Firms as Buyers of Last Resort

Transcription

1 Firms as Buyers of Las Resor Harrison Hong Princeon Universiy Jiang Wang MIT and CCFR Jialin Yu Columbia Universiy Firs Draf: May 005 This Draf: April 007 Absrac: We develop a model o explore he asse pricing implicaions of firms being buyers of las resor for heir own socks. Those wih more abiliy o repurchase shares when prices drop far below fundamenal value (i.e., less financially consrained ones) should have lower shor-horizon reurn variance (conrolling for fundamenal variance) han oher firms. Using sandard proxies for financing consrains such as pas repurchases, firm age and he Kaplan and Zingales (1997) index, we find srong suppor for his prediced relaion. Moreover, our heory predics ha his relaion should be sronger in environmens where repurchases are legally easier o execue. Consisen wih our heory, we find ha his relaion is indeed sronger in he U.S. afer 198 when regulaory reforms lowered he legal cos of conducing repurchases; and among he en larges sock markes in he world, hey are sronger in counries where share repurchases are legally easier o execue. We hank an anonymous referee and Heior Almeida, Doug Diamond, Diego Garcia, Jeffrey Kubik, Hamid Mehran, Lasse Pedersen, Ronnie Sadka, Jeremy Sein, Sheridan Timan, and seminar paricipans a he Universiy of Briish Columbia, Ramon Areces Foundaion Conference on Financial Economics, Drexel, New York Federal Reserve Bank, Princeon-New York Federal Reserve Bank Liquidiy Conference, Pompeau Fabra, and Economeric Sociey Meeing, for a number of helpful commens.

2 1. Inroducion In his paper, we explore he idea of firms being buyers of las resor for heir own socks. The phrase buyers of las resor is inspired by he vas lieraure sared by Bageho (1873) on he role of cenral banks as lenders of las resor for heir economies. Jus as cenral banks make funds available o markes in imes of crises, a firm can provide liquidiy o is invesors, when no one else will, by repurchasing shares of is own sock. Such firm inervenion no only influences he price of individual socks, bu also has macroeconomic consequences. For insance, many companies quickly bough back a large fracion of heir shares afer he sock marke crash of Via he coordinaion of sock exchanges, a large number of firms also announced repurchase programs immediaely afer he evens of Sepember 11, 001. These anecdoes sugges ha companies were and can be imporan liquidiy providers. There is evidence beyond hese anecdoes ha firms inervene in heir socks when prices move significanly away from fundamenal value. In a survey by Brav, Graham, Harvey, and Michaely (004) of 384 CFOs, he mos popular response for why firms repurchase socks (86.6% of hose surveyed agree) is ha heir sock is cheap relaive o is rue value. Using large panel daases, several sudies confirm he relaive imporance of valuaion (low price-o-book raios or poor pas reurns) as a moive for his financial decision (see e.g., Dimar (1999) and Sephens and Weisbach (1998)). In addiion, oher works find posiive drif in abnormal reurns following announcemens of firms conducing repurchases (Ikenberry, Lakonishok and Vermaelen (1995, 000)). For insance, Ikenberry, Lakonishok and Vermaelen (1995) find for he U.S. sock marke ha he average abnormal four-year buy-and-hold reurn measured afer he iniial announcemen is 1.1 percen. They also find ha for low price-o-book socks, companies more likely o be repurchasing shares because of undervaluaion, he average abnormal reurn is 45.3 percen. For repurchases announced by high-price-o book socks where undervaluaion is less likely o be an imporan moive, no posiive drif in abnormal reurns is observed. Ikenberry, Lakonishok and Vermaelen (000) find similar evidence for Canada and in addiion ha rades also appear linked o price movemens as managers buy more shares when prices fall. 1

