volailiy iming in muual funds: Evidence from daily reurns, Review of Financial Sudies 12, Carhar, M., 1997, On persisence in muual fund performance, Journal of Finance 52, Chen, Z. and P. Knez, 1996, Porfolio performance measuremen: Theory and applicaions, Review of Financial Sudies 9, Dahlquis, M. and P. Soderlind, 1999, Evaluaing porfolio performance wih sochasic discoun facors, Journal of Business 72, Daniel, K., M. Grinbla, S. Timan, and R. Wermers, 1997, Measuring muual fund performance wih characerisic-based benchmarks, Journal of Finance 52, Fama, E., 1965, The behavior of sock marke prices, Journal of Business 38, Fama, E. and K. French, 1993, Common risk facors in he reurns on socks and bonds, Journal of Financial Economics 33, Farnsworh, H., W. Ferson, D. Jackson, and S. Todd, 1999, Performance evaluaion wih sochasic discoun facors, working paper, Universiy of Washingon. Ferson, W. and V. Warher, 1996, Evaluaing fund performance in a dynamic marke, Financial Analyss Journal 52, Freedman, D. and S. Peers, 1984, Boosrapping an economeric model: Some empirical resuls, Journal of Business and Economic Saisics 2, Fung, W. and D. Hsieh, 1997, Empirical characerisics of dynamic rading sraegies: The case of hedge funds, Review of Financial Sudies 10,

26 Goezmann, W., J. Ingersoll and Z. Ivkovic, 1998, Monhly measuremen of daily imers, working paper, Yale School of Managemen. Graham, J. and C. Harvey, 1996, Marke iming abiliy and volailiy implied in invesmen newsleers asse allocaion recommendaions, Journal of Financial Economics 42, Grinbla, M. and S. Timan, 1994, A sudy of monhly muual fund reurns and performance evaluaion echniques, Journal of Financial and Quaniaive Analysis 29, Henriksson, R., 1984, Marke iming and muual fund performance: An empirical invesigaion, Journal of Business 57, Henriksson, R. and R. Meron, 1981, On marke iming and invesmen performance. II. Saisical procedures for evaluaing forecasing skills, Journal of Business 54, Invesmen Company Insiue, 1999, Muual Fund Fac Book, Invesmen Company Insiue, Washingon D.C. Jagannahan, R. and R. Korajczyk, 1986, Assessing he marke iming performance of managed porfolios, Journal of Business 59, Jarque, C. and A. Bera, 1980, Efficien ess for normaliy, heeroskedasiciy, and serial independence of regression residuals, Economics Leers 6, Kon, S., 1983, The marke-iming performance of muual fund managers, Journal of Business 56, Mandelbro, B., 1963, The variaion of cerain speculaive prices, Journal of Business 36, Scholes, M. and J. Williams, 1977, Esimaing beas from nonsynchronous daa, Journal of Financial Economics 5, Sharpe, W., 1964, Capial asse prices: A heory of marke equilibrium under condiions of risk, Journal of Finance 19, Treynor, J. and K. Mazuy, 1966, Can muual funds ouguess he marke? Harvard Business Review 44, Warher, V., 1995, Aggregae muual fund flows and securiy reurns, Journal of Financial Economics 39,

27 Table I. Summary Saisics Lised are average summary saisics of he 230 muual funds in our sample and wo marke indexes. The sample period is January 1, 1985 o December 29, 1995, a oal of 2,780 rading days or 132 rading monhs. The mean (µ) and sandard deviaion (σ) are sample esimaes. Skewness (S) is compued as: and excess kurosis (K) is compued as: 1 3 S = σ T T ( R ) µ = 1 1 K = 4 R µ σ T T = ( ) 3 The Jarque-Bera (JB) es for normaliy is disribued χ 2 2 under he null and is given by: 2 T 2 K JB = S Panel A. Daily Saisics µ σ S K JB Tes Muual Funds Daily 0.056% 0.898% , Monhly 1.223% 4.756% Marke Proxy Daily 0.060% 0.846% , Monhly 1.289% 4.202% Panel B. Annual Saisics Year # Funds µ σ % 9.6% % 12.7% % 27.4% % 13.2% % 11.0% % 14.7% % 14.0% % 11.1% % 10.1% % 10.7% % 9.7% 26

28 Table II. Size and Power Analysis Panel A summarizes iming coefficiens when fund reurns are generaed wihou iming abiliy and abiliy is measured using he four-facor Treynor-Mazuy (TM), Henriksson-Meron (HM), and Goezmann- Ingersoll-Ivkovic (GII) iming models. Lised for each model is he fracion of simulaed funds wih posiive (significan posiive) iming coefficiens. Each resul is based on 1,000 simulaions. Significance is 4 p, = p p, i i, p m, p, i= 1 a he 5% level (wo-ailed). The iming models are all of he form: r α + β r + γ f ( r ) + ε, where r is excess reurn, f ( r m, ) = rm 2, for TM, f ( r m, ) I { r m, > 0} r m, = for HM, and f is he value of a monhly iming facor consruced from daily index reurns for GII. The GII facor is compued N as: Pm, = max { 1 Rm,,1 R f, } 1 Rm,, + τ + τ where here are N days in he monh and R is reurn. τ = 1 Panel B shows he resuls under he TM alernaive for differen values of γ, and panel C shows he resuls under he HM alernaive where p indicaes he percenage of observaions for which he iming decision is made correcly. Panel A. Size Daily Monhly Posiive Negaive Posiive Negaive TM (0.023) (0.025) (0.045) (0.017) HM (0.024) (0.025) (0.038) (0.019) GII (0.050) (0.021) Daily, γ Panel B. Treynor-Mazuy Monhly, γ TM (0.915) (0.947) (0.955) (0.961) (0.966) (0.340) HM (0.831) (0.936) (0.964) (0.983) (0.988) (0.250) GII (0.333) Panel C. Henriksson-Meron (0.605) (0.445) (0.572) (0.794) (0.626) (0.758) (0.923) (0.863) (0.921) (0.971) (0.934) (0.967) Daily, p Monhly, p TM (0.596) (0.652) (0.769) (0.879) (0.978) (0.388) HM (0.608) (0.740) (0.900) (0.991) (1.000) (0.303) GII (0.375) (0.455) (0.444) (0.534) (0.608) (0.651) (0.757) (0.811) (0.858) (0.916) (0.964) (0.970) (0.991) 27

29 Table III. Boosrap Analysis of Marke Timing Coefficiens Lised are he fracion, mean iming coefficien, and mean inercep of muual funds ha exhibi posiive/negaive (+/-) and significan posiive/significan negaive (++/--) marke iming abiliies. Abiliy is measured using he four-facor Treynor-Mazuy (TM) and Henriksson-Meron (HM) iming models. The 4 p, = p p, i i, p m, p, i= 1 iming models are of he form: r α + β r + γ f ( r ) + ε, f ( r m, ) = rm 2, for TM, and f ( r m, ) I { r m, > 0} r m, where r is excess reurn, = for HM. Significance is a he 5% level (wo-ailed) and is based on boosrap sandard errors. Panel A shows he resuls from he muual fund sample, and panel B shows he resuls from he synheic conrol sample. Panel A. Muual Fund Sample Monhly Daily Monhly Daily Fracion TM HM Timing Coefficien TM HM Inercep TM HM Panel B. Synheic Conrol Sample Monhly Daily Monhly Daily Fracion TM HM Timing Coefficien TM HM Inercep TM HM

30 Table IV. Relaion beween Inerceps and Timing Coefficiens in Timing Models Lised are resuls from cross-secional OLS regressions of he inerceps of individual fund iming regressions on he corresponding iming coefficiens. The individual fund iming regressions are he fourfacor Treynor-Mazuy (TM) and Henriksson-Meron (HM) iming models. The iming models are of he 4 p, = p p, i i, p m, p, i= 1 f ( r m, ) = I { r m, > 0} r m, for HM. form: r α + β r + γ f ( r ) + ε, where r is excess reurn, ( r m, ) rm 2, f = for TM, and α p-value β p-value R 2 Monhly TM HM Daily TM HM

31 Table V. Comparison of Acual and Synheic Funds Lised are he fracion of muual funds in which he difference beween he iming coefficien of he acual fund and he synheic fund is posiive/negaive (+/-) and significan posiive/significan negaive (++/--). Abiliy is measured using he four-facor Treynor-Mazuy (TM) and Henriksson-Meron (HM) iming 4 p, = p p, i i, p m, p, i= 1 models. The iming models are of he form: r α + β r + γ f ( r ) + ε, reurn, f ( r m, ) = rm 2, for TM, and f ( r m, ) I { r m, > 0} r m, where r is excess = for HM. Significance is a he 5% level (woailed) and is based on boosrap sandard errors. The sandard error of he difference equals he square roo of he sum of he squared boosrap sandard errors of he acual fund and is synheic counerpar. Monhly Daily Monhly Daily TM HM

32 Figure 1. Power Analysis The figure shows he resuls from running four-facor Treynor-Mazuy (TM), Henriksson-Meron (HM), and Goezmann-Ingersoll-Ivkovic (GII) iming models on boosrap fund reurns under he alernaive 4 p, = p p, i i, p m, p, i= 1 hypohesis of iming abiliy. The iming models are all of he form: r α + β r + γ f ( r ) + ε, where r is excess reurn, f ( r m, ) = rm 2, for TM, f ( r m, ) I { r m, > 0} r m, = for HM, and f is he value of a monhly iming facor consruced from daily index reurns for GII. The GII facor is compued N as: Pm, = max { 1 Rm,,1 R f, } 1 Rm,, + τ + τ where here are N days in he monh and R is reurn. The τ = 1 figure show he fracion of boosrap funds wih significan posiive iming coefficiens for funds ha ime he marke a one day, wo day, one week, wo week, and one monh frequencies. The TM alernaive uses γ=10, and he HM alernaive uses a skill level of p=0.7. Each resul is based on 1,000 boosraps. Significance is a he 5% level (wo-ailed). 31

33 Figure 1. Power Analysis (coninued) Treynor-Mazuy Fracion Significanly Posiive TM-daily TM-monhly HM-daily HM-monhly GII 0 One Day Two Days One Week Two Weeks One Monh Timing Frequency Henriksson-Meron Fracion Significanly Posiive TM-daily TM-monhly HM-daily HM-monhly GII One Day Two Days One Week Two Weeks One Monh Timing Frequency 32

34 Foonoes 1 According o he Wall Sree Journal (pg. C1 on 3/16/99) 91% of acively managed sock funds generaed lower reurns han he S&P 500 index over he en years ending in December 1998, and 84% railed he Wilshire 5000 over he same period. 2 As poined ou by he referee, sandard ess of sock selecion, which use he inercep of facor regressions o measure sock-picking abiliy, are heoreically robus o observaion frequency since he esimae is more a funcion of sample lengh raher han observaion frequency. 3 A muual fund manager s abiliy o shif a fund s allocaion is consrained o varying degrees by he invesmen objecives of he fund, as esablished in he fund s Saemen of Addiional Informaion. A manager consrained o holding equiies migh hen ime he marke by adjusing he correlaion beween a porfolio s reurn and he marke reurn as he marke rises and falls. In addiion, marke iming aciviy may be hindered by resricions on he use of leverage and derivaives placed on muual funds by he Securiies and Exchange Commission s Invesmen Company Ac of Hedge fund managers are no consrained by hese sors of limis, hence we may expec more evidence of marke iming and oher dynamic sraegies among hedge fund managers han muual fund managers, as indicaed by he resuls of Fung and Hsieh (1997). 4 Anoher approach o address he issue of benchmark efficiency is o use sochasic discoun facors, as in Chen and Knez (1996), Dahlquis and Soderlind (1999), and Farnsworh, Ferson, Jackson and Todd (1999). 5 We also assess significance by soring he boosrap disribuion of iming coefficiens by size, and comparing he magniude of he acual iming coefficien o he 25h and 975h boosrap iming coefficiens. This avoids he disribuional assumpion. The resuls are almos idenical. 33