IS STOCK PICKING DECLINING AROUND THE WORLD? *

Transcription

1 IS STOCK PICKING DECLINING AROUND THE WORLD? * Upal Bhaacharya Kelley School of Business Indiana Universiy ubhaac@indiana.edu Neal Galpin Kelley School of Business Indiana Universiy ngalpin@indiana.edu November 15, 2005 Key words: modern porfolio heory; indexing; sock picking JEL number: G11, G14, G15 * We are graeful for suggesions from Craig Holden, Chris Lundblad, and seminar paricipans a Indiana Universiy.

2 IS STOCK PICKING DECLINING AROUND THE WORLD? Absrac We do hree hings in his paper. We firs develop a meric o measure he maximum fracion of volume explained by sock picking in a marke. We hen use our meric o measure sock picking around he world. We find ha hough here is more sock picking in emerging markes han in developed counries, i is declining everywhere. In he Unied Saes, for example, sock picking has secularly declined from a high of 60% in he 1960s o a low of 24% in he 2000s. Finally, as markes canno be efficien if everyone believes ha hey are efficien and, herefore, do no sock picking he Grossman and Sigliz (1980) paradox we ask wha is he long-run seady sae fracion of sock pickers? We develop a simple heoreical model, and calibrae his model o he Unied Saes economy o conclude ha sock picking will evenually sele a 11% of rading volume in he Unied Saes.

3 IS STOCK PICKING DECLINING AROUND THE WORLD? I. INTRODUCTION A small gamble in a large number of differen companies where I have no informaion o reach a good judgmen, as compared wih a subsanial sake in a company where one's informaion is adequae, srikes me as a ravesy of invesmen policy John Maynard Keynes, John Maynard Keynes was a good sock picker. From 1928 o 1945, he fund he managed for King s College, Cambridge, produced posiive reurns a a ime when he U.K. sock marke was declining by 0.5% per year. 1 The inellecual foundaions of sock picking were laid ou in he classic ex on valuaion by Graham and Dodd (1934), who showed us how o figure ou wheher a sock was a buy. Many of oday s famous invesors like Warren Buffe have been influenced by heir heories. Indexing, which is he pracice of passively invesing in a porfolio conaining a large number of socks, is he philosophical opposie of sock picking. Insead of picking winners and losers, indexing emphasizes diversificaion. The inellecual foundaions of indexing are in Markowiz s (1952) paper on modern porfolio heory and Tobin s (1958) paper on wo-fund separaion. 2 Indexing also has is fans in he invesmen world, of which perhaps he mos influenial is he Vanguard group of muual funds. Ironically, he index funds ha Vanguard popularized as an asse class now face serious compeiion from Exchange Traded Funds ha exchanges have inroduced o cash in on he populariy of passive indexing. 3 The purpose of his paper is o find ou which invesmen philosophy, sock picking or indexing, is dominan in he sock markes around he world. This is an imporan research quesion because, hough here is much anecdoal evidence ha he ideas in Markowiz (1952), a paper which led o he birh of modern financial economics (Rubinsein (2002)), have permeaed invesmen pracice, here has been, o he bes of our 1 This daa and he quoe above come from Wikipedia, an online user-conribued encyclopedia (hp:// 2 The pracice of diversificaion exised before Markowiz (1952). See Goezmann and Ukhov (2005) for an empirical sudy of Briish overseas invesmens in Wall Sree Journal, November 5-6,

4 knowledge, no paper formally measuring his permeaion. 4 Our paper makes a modes firs aemp o formally measure how he invesmen communiy has acceped one of he ideas of modern porfolio heory indexing. The prevalence of indexing can only be measured if here exiss a measure for indexing. No such measure exiss in he lieraure. So he firs par of our paper develops a meric for he opposie of indexing sock picking. The idea behind his measure is inspired by a heoreical insigh in Lo and Wang (2000). They proved ha, if he wo-fund separaion heorem holds, dollar urnover of a sock, which is defined as he dollar volume of shares raded divided by he dollar marke capializaion of he sock, should be idenical for all socks. An empirical implicaion of he above heoreical insigh is ha if every person in he world indexes beween a risk-free porfolio and he marke porfolio (or a value-weighed porfolio ha is a proxy for he marke porfolio), rading volume in sock i should be explained compleely by he marke capializaion of sock i. This would mean ha (1-R 2 ) of he cross-secional regression of he log of volume agains he log of marke capializaion would reflec he deviaion from he indexing invesmen philosophy. This deviaion will occur because some agens pick individual socks. This deviaion will also occur if some agens index o porfolios oher han he value-weighed porfolio. This means ha he (1-R 2 ) of he above cross-secional regression beween log dollar volume and log dollar marke capializaion will be a measure of he maximum proporion of rade ha can be explained by sock picking. We run hese cross-secional regressions every monh, for every counry for which we have daa, for as long as we have he daa. We plo he (1-R 2 ) over ime for 43 counries. We ge wo big resuls, and many small resuls. Our firs big resul is ha, on an average, here is more sock picking in emerging markes han in developed markes. As a maer of fac, he maximum fracion of volume explained by sock picking in emerging markes in he period is 63%, whereas he maximum fracion of volume explained by sock picking in developed counries in he same period is only 45%. In our sample of 43 counries, he maximum fracion of 4 Rubinsein (2002), in his rerospecive of Markowiz s (1952) paper, saes ha Markowiz s approach is now commonplace among insiuional porfolio managers who use i boh o srucure heir porfolios and measure heir performance. I has been generalized and refined in innumerable ways, and is even being used o manage he porfolios of ordinary invesors. The websie of Yahoo Finance (hp://biz.yahoo.com/edu/bi/ir_bi5.ir.hml), a popular sie for individual invesors, saes: You can divide he hisory of invesing in he Unied Saes ino wo periods: before and afer Tha was he year ha an economics suden a he Universiy of Chicago named Harry Markowiz published his docoral hesis

5 volume explained by sock picking in he period is he leas in he Unied Saes (29%) and is he mos in China (80%). Our second big resul is ha, on an average, sock picking is declining around he world. Of he 43 counries under invesigaion, we record ha for 38 counries, he maximum fracion of volume explained by sock picking is lower in he las five years ( ) han in he previous five years ( ). The declines in sock picking are quie dramaic, especially in he emerging markes. The mos dramaic decline in he populariy of sock picking is recorded in he Unied Saes, bu ha is probably because we have a longer imeseries daa for he Unied Saes. In he Unied Saes, he maximum fracion of volume explained by sock picking has secularly declined from a high of 60% in he 1960s o a low of 24% in he 2000s. As we have a lo more daa on he Unied Saes, we are able o ge many small cross-secional resuls for he Unied Saes. We find ha hough sock picking is less in S&P 500 socks han in non S&P socks, he difference seems o have disappeared in recen imes. This fac shows ha he hough he acual mechanics of indexing in S&P 500 socks is easier, he mechanics do no maer much anymore because indexing seems o be popular even in socks no in he S&P 500 index. In erms of exchanges, here is more sock picking in AMEX han in NYSE. Nasdaq sars ou looking like he AMEX, bu i looks like he NYSE oday. In erms of size, here is more sock picking in small socks han in large socks. In erms of age, here is more sock picking in young firms han in old firms. In erms of indusries, sock picking is highes in he elecommunicaion indusries, and lowes in he uiliies indusries. Our las cross-secional resul is ha here is more sock picking in socks ha are covered by fewer analyss han in socks ha are covered by more analyss. As analyss are he quinessenial sock pickers, i seems ha invesors who pick socks avoid socks ha analyss pick. Finally, whaever he above cross-secional resuls, we record ha sock picking is declining over ime in each and every caegory. Our summary of findings from he firs wo pars of he paper is ha sock picking is more pronounced in emerging markes han in developed markes, bu i is declining in nearly all sock markes of he world. Though our paper is he firs o formally documen he declining populariy of sock picking around he world, indicaions ha his may be happening are in a paper by Fernando e al (2003), who documen he explosive growh of muual - 3 -

6 funds around he world. Also, hough our paper is he firs paper o formally documen he large cross-secional variaion in he populariy of sock picking across counries, indicaions ha his may occur are in a paper by Khorana, Servaes and Tufano (2004), who documen ha he muual fund indusry is larger in counries wih beer laws and regulaions and more wealh. Ineresingly, hese are he counries wih he lowes sock picking in our sample. The above wo argumens implicily assume ha muual funds emphasize diversificaion over sock picking. Tha may be a reasonable assumpion, bu as Wermers (2000) shows, sock picking is alive and well in some Unied Saes muual funds. Furher, he explosive growh of hedge funds in recen years, also means ha sock picking may be making a comeback. Our resuls show ha modern porfolio heory has won. However, i is premaure o wrie he epiaph for sock picking. News of he deah of sock picking will be an exaggeraion. The reason no sock picking canno be an equilibrium sraegy is because of he Grossman-Sigliz (1980) paradox: if no one picks socks, informaion ha sock pickers communicae wih heir rades canno be impounded in prices, and so markes become inefficien, and so develops an opporuniy o gaher informaion, pick socks, and make rading profis. This begs he quesion: how many sock pickers will exis in equilibrium? In oher words, wha is he long-run seady sae fracion of sock pickers? We develop a simple heoreical model. Our heoreical model is based on a crucial insigh ha comes from an early heoreical model by Treynor and Black (1973): in a mean-variance opimizing framework, even acive sock pickers would like o maximize heir Sharpe raio, which is he raio of he risk premium of he porfolio hey choose divided by he sandard deviaion of he reurn of he porfolio (assumed o be he measure of risk). This implies ha if we resric an invesor o be eiher a passive invesor in he marke porfolio or an acive invesor in a single sock, his would mean ha his invesor would be indifferen if he Sharpe raios are he same. The Sharpe raio of he marke porfolio is simply he marke price of risk. The acive invesor, who we allow o hedge he sysemaic risk of he single sock by aking an opposie posiion in he marke porfolio, has he following Sharpe raio. I is his excess profi from his superior informaion divided by he cos of acive invesing. The voluminous lieraure on marke microsrucure, which begins wih Kyle (1985) and Glosen and Milgrom (1985), ells us ha he excess profi an insider obains from his inside informaion is his profi based on - 4 -

7 his superior informaion (Jensen s alpha) minus his adverse selecion cos and oher ransacion coss of rading. We should also subrac his cos of obaining he superior informaion from his number. Modern porfolio heory ells us ha he cos of acive invesing is he exposure o idiosyncraic risk. Equaing he wo Sharpe raios allows us o express he excess profi of he indifferen invesor as a produc of he marke price of risk and he idiosyncraic risk. Noe ha he excess profi ha makes an invesor indifferen beween sock picking and passive indexing is he produc of he marke price of risk and he idiosyncraic risk. We call his value he indifferen excess profi. This implies ha sock picking would become less popular if he marke price of risk is increasing and/or idiosyncraic risk is increasing. The inuiion is obvious. If he reward for holding marke risk is increasing, invesing in he marke porfolio is more aracive, and so sock picking is less popular. If idiosyncraic risk is increasing, he cos of non-diversificaion, which is wha sock picking enails, is increasing, and so sock picking is less popular. The marke price of risk is ime-varying. See Leau and Ludvigson (2003) for an excellen survey of his voluminous lieraure. There are many mehods o esimae he marke price of risk. We use he Whielaw (1994, 1997) mehodology as our primary mehod o esimae he marke price of risk, hough we repor our esimaes for he oher mehods as well. Idiosyncraic risk is also ime-varying. As a maer of fac, a growing lieraure has documened ha idiosyncraic risk has secularly increased over ime in he Unied Saes (see Campbell e al. (2001)) and all over he world (see Morck, Yeung and Yu (2000). We use he mehod of Morck, Yeung and Yu (2000) o back ou idiosyncraic risk for he Unied Saes. Our esimae of idiosyncraic risk allies wih heir esimae. I also allies wih he esimae of Campbell e al. (2001), who use a variance decomposiion mehod of esimaing idiosyncraic risk. Wha is imporan, however, is ha we ge he same resul: idiosyncraic risk is increasing in he Unied Saes. We hen esimae he indifferen excess profi every year, which makes an invesor indifferen beween sock picking and passive indexing, as a produc of he esimaed marke price of risk every year and he esimaed idiosyncraic risk every year. We find ha his indifferen excess profi is increasing over ime. If we assume ha every agen in he economy has a differen excess profi from sock picking, which depends on skill and/or - 5 -

8 luck, i is reasonable o assume ha his excess profi is drawn from a disribuion ha is sable over ime. The people who pick sock have a draw ha is higher han he indifferen excess profi. So, if he indifferen excess profi is increasing over ime, his would imply ha he proporion of sock pickers is declining. We, herefore, conclude ha sock picking is declining in he Unied Saes, because he oal cos of sock picking is increasing in he Unied Saes. This oal cos is increasing because he direc cos of sock picking idiosyncraic risk is increasing in he Unied Saes, hough he indirec opporuniy cos of sock picking he forgone marke reward for risk does no seem o have a rend. As oal risk is no changing (see Schwer (1989) and Campbell e al (2001)), idiosyncraic risk canno increase wihou bound. This suggess ha idiosyncraic risk may asympoe o a seady-sae. As he marke price of risk seems no o have a rend (see Leau and Ludvigson (2003)), he produc of idiosyncraic risk and he marke price of risk he indifferen excess profi curve -- may asympoe as well. Therefore, if we assume ha he disribuion of excess profis in he economy is sable, hen he proporion of invesors whose excess profi is above he indifferen excess profi curve he sock pickers will sabilize where he indifferen excess profi curve asympoes. This is he seady-sae proporion of sock pickers. For he Unied Saes, our model esimaes ha sock picking will evenually sele a 11% in he Unied Saes. The paper is organized as follows. We develop a meric for sock picking in secion II. Secion III describes our daa. Secion IV is he main resul of his paper. I documens ha here is more sock picking in emerging markes han in developed counries, bu i is declining everywhere. As we have more daa on he Unied Saes, secion V covers he Unied Saes in greaer deail, and repors resuls for differen caegorizaions of socks. Secion VI explores he seady sae proporion of sock pickers, and due o daa availabiliy, we resric ourselves o he Unied Saes Secion VII concludes. In his secion, we discuss exensions of our paper, of which he mos imporan exension is a deeper exploraion of why here is so much cross-secional variaion in sock picking

9 II. A METRIC FOR STOCK PICKING Lo and Wang (2000) proved ha, if he wo-fund separaion heorem holds, dollar urnover of a sock, which is defined as he dollar volume of shares raded divided by he marke capializaion of he sock, should be idenical for all socks. The inuiion behind heir resul was simple. If an agen jus invess in he risk-free asse and he marke porfolio, and if he marke porfolio has $85 million of sock A and $15 million of sock B, hen if he agens buys (sells) $100 of he marke porfolio, she buys (sells) $85 of sock A and $15 of sock B. If prices do no change beween rades, he share urnover of a sock, which is defined as volume of shares raded divided by he number of shares ousanding of he sock, should also be idenical for all socks if he wo-fund separaion heorem holds. We run he following cross-secional regression model every monh for every marke ln (volume of shares) i = a + b ln (number of shares ousanding) i +, i (1) where Volume of shares i is he monhly rading volume of sock i, Number of shares ousanding i is he number of shares ousanding a he end of he monh for sock i, and, i is he volume of shares of sock i ha canno be explained by he number of shares ousanding a he end of he monh for sock i. If every person in he world indexes beween a risk-free porfolio and he marke porfolio (or a valueweighed porfolio ha is a proxy for he marke porfolio) wih lile error, rading volume in sock i should be explained compleely by he marke capializaion of sock i. So we should obain he following esimaes in our above regression equaion: a = ln (urnover), b = 1, and R 2 = 1. If we do no obain 1 as our esimae for R 2 in he above regression, his would mean ha here is deviaion from he indexing invesmen philosophy. This deviaion will occur because some agens pick - 7 -

10 individual socks. This deviaion will also occur if some agens index o porfolios oher han he marke porfolio. As a maer of fac, for K facors, as Lo and Wang (2000) showed, indexing will occur in K funds. This means ha he (1-R 2 ) of he above cross-secional regression beween log volume and log number of shares ousanding will be a measure of he maximum proporion of rade ha can be explained by sock picking. So our meric for sock picking every monh in a marke is he (1-R 2 ) of a cross-secional regression of log volume of sock i agains he number of shares ousanding of sock i in ha marke. To be precise, he esimae of (1-R 2 ) gives us he maximum proporion of rade ha can be explained by sock picking ha monh in a marke. This (1-R 2 ) meric has he following advanages. Firs, i is simple o esimae. Second, he daa requiremen is minimal. Volume and shares ousanding daa are publicly available for nearly all sock markes of he world. Third, he definiion of a marke is flexible. Markes could be he various counry sock markes, which would allow us o compare sock picking across he world. Markes could be local markes wihin a counry, like NYSE, AMEX or Nasdaq, which would allow us o compare sock picking across hese local markes. Markes could be defined by differen ypes of sock caegorizaion like size, age of firm, indusry, ec., which would allow us o compare sock picking across differen sizes, differen ages, differen indusries, ec. The fourh and he bigges advanage of his meric is ha he cross-secional regression can be esimaed a differen poins in ime, which would allow us o deec ime-rends, if any, in he populariy of sock picking. This (1-R 2 ) meric has he following disadvanage. I does no give us an esimae of he proporion of rade ha can be explained by sock picking; i gives us an esimae of he maximum proporion of rade ha can be explained by sock picking. Our esimae of sock picking is, herefore, biased upward. We can decrease his bias by inroducing addiional independen variables in our cross-secional regression. These variables could be facors ha mimic possible facor porfolios ha invesors also index o, or i could be variables ha have appeared in he volume lieraure (see Lo and Wang (2000) for a descripion). These addiional explanaory variables would reduce 1-R 2, hus reducing he bias in our esimae. We, however, refrain from his exercise for wo reasons. Firs, i complicaes a simple meric. Second, as hese addiional independen variables are quie ad hoc and are no moivaed by well-esablished heories, we would no know how o inerpre our new resuls

11 III. DATA Broadly speaking, he daa for his paper can be classified ino hree ypes. Firs, we require basic socklevel variables o esimae he maximum fracion of rade explained by sock picking. Second, we require oher variables ha help us explore he deerminans of sock picking. Third, we use macroeconomic variables o esimae he long-run fracion of volume explained by sock picking. A. Basic variables Esimaing he maximum fracion of volume explained by sock picking requires only wo daa iems: he share volume and he number of shares ousanding. These daa iems are readily available from well-known sources for mos socks. For Unied Saes firms, we collec share volume and shares ousanding daa from CRSP. Share volume is he number of shares raded wihin a given monh. The number of shares ousanding is he number of shares of common equiy ousanding as of he end of he monh. In order o be included in he final sample, a sock mus be lised on he NYSE, AMEX, or Nasdaq. In addiion, he share mus be an ordinary common share; we exclude, for example, ADRs and REITs from he analysis. 5 Since share volume is no available before July of 1962, his is where we begin our analysis for he Unied Saes. For non-unied Saes firms, we collec share volume and shares ousanding a he individual sock level from Daasream. As we did for Unied Saes firms, we calculae he volume of shares raded wihin a given monh. Again, we measure shares ousanding a he end of each monh. Daasream provides liss of socks associaed wih a counry. 6 Wihin hese liss, some socks have daa colleced from an exchange in a given counry, bu have anoher home counry. Oher socks in hese liss have a given counry lised as heir home 5 Share codes 10 and 11 in CRSP. 6 These liss are ypically named FXX and DEADXX, where XX is an abbreviaion for he counry name. There are a few excepions o his rule. The FXX file includes firms mainaining Daasream coverage as of 2004, while he DEADXX file includes firms ha have in he pas been covered by Daasream, bu for whom coverage has ceased

12 counry, bu have daa colleced on an exchange in anoher counry. We include in a counry only hose firms boh headquarered and lised on an exchange wihin ha counry. 7 The overall coverage by Daasream improved dramaically in he mid 1990s (see, also, Morck, Yeung, and Yu, 2000), hough some counries have daa available well before his ime. Therefore, we focus on he period from 1995 hrough 2004 for our cross-counry analysis. B. Oher variables For he counry cross-secional analysis, we compare sock picking in emerging markes versus developed markes. We classify a marke as developed if MSCI has a developed marke index in ha counry. We classify any markes no on his lis as emerging. 8 The oal number of counries in our analysis is 43, of which 21 are classified as developed counries, and he remaining 22 are classified as emerging markes. A lis of hese 43 counries appears in Table 1. In he Unied Saes, we esimae he maximum fracion of volume explained by sock picking for socks wih differen characerisics. We firs esimae he amoun of sock picking based on wheher he firm is included in he S&P 500 index. Second, we esimae sock picking based on he exchange on which he firm s equiy is lised. Third, we break firms ino size quiniles based on marke capializaion o esimae he effec of firm size on sock picking. Fourh, we break firms ino quiniles according o age, which we proxy for using he number of monhs for which he firm has had daa available in CRSP. Fifh, we consider he indusry effec on sock picking. We classify firms ino indusries based on he en indusry classificaions provided by Fama and French (1997). 9 Excep for he las variable, he oher daa iems are available direcly from CRSP. In addiion o he above variables ha are available from CRSP, we classify firms ino quiniles according o he number of analyss following he firm. We obain his by couning he number of analyss making annual EPS forecass made in he monh prior o he firm s fiscal year end. This iming convenion allows us o capure 7 We use he Daasream variable GEOGC o deermine he home counry of a company and EXNAME o deermine he exchange from which he volume is repored. 8 We cross-checked his definiion of emerging wih counries explicily labeled as emerging by MSCI. The only counry ha does no explicily appear is Cyprus, which we classify as emerging. 9 The indusry classificaions are available from Kenneh French s websie: hp://mba.uck.darmouh.edu/pages/faculy/ken.french/daa_library.hml

13 he maximum number of analyss making forecass abou he firm, as more analyss make earnings forecass as he forecas period end dae nears. Daa on analys following comes from I/B/E/S and becomes available in C. Macroeconomic variables used for esimaing he seady sae sock-picking measure We follow he model of Whielaw (1994, 1997), and model he expeced marke risk premium as a funcion of hree macroeconomic variables. Firs, we use he yield spread beween Baa raed companies and Aaa raed companies o proxy for defaul risk premia. Second, we include he hree-monh reasury yield. Third, we include he dividend yield on he S&P composie index. Global Insigh provides hese daa iems. As in Whielaw (1994, 1997), we also model he volailiy of marke reurns based on wo macroeconomic variables. We again include he hree-monh reasury yield. In addiion, we include he spread beween yields on commercial paper and he hree-monh reasury yield. We collec his series from he Federal Reserve Board of Governors. IV. STOCK PICKING IN THE WORLD Every monh, beginning from January of 1995 and ending in July of 2004, for each counry, we run a simple OLS regression of log monhly sock volume (measured by number of shares raded in ha monh for sock i in a counry) agains he log of monhly shares ousanding (measured by number of shares ousanding in he beginning of he monh for sock i). We run his regression for 43 counries, of which 21 are classified as developed markes and 22 are classified as emerging markes. We begin in January of 1995 because ha is when we can obain daa for all of our counries. Since we have daa for he Unied Saes beginning July 1962, we sudy he Unied Saes in greaer deail in he nex secion. Each monh, we find he median (1-R 2 ) for he 21 developed counries o obain a (1-R 2 ) for he developed markes as a group, and he median (1-R 2 ) for he 22 emerging markes o obain a (1-R 2 ) for he emerging markes as a group. Figure 1 plos he (1-R 2 ) of his cross-secional regression over ime for developed markes and emerging markes. Figure 1 depics he wo big resuls of our paper. The firs big resul ha Figure 1(a) illusraes is ha here is more sock picking in emerging markes han in developed markes. Panel A of Table 1 confirms his. The maximum fracion of volume explained by sock

14 picking in emerging markes in he period is 63%, whereas he maximum fracion of volume explained by sock picking in developed counries is only 45%. Figure 1(b) depics sock picking for a few selec markes: wo developed markes (Japan and he Unied Saes) and wo emerging markes (Mexico and Taiwan). As can be seen, he maximum fracion of volume explained by sock picking in he wo developed markes is less han he maximum fracion of volume explained by sock picking in he wo emerging markes in he period. Panel B of Table I confirms his. The maximum fracion of volume explained by sock picking in Unied Saes, Japan, Taiwan and Mexico in he period is 29%, 41%, 61% and 72% respecively. Panel B of Table I sors he 43 counries under invesigaion in ascending order of he populariy of sock picking in As can be seen, he maximum fracion of volume explained by sock picking in he period is he leas in he Unied Saes (29%) and is he mos in China (80%). As can also be seen, populariy of sock picking is generally lower in he developed markes (hey usually are on he op of he lis) han in he emerging markes (hey usually are on he boom of he lis). Germany is an imporan excepion because, considering ha i is a developed marke, i has oo much sock picking. Russia is also an imporan excepion because, considering ha i is an emerging marke, i has oo lile sock picking. The second big resul ha Figure 1(a) illusraes is ha, on an average, sock picking is declining around he world. The declines in sock picking are quie dramaic, especially in he emerging markes. Panel A of Table 1 shows ha he maximum fracion of volume explained by sock picking fell from 72% in o 59% in in emerging markes, whereas he maximum fracion of volume explained by sock picking fell from 51% in o 41% in in developed markes. Figure 1(b) depics he decline in sock rading for a few selec markes: wo developed markes (Japan and he Unied Saes) and wo emerging counries (Mexico and Taiwan). Panel B of Table I confirms his. The maximum fracion of volume explained by sock picking in Unied Saes, Japan, Taiwan and Mexico in he earlier period is 36%, 43%, 66% and 76% respecively, whereas he maximum fracion of volume explained by sock picking in Unied Saes, Japan, Taiwan and Mexico in he laer period is 24%, 40%, 59% and 67% respecively

15 Panel B of Table 1 shows ha, of he 43 counries under invesigaion, he maximum fracion of volume explained by sock picking is lower in he las five years ( ) han in he previous five years ( ) for 38 counries. The mos dramaic decline in he populariy of sock picking is recorded in he Unied Saes, bu ha is probably because we have a longer ime-series daa for he Unied Saes. In he Unied Saes, he maximum fracion of volume explained by sock picking has secularly declined from a high of 60% in he 1960s o a low of 24% in he 2000s. V. STOCK PICKING IN THE UNITED STATES (DETAILS) Every monh, beginning from July of 1962 and ending in December of 2004, for he Unied Saes, we run a simple OLS regression of log monhly sock volume (measured by number of shares raded in ha monh for sock i) agains he log of monhly shares ousanding (measured by number of shares ousanding in he beginning of he monh for sock i). Figure 1 plos he (1-R 2 ) of his cross-secional regression over ime. As he number of lised socks change over ime, he sample sizes of he cross-secional regressions change over ime. To correc for his, we run he same cross-secional regression for 400 socks randomly seleced each period. As can be seen in Figure 2, his does no make much difference. Figure 2 is he main resul for he Unied Saes. I shows ha he maximum fracion of volume explained by sock picking has secularly declined over ime. Sock picking could explain a maximum of 60% of volume in he lae 1960s, bu i could explain only a maximum of 24% of volume in he 2000s. This reflecs a huge decline in he populariy of sock picking in he las fory years. We now run he cross-secional regression for various sub-samples of he daa. Figure 3 plos he (1-R 2 ) of hese cross-secional regressions over ime for he various sub-samples. These are depiced in various panels in Figure 3. The objecive of he various panels of Figure 3 is o graphically explore which markes exhibied he greaes decline in sock picking. Figure 3 is an informal eyeball es. The corresponding panels of Table 2 show formal saisical ess ha confirm our informal eyeball ess from Figure 3. Figure 3(a) shows ha here is more sock picking in he non-s&p 500 socks han in he S&P 500 socks a nearly all poins in ime. This is o be expeced, because belief in modern porfolio heory exhibis iself

16 hrough he pracical echnique of indexing, and indexing is far easier for he S&P 500 socks. Wha may be surprising, however, is ha indexing is becoming popular over ime no only in he S&P 500 socks, bu even in he non-s&p 500 socks. As a maer of fac, in recen imes, i seems ha here is more indexing in he non-s&p 500 socks han in he S&P 500 socks! Panel A of Table 2 confirms he above conclusion. The (1-R 2 ) of he S&P 500 socks is saisically significanly lower han he (1-R 2 ) of he non-s&p 500 socks. The es we use is o sor he monhly (1-R 2 ) of he OLS regressions of each of he wo sub-samples, and es which group has a higher median. We do he same es for he inercep erm as well as he coefficien erm. Panel A of Table 2 shows some ineresing angenial resuls. As he inercep erm is he log of he urnover, i shows ha here is more rade in S&P 500 socks han in non-s&p 500 socks. As he coefficien erm ells us wheher volume is linear in shares ousanding a coefficien of 1 means lineariy i does seems ha volume is roughly proporional o shares ousanding for he S&P 500 socks, bu i seems ha here is higher urnover for he larger socks in he non-s&p 500. Figure 3(b) examines sock picking among he Unied Saes exchanges. I shows ha here is less sock picking in he NYSE han in he AMEX a all poins in ime. The case of Nasdaq is fascinaing. In erms of he populariy of sock picking, i sars ou looking like he AMEX in he 1980s, and ends up looking like he NYSE in he 2000s. The dramaic change occurs in he year This is he year ha he Nasdaq bubble burs and, we believe, day raders and oher invesors who were sock pickers in Nasdaq became disillusioned. Finally, i should be noiced ha sock picking is becoming less popular over ime for all he hree markes. Panel B of Table 2 confirms he above conclusion. The (1-R 2 ) of he AMEX socks is saisically significanly higher han he (1-R 2 ) of he Nasdaq socks, which in urn is saisically significanly higher han he (1-R 2 ) of he NYSE socks. The inercep erms in Panel B of Table 2 shows ha urnover is highes in NYSE and lowes in AMEX. The coefficien erms in Panel B, as hey are all above 1, shows ha here is a higher urnover in he larger socks in all he hree markes. As sock picking was less popular for he larger S&P 500 socks han for he smaller non-s&p 500 socks (Figure 3(a) and Panel A of Table 2), and as sock picking was less popular for he larger NYSE socks han for he smaller AMEX socks (Figure 3(b) and Panel B of Table 2), we suspec a size effec. Figure 2(c) examines

17 sock picking among various sizes. We measure size every monh by soring he number of shares ousanding ha monh ino five quiniles. Figure 3(c) shows ha here is less sock picking in he larges quinile of socks han in he smalles quinile of socks mos of he ime. The resul is, however, no unambiguous. There was more sock picking in he larges quinile socks in he early 1960s. This finding plus he finding ha sock picking in Nasdaq and NYSE are roughly similar in recen imes (Figure 1(b) and Panel B of Table 1) hin o us ha he size effec is no he only sory. Finally, i should be noiced ha sock picking is becoming less popular over ime for all size socks. Panel C of Table 2 confirms he above conclusion. The (1-R 2 ) of he smalles quinile socks is saisically significanly higher han he (1-R 2 ) of he larges quinile socks. The inercep erms in Panel C of Table 2 shows ha urnover is higher in he larges quinile socks han in he smalles quinile socks. The coefficien erms in Panel C shows ha, among he smalles quinile socks, here is a higher urnover in he larger socks, bu his size effec is non-exisen in he larges quinile socks. As informaion abou young firms is difficul o come by, i would seem o sugges ha finding ou informaion abou young firms and rading on ha informaion would be more profiable han sock picking older firms. We measure age every monh by soring he ages of firms ha monh ino five quiniles. Figure 3(d) shows ha here is less sock picking in he oldes quinile of socks han in he younges quinile of socks all he ime. Finally, i should be noiced ha sock picking is becoming less popular over ime for firms of all ages. Panel D of Table 2 confirms he above conclusion. The (1-R 2 ) of he younges quinile socks is saisically significanly higher han he (1-R 2 ) of he oldes quinile socks. The inercep erms in Panel D of Table 2 shows ha urnover is higher in he younges quinile socks han in he oldes quinile socks. The coefficien erms in Panel D shows ha here is a size effec in firms of all ages: here is a higher urnover in he larger socks. Indusry is an imporan elemen in he money managemen indusry. Specializaion occurs by indusry. So we do an indusry classificaion, and ask wheher sock picking is more popular in some indusries. Our priors are he same as before. As informaion abou new indusries is difficul o come by, i would seem o sugges ha finding ou informaion abou new indusries and rading on ha informaion would be more profiable han sock

18 picking in older boring indusries. We use a 10-indusry classificaion based on Fama and French (1997). Figure 3(e) confirms our inuiion. I shows ha he exciing elecommunicaion indusry has he highes amoun of sock picking, whereas he boring uiliies indusry has he leas amoun of sock picking. Finally, i should be noiced ha sock picking is becoming less popular over ime for all indusries. Panel E of Table 2 shows a ranking for all indusries. The ranking, from he indusry where sock picking is leas popular o he indusry where sock picking is mos popular is: uiliies, medical, high ech, manufacuring, durables, ohers, non-durables, reail/wholesale, energy and elecommunicaions. The inercep erms in Panel E of Table 2 shows ha urnover is generally lower in he indusries where here is less sock picking. The coefficien erms in Panel E show ha hough here is a size effec in socks of nearly all indusries here is a higher urnover in he larger socks in he indusry here seems o be a reverse size effec in he elecommunicaion indusry here is a smaller urnover in he larger socks in his indusry. The quinessenial sock picker in he money managemen indusry is he research analys. He ges paid a lo o pick socks. So i would seem naural ha we should end his secion by classifying socks by he number of analyss who follow hem. Our priors are ha analyss pick socks ha ohers pick laer. We measure he number of analyss following a sock every monh by soring he number of analyss following he sock ha monh ino quiniles. Figure 3(f) shows ha our priors are wrong: i seems ha invesors do more sock picking in socks ha analyss do no pick mos of he ime, and invesors do less sock picking in socks ha analyss do pick mos of he ime. A hypohesis o explain his seemingly couner-inuiive finding is ha analyss improve he informaion environmen of he socks hey are picking, hus, paradoxically, reducing he reurn o informaion gahering and sock picking for hemselves as well as for ohers. Serious sock pickers, herefore, avoid he socks ha analyss pick. To he bes of our knowledge, his is he firs ime someone has provided empirical evidence in favor or agains his hypohesis. Our evidence also suggess ha sock picking is becoming less popular over ime for all socks, wheher hese socks are followed by a large number of analyss or followed by a small number of analyss. Panel F of Table 2 confirms he above conclusion. The (1-R 2 ) of he socks ha are covered by a small number of analyss is saisically significanly higher han he (1-R 2 ) of he socks ha are covered by a large

19 number of analyss. The inercep erms in Panel F of Table 2 shows ha urnover is much higher in he socks ha are covered by a large number of analyss han in he socks ha are covered by a small number of analyss. The coefficien erms in Panel E show ha hough here is a size effec in socks which are covered by few analyss here is a higher urnover in he larger socks in his sub-group here seems o be no size effec in socks ha a large number of analyss follow. VI. STOCK PICKING IN THE STEADY STATE IN THE UNITED STATES A. A simple model An economy consiss of a large number of asses whose reurns are risky, and one single risk-free asse wih a one-period reurn of r f. The one-period reurn of a represenaive risky asse i is ~ ~ r = E( ) + δ + ~ α + ~ ε (2), i r i i i and he one-period reurn of he marke porfolio is ~ r E( r ) + ~ δ (3), m = m where δ = marke risk componen, wih mean = 0 and sandard deviaion = F m, " i and, i = idiosyncraic risk componen, wih means equal o 0 and sandard deviaions equal o F " and F, respecively. Invesors have a one-period invesmen horizon. They care only abou he mean reurn (which hey like) and he sandard deviaion of he reurn (which hey dislike) of heir porfolios. This implies ha every invesor ries o maximize he Sharpe raio of her porfolio. An invesor can choose o be a passive invesor who invess in he marke porfolio and in he risk-free asse, or an acive invesor who picks he represenaive risky asse i. If he invesor chooses o be a passive invesor, her Sharpe raio is S passive ( E( rm ) rf ) = (4) σ m

20 If he invesor chooses o be an acive invesor, she obains " i, which is a privae signal. She hen akes a posiion in he represenaive risky asse and an opposie posiion in he marke porfolio. This allows her o ge rid of he marke risk componen, δ, of he represenaive risky asse. However, she canno ge rid of he firmspecific risk componen,, i. Moreover, she canno fully exploi her inside informaion, " i. This is because he voluminous lieraure on marke microsrucure, which begins wih Kyle (1985) and Glosen and Milgrom (1985), ells us ha he excess profi an insider obains from her inside informaion, is her profi based on her superior informaion minus her adverse selecion cos. There are also oher ransacion coss of rading like commissions. We subrac all hese coss from " i o obain he profi from obaining inside informaion, " ne. The Sharpe raio of he acive invesor is hen acive α ne σ ε S = (5) We now obain he " ne ha makes (4) equal o (5). α ne, indifferen ( E ( rm ) rf ) = σ ε (6) σ m This implies ha any invesor who obains he " ne ha is higher (lower) han " ne, indifferen will choose o be an acive (passive) invesor. Now assume ha every agen in he economy has a differen " ne, which depends on skill and/or luck, and his " ne is drawn from a disribuion ha is sable over ime. This addiional assumpion implies ha if " ne, indifferen is increasing over ime, he proporion of sock pickers is declining. We now go on o check wheher " ne, indifferen is really increasing over ime. As " ne, indifferen from (6) is he produc of he Sharpe raio of he marke and he idiosyncraic risk of he represenaive sock, we need o esimae hese wo variables from Unied Saes daa. B. Esimaion We firs esimae he average idiosyncraic risk of socks in CRSP. For each sock each monh, we fi a marke model o monhly reurns using he railing 5 years of daa. We hen calculae he sandard deviaion of he residuals from hese regressions o esimae he idiosyncraic risk. The overall idiosyncraic risk measure is

21 he equal-weighed average of he individual sock idiosyncraic risk. This is he same mehod used in Morck, Yeung and Yu (2000) o back ou idiosyncraic risk. Our esimae of idiosyncraic risk allies wih heir esimae. I also allies wih he esimae of Campbell e al. (2001), who use a variance decomposiion mehod of esimaing idiosyncraic risk. Figure 4 shows ha idiosyncraic risk is increasing in he Unied Saes. Morck, Yeung and Yu (2000) as well as Campbell e al. (2001) have documened his as well. Alhough he fac ha idiosyncraic risk, or firmspecific risk, is increasing over ime is no dispued, he jury is sill ou on why his is so. 10 Figure 4 also shows he marke model R 2. Again, as seen in Morck, Yeung and Yu (2000), his is declining over ime. This should no be surprising. If idiosyncraic risk is increasing, he explanaory power of he marke facor o explain firmspecific reurn should be declining. Figure 4 also shows he (1- R 2 ) of our cross-secional regression. I shows ha sock picking is becoming less popular when idiosyncraic risk is rising. We nex esimae he marke price of risk, he marke Sharpe raio. We use he mehodology described in Whielaw (1994, 1997). Whielaw suggess fiing expeced reurns and sandard deviaions as a funcion of macroeconomic variables using GMM. The momen condiions are E ( r π ( r 2 m, + 1 m, + 1 X X β ) X = 0 ). β Xθ X We esimae he marke Sharpe raio using he prediced values of expeced marke excess reurn and volailiy from his wo equaion sysem. We include he spread beween Baa and Aaa raed firms yields, he hree-monh reasury yield, he spread beween commercial paper and he reasury yield, and he dividend yield as insrumens. 10 Morck, Yeung and Yu (2000) invesigae hree hypoheses o explain why idiosyncraic risk is increasing over ime. The firs hypohesis is he obvious one, and his is he hypohesis hey find he leas evidence for: correlaions among firmspecific cash flows are becoming weaker. The oher wo hypoheses are based on he dark side of finance. They surmise ha as propery righs srenghen, risk arbirage srenghens, and so more firm-specific informaion is incorporaed in sock prices. Their las hypohesis is ha as firm-specific informaion becomes more credible due o more credible accouning saemens, more firm-specific informaion is incorporaed in sock prices. Campbell e al. (2001), on he oher hand, do no ake a paricular view as o wha is causing he increase in volailiy. They lay down a lis of reasons ha, in heir view, are plausible. Here is he lis. Firs, conglomeraes are breaking up ino single-uni firms. Second, iniial public offerings come earlier, when firm-specific informaion is sill very imprecise. Third, sock opions may emp managers from increasing firm-specific risk. Fourh, here are he reasons expounded by Morck, Yeung and Yu (2000). Fifh, i could be day raders

22 We hen consruc a ime-series of esimaed " ne, indifferen as he produc of he esimaed idiosyncraic risk and he esimaed marke Sharpe raio. We are ineresed in he long-run rend of his series oward an asympoe. This is he reason why. If we assume ha he disribuion of excess profis in he economy is sable, hen he proporion of invesors whose excess profi is above he indifferen excess profi curve he sock pickers will sabilize where he indifferen excess profi curve asympoes. This is he seady-sae proporion of sock pickers. We esimae he asympoe of " ne, indifferen by choosing esimaes of a 0 and a 1 o minimize he funcion a α ne indifferen ( a e 1, 0 ). We find he esimaes of a 0 and a 1 o be and -5.0e -6, respecively. This ells us ha our long-run esimae of " ne, indifferen is We now need o esimae he relaionship beween " ne, indifferen and he percen of volume explained by sock picking. The volume explained by sock picking (indexing) represens he percen of invesors wih " ne above (below) " ne,indifferen. We assume ha invesors " ne are drawn from a normal disribuion wih parameers μ and σ. This means ha he R 2 from he regression of share volume on shares ousanding each monh is he cumulaive normal densiy funcion evaluaed a " ne, indifferen. We esimae he values of μ and σ o minimize he funcion 2 ne, indifferen R N( α, μ, σ ), where N(x, :, F) is he cumulaive densiy funcion for a normal disribuion wih mean μ and deviaion σ evaluaed a x. Our esimaes of μ and σ are and 1.064, respecively. Since μ is negaive, i implies ha he average person loses if he picks socks. Now ha we know all he parameers of he normal disribuion ha " ne is drawn from, we calculae he cumulaive densiy funcion of his normal disribuion a our long-run esimae of " ne, indifferen, which had urned

23 ou o be This is our long-run esimae of R 2, which urns ou o be So (1- R 2 ) is roughly 11%. This implies ha our esimae of he seady-sae fracion of sock pickers in he Unied Saes is 11%. Figure 5 shows he acual (1-R 2 ) of our cross-secional regression. I also shows he in-sample prediced (1-R 2 ), he ou-of-sample forecased (1-R 2 ), and he esimaed seady sae (1-R 2 ). The las hree variables are 1 minus N(x,μ,σ) (he cumulaive densiy funcion for a normal disribuion wih mean μ and sandard deviaion σ evaluaed a x). The value of x o obain he in-sample prediced (1-R 2 ), o obain he ou-of-sample forecased (1- R 2 ), and o obain he esimaed seady sae (1-R 2 ) is he value of he in-sample " ne,indifferen, he value of he ouof-sample forecased " ne,indifferen, and he value of he esimaed seady sae " ne,indifferen, respecively. As a robusness check, we use hree alernaive mehods o esimae he marke price of risk. All of hese mehods assume ha he marke price of risk is consan. The firs mehod is he simples. We calculae he average marke excess reurn, and divide his average by he sandard deviaion of marke reurns. The second and hird mehods are from Harvey (1989), who esimaes he marke price of risk using GMM. The wo mehods differ only based on heir definiion of risk. The momen condiions for he second mehod, in which he absolue value of residuals measure risk, are: E ( r X β ) X = 0 ( r λ r X β ) X m, + 1 m, + 1 m, + 1. The momen condiions for he hird mehod, in which he squared value of residuals measure risk, are: ( r X β ) X m, + 1 = 0 ( r λ( r X β ) ) X E 2 m, + 1 m, + 1. We compare he resuls from hese hree alernaive mehods wih he resuls from he Whielaw (1994, 1997) model in Table 3. The properies of " ne,indifferen are quie similar under all of he measures. The " ne,indifferen asympoes o jus over 1 using all of he four models. The bigges differences come in he esimae of he mean of he normal disribuion, which is wha causes he difference in he esimaes. Since he average of he gross Jensen s alpha for all socks is likely o be zero, he average of he ne Jensen s alpha for all socks is likely o be 11 N(1.007, , 1.064)=

24 negaive. As his average is negaive for he Whielaw (1994, 1997) model, we repor primarily he resul from his model in our ex, hough Table 3 repors all resuls from all our four models. VII. CONCLUSION We do hree hings in his paper. We firs develop a meric o measure he maximum fracion of volume explained by sock picking in a marke. We hen use our meric o measure sock picking around he world. We find ha hough here is more sock picking in emerging markes han in developed counries, i is declining everywhere. In he Unied Saes, for example, sock picking has secularly declined from a high of 60% in he 1960s o a low of 24% in he 2000s. Finally, we ask wha is he long-run seady sae fracion of sock pickers? We develop a simple heoreical model, and calibrae his model o he Unied Saes economy o conclude ha sock picking will evenually sele a 11% in he Unied Saes. Though his paper shows cross-secional variaion in sock picking across markes, i does no formally invesigae hypoheses ha may explain his cross-secional variaion. Neiher does i formally invesigae hypoheses ha explain why sock picking is declining over ime. An overall heme ha comes hrough from our descripive saisics is ha sock picking is more in markes where here is less public disclosure of sock-specific informaion. I may be ha as his disclosure is improving over ime, sock picking is becoming less profiable and, herefore, declining in populariy. The above are jus conjecures. We leave i o fuure research o formally explore he deerminans of sock picking. Anoher area of research is furher developmen of our meric. The firm-specific error in our crosssecional regression is really a measure of abnormal volume a he firm-level. Is abnormal volume a he firmlevel linked o some firm-specific variables like size or book-o-marke? Can abnormal volume predic reurns? We leave hese ineresing quesions o fuure research