3 In sum, hese findings sugges ha repurchases are consisen wih firms inervening opporunisically much like speculaors or marke-makers would afer price falls significanly below fundamenal value and earning long-run abnormal reurns for hese rading aciviies. 1 There is also a similar se of evidence suggesing ha firms issue equiy when hey perceive heir shares o be over-valued (see Baker, Ruback and Wurgler (004) for a review of his evidence). We develop a model o explore he effecs of firms being buyers of las resor for heir socks. We exend he Grossman and Miller (1988) model o allow firms o inervene in heir own socks when liquidiy shocks are sufficienly large. We are agnosic abou he source of hese shocks leading o deviaions of price from fundamenal value. We will call hese liquidiy shocks, hough we are equally comforable wih idenifying hem as demand shocks due o, say, shifs in invesor senimen. While he Grossman-Miller model is ypically applied o reurns of very shor-horizons, we hink of our exension as applying o longer-horizons in which shocks have o be big enough (accumulae over a long enough ime) for he firm o profiably inervene. 3 Our firs predicion is ha hose firms wih less abiliy o inervene should prices deviae oo far from fundamenal value ough o have a higher shor-horizon reurn variance conrolling for an appropriaely scaled version of fundamenal or long-horizon reurn variance. Inuiively, firms wih low-inervenion abiliy end up wih greaer deviaions of price from fundamenal value and hence greaer reversals as liquidiy shocks are assumed o mean rever over long enough horizons. This means a higher shor-horizon conrolling for fundamenal or long-horizon reurn variance (since longerm reurn variance corresponds o fundamenal variance in our model) compared o high-inervenion abiliy firms. 1 I is also possible ha a firm buys back is own shares due o informaion ha only he firm has. This, however, seems less likely for wo reasons. Firs, repurchases ofen follow a fall in share prices, i.e. hey are predicable given pas reurns or valuaion raios. Second, repurchases are announced publicly, and ye price adjusmens ake several years. Firms are no in he business of being marke makers. They only inervene when he liquidiy shocks are sufficienly large. We model his by assuming ha firms have a higher cos of paricipaing in he marke han oher raders. 3 Recen evidence by Coval and Safford (005) and Frazzini and Lamon (005) confirm ha liquidaion of socks by muual funds lead he prices of hese socks o be depressed relaive o fundamenal value for long-periods of ime, suggesing he possibiliy of firms profiably buying shares o profi from his deviaion, i.e. he fricions imagined in he Grossman-Miller framework apply beyond he very shorhorizon seing o which he model is ypically applied.

4 We es his predicion by measuring he abiliy of differen firms in he crosssecion o be buyers of las resor for heir own socks and relaing his o he sock s reurn variance. Our basic premise is ha he capabiliy of he firm o be he buyer of las resor for is own sock or o inervene more generally depends on he exen o which i is financially consrained. In paricular, firms ha are equiy dependen are unlikely o execue repurchases. As such, he firs predicion of our model is ha more financially consrained firms ough o have a higher shor-horizon reurn variance conrolling for fundamenal variance. To avoid daa-mining biases, we use sandard measures of financing consrains from he recen corporae finance lieraure. In paricular, we use he measures advocaed by Kaplan and Zingales (1997), Lamon, Polk and Saa-Requejo (001), Baker, Sein and Wurgler (003). 4 The firs and closes o our heory is sock repurchases (relaive o dollar urnover or marke capializaion) since our model emphasizes he abiliy of firms o execue share repurchases o couner liquidiy shocks. A broader raionale is ha since repurchases and invesmens are compeing uses of funds, firms facing severe financing consrains would do less buy backs. Our second measure is firm age, which is based on he premise ha younger firms have a harder ime geing access o public deb markes. Corporae-finance consideraions also sugges ha equiy-dependen firms will end o have high leverage (eiher marke or book), low cash balances and pay less dividends. So our hird measure is he Kaplan-Zingales index and various versions of i, which ake ino accoun wheher a firm is paying dividends, leverage, cash balances, cash flow, and a firm s Tobin s Q (i.e. is marke-o-book raio). 5 Using daa from 1963 o 005, we begin our empirical invesigaion by confirming our premise ha financially consrained firms are less likely o inervene in heir socks. No surprisingly, our hree ses of financing consrain measures are quie correlaed. Noneheless, we find ha all hree measures have incremenal predicive power on firm repurchase aciviy: firms ha have done pas repurchases, older firms and 4 Noe ha a number of he variables in hese hree recen papers are used in earlier work on financing consrains such as Gerler and Gilchris (1994) and Fazzari, Hubbard and Peersen (1988). 5 As we explain below, firm leverage and marke-o-book may be difficul o inerpre in cerain conexs, so we will end up conrolling for hese wo firm characerisics in some of our regressions below. 3

5 lower KZ index firms are more likely o execue repurchases. As such, our empirical analysis below feaures all hree proxies. We hen es our firs predicion in he U.S. sock marke by using cross-secional variaion o see wheher shor-horizon reurn variance (anywhere from daily o quarerly reurns) is higher for financially consrained firms, conrolling for fundamenal or longhorizon reurn variance, which we ake o be eiher he variance of reurn-on-equiy (compued along he lines suggesed by Cohen, Polk and Vuoleenaho (006)) or he variance of hree-year reurns. 6 The resuls are similar so we feaure he variance of reurn-on-equiy. Consisen wih our model, we find ha our measures of financing consrains all come in wih he righ sign and are saisically and economically significan, regardless of he frequency a which we measure shor-horizon reurn variance. For insance, a wo-sandard deviaion increase in KZ (more financially consrained) leads o an increase in weekly reurn variance ha is anywhere from 30% o 40% of he sandard deviaion of weekly reurn variance depending on he version of he KZ index used. We hen aemp o rule ou a number of alernaive hypoheses for hese findings. Indeed, one naural explanaion for why financially consrained firms have higher shorhorizon variance conrolling for fundamenal variance migh have o do wih leverage and disress. While we can conrol o some degree for firm leverage and oher covariaes (such as firm size, ec ), i is impossible o fully rule ou he plausibiliy of alernaive hypoheses such as he leverage/disress hypohesis or oher forms of omied variables wih his approach. As such, we urn o our second predicion, which cus more decisively in favor of our inervenion-repurchase effec: he documened relaion beween variance and consrain ough o be sronger in environmens (regimes) where repurchases are legally easier o execue. Our premise is ha he relaionship beween financing consrains (e.g. firm age) and variances is due o he abiliy of firms o repurchase in he firs place (so ha our financing consrain measures accuraely capure he rue cos of inervenion). So in regimes where repurchases are legally cosly o execue or perhaps even illegal, we 6 An imporan cavea is ha reurn on equiy (ROE) and long-horizon reurn variance are noisy measures of fundamenal volailiy. 4

6 should no find an effec since he rue cos of inervenion for a firm is no simply financing consrains. More echnically, our idenificaion sraegy is o consider a difference-indifference (diff-in-diff) esimae of he effec of financing consrains on shor run variance conrolling for fundamenal variance. Loosely, we firs esimae he crosssecional relaion beween consrains and variances (he firs difference) in he difficulo-repurchase regime. We ake for graned ha his relaion may no be due o our inervenion-repurchase hypohesis bu perhaps o some oher mechanisms. We hen esimae he same relaionship during he easy-o-repurchase regime (he second difference). The difference in hese wo differences is aribued o our inervenionrepurchase effec on he basis ha he oher mechanisms such as leverage risk ough no o vary wih legal regimes regarding repurchases. We are expecing a sronger relaionship in he easy-o-repurchase regime han he difficul-o-repurchase regime. We use wo sources of exogenous variaion o beer idenify our heory. The firs is he regulaory reform in he U.S. sock marke in 198 in he form of SEC Rule 10b-18 ha encouraged repurchases. While share repurchases had always been legal in he U.S., companies sill worried abou class-acion lawsuis accusing hem of manipulaing heir sock prices wih repurchases. The passage of SEC Rule 10b-18 shielded firms from such lawsuis. This law is aribued by many for he rise of share repurchases since (see, e.g., Grullon and Michaely (00)). Since he price effecs arise from firms being able o legally execue repurchases in he firs place, our heory predics ha he (cross-secional) relaions beween financing consrains and reurn variances ough o be sronger afer 198 when he legal cos of doing repurchases wen down. 7 We find ha his is indeed he case---our effec is indeed sronger (boh economically and saisically) afer he regulaory reforms regardless of he financing consrain measures we use. The second source of variaion we use o beer idenify our heory comes from he cross-secion of sock markes around he world. Survey evidence from Kim, Schremper and Varaiya (004) on sock repurchases across he en larges sock markes, U.S., Japan, U.K., France, Germany, Canada, Ialy, he Neherlands, Swizerland and 7 More specifically, in periods in which repurchases are difficul or illegal, a firm s financing consrain under-esimaes he rue cos of inervenion and hence he relaion beween financing consrain measures and firm reurn variances will be weaker during hese periods. A similar saemen applies across counries. 5

7 Hong Kong, indicaes ha hese counries fall naurally ino hree groups in erms of legal ease of repurchases: easy, medium and difficul. Our ime period of analysis is During his period, he easy group comprises of he U.S., U.K. and Canada, and he difficul group comprises of France and Germany (in which repurchases were basically illegal). The oher five counries in he medium caegory are more heavily regulaed han he U.S. bu repurchases were no illegal during his period. We do no have a consisen se of repurchase and firm age daa across counries bu are able o consruc he KZ measures and use he laer in our analysis. Remarkably, we find, consisen wih our heory and following he same logic (diff-in-diff esimae) as for he US regulaory experimen, ha he prediced relaions beween he KZ measures and reurn volailiy are sronger in he easy group han in he medium group and sronger in he medium group han in he difficul group. Imporanly, for he difficul group, he relaion beween KZ and reurn volailiy is acually of he wrong sign. For he medium group where repurchases are possible, we ge he righ sign and he relaion is marginally significan in some cases. For he easy group, we ge resuls very similar o hose of he U.S. as expeced. Again, hese differences and he ordering of magniude of he coefficiens across hese hree groups are very economically and saisically significan. These wo ess form he crux of our paper. I is imporan o emphasize ha wihou hem, i would be impossible for us o disinguish beween our inervenion sory from he alernaive leverage sory. As such, we make sure ha our ess are robus. Toward his end, we perform diagnosics associaed wih hese diff-in-diff esimaes (as suggesed by Berrand, Duflo and Mullainahan (00)) such as randomizing where o pu he breaks for he US daa and which counries o pu in he differen groups for he inernaional daa. If our findings are spurious, hen we should see he same diff-in-diff resuls as above using hese randomizaion procedures. This is no he case. The randomizaion procedures yield resuls far differen from our diff-in-diff esimaes. Moreover, hese procedures also allow us o confirm ha our sandard errors are reasonable. We also perform a number of addiional robusness checks such as rerunning our regressions as a pooled panel wih clusered sandard errors, rying differen 6

8 specificaions and differen measures of financing consrains and fundamenal variance. And in each insance, we obain remarkably consisen resuls. Finally, we furher srenghen he case for our firm inervenion effec by relaing he skewness of sock reurns o financial consrains. Wih an addiional assumpion ha financing consrain is likely o affec sock repurchases and no issuances, our model delivers a hird predicion---ha hose less financially consrained firms wih more capaciy o repurchase shares quickly afer a marke crash (e.g. crash of 1987) should have more posiively skewed shor-horizon (e.g. daily) reurns. We discuss he meris of he assumpion ha here is an asymmery in he likelihood or cos of inervenion below. Noneheless, we do find suppor for his addiional predicion. Though skewness is more difficul o measure han volailiy and our parameers are esimaed less precisely han in he case of volailiy, we do find ha financially unconsrained firms have more posiively skewed daily reurns and ha his relaionship is sronger afer 198, when repurchases became legally easier o execue. Our paper is novel in exploring he effecs of firm inervenion (paricularly of firms being buyers-of-las resor for heir own sock) on sock reurns and liquidiy. Our findings furher develop he connecion beween corporae finance (e.g. he financing consrains lieraure) and asse pricing/marke micro-srucure (see Sein (1996) and Baker and Wurgler (00)). Our paper inroduces he firm as an imporan se of paricipans in he marke and is of general ineres since he model and is implicaions developed here apply equally well in oher conexs such as he Federal Reserve Bank or he governmen more generally being lenders-of-las resor for he aggregae marke. 8 Our paper proceeds as follows. We develop a simple model o analyze he effec of firm inervenion on sock reurn variance in Secion. We describe he daase in 8 One migh also wonder why we do no exend our model o develop implicaions for expeced reurns and relae hem o financing consrains. One poenial implicaion is ha financing consrained firms have higher expeced reurns precisely because hey are less liquid. There is already a large lieraure ha looks a he relaion beween liquidiy and expeced reurns (see, e.g., Amihud and Mendelson (1986) and Brennan and Subrahmanyam (1996)) and some find ha more illiquid socks indeed have higher expeced reurns. Addiional regressions of reurns on financing consrains would be difficul o inerpre since here are mechanisms oher han liquidiy hrough which financing consrains migh affec expeced reurns (e.g. financially consrained firms underake less of cerain kinds of invesmens, hereby giving he company a differen risk profile). 7

9 Secion 3 and he main empirical resuls in Secion 4. We conclude in Secion 5. All proofs are in he Appendix.. Model In his secion, we develop a simple model which capures how a firm's inervenion in he marke in response o large liquidiy shocks affecs he price behavior of is own sock. The framework we use is similar o ha of Grossman and Miller (1988), in which liquidiy shocks o a subse of invesors give rise o emporary shifs in he demand of a sock. 9 These shifs in demand cause emporary deviaions in he sock price, given limied marke making capaciy in he marke. When he firm inervenes in he marke for is own sock, i effecively serves as a marke maker ogeher wih he oher marke makers. We wan o use he erm marke-maker in he broades possible sense---he firm acs a speculaor (buyer) of las resor in is own sock in conjuncion wih oher speculaors in he marke such as hedge funds. Thus, when a firm is less consrained and more willing o ac as a marke maker, he liquidiy for is own sock also increases. We do no explicily model he overall objecive of he firm (i.e. he agen running he firm). We simply assume he reduced form ha he firm inervenes when prices deviae significanly from fundamenal value. One jusificaion is ha accommodaing liquidiy shocks can someimes be a profiable aciviy because of fricions oulined in Grossman and Miller (1988). Suppose invesors are heerogeneous in facing liquidiy shocks. If some invesors wan o cash ou for liquidiy reasons, oher exising invesors (he firm) can provide liquidiy by buying heir shares if here are no enough marke makers around Se-up 9 Here, we ake he liquidiy shock as exogenous, as in Grossman and Miller (1988). In a recen paper, Huang and Wang (006) show ha hese liquidiy shocks can arise endogenously in he presence of marke fricions. 10 Anoher jusificaion is based on agency heory in which he manager ges compensaed for a high sock price and couners liquidiy shocks so ha he sock price more accuraely reflecs his abiliy (i.e. fundamenals). See Sein (1996) and Baker, Ruback and Wurgler (004) for addiional jusificaions. 8

10 Suppose here are hree daes: = 0,1,. A sock is raded in a compeiive marke, whose cash flow is v ~ a = 1, and v ~ is an i.i.d. normal random variable wih a mean of zero and a variance of σ v. A = 1, ~ x shares of he sock is dumped ino he marke by a se of invesors for liquidiy reasons, where x ~ is a normal random variable (hus can be negaive) wih a mean of zero and a variance of σ x. There is a se of marke makers in he marke who can absorb he liquidiy shock. For now we assume ha heir populaion is µ and heir risk olerance is τ. The oal risk olerance of marke makers is τ M = µτ. 11 Moreover, he firm can also inervene in he marke of is own shares when shor-erm liquidiy shocks move he price of he sock far away from is fundamenal value. In deciding on is inervenion policy, he firm has an effecive risk olerance of τ F and faces a cos o inervene. For convenience, we assume ha boh he marke makers and he firm are iniially endowed wih no shares of he sock. 1 Le θ F denoe he posiion he firm akes in he sock marke o moderae is share price. We assume ha he inervenion cos is linear in he size of he posiion: κ + θ F, θ F > 0 c( θ F ) = 0, θ F = 0 (1) κ θ F, θ F < 0. The inervenion cos assumed above is inended o capure several characerisics of a firm's inervenion behavior. Firs, he cos o inervene prevens he firm from rading is own shares a all imes. Insead, i inervenes only when price deviaions caused by he liquidiy shock is sufficienly large. Second, he hreshold and he srengh of he inervenion may boh depend on he firm's abiliy o adjus is financial posiion. In he 11 These marke makers are needed o se he price under normal circumsances when he firm is no inervening. 1 I may seem arificial o assume ha he firm has zero shares of is own sock. Oher han simpliciy, he moivaion for such an assumpion is as follows. A firm's inervenion in he marke is an aciviy separae from is usual business operaions. Thus, i may rea i separaely when considering is meri, in paricular, is risk-reurn rade-off. Our resuls do no depend on his simplifying assumpion. 9

11 case of share repurchase, for example, he firm's abiliy o inervene in he marke clearly depends on how consrained i is in amassing he funds needed. In he case of seasoned equiy issues, is abiliy depends on he cos o issue new equiy. The linear form of he cos funcion makes he cos dependen on he size of he inervenion. The proporionaliy coefficiens, κ+ and κ, reflec he firm's abiliy o inervene. Moreover, he cos coefficien is in general differen beween share repurchases and sales, reflecing he fac ha consrains and coss can be asymmeric beween hese wo operaions. In paricular, we will assume ha κ > κ +. Tha is, oher hings equal, i is easier for he firm o repurchase is shares from he marke han issuing new shares. In he remainder of he paper, we will furher assume haκ =. Thus, he firm's inervenion only akes he form of share repurchase. Also, we seτ F =, i.e., he firm is risk neural. These wo assumpions help o simplify he analysis, bu are no criical o he resuls. To simplify noaion, we le κ = κ+.. Equilibrium and Price Behavior We now consider he marke equilibrium in he simple model described above and he resuling sock price. Le p~ denoe he sock price a, afer payoff v ~, = 0, 1, (wih v ~0 = 0 ). No arbirage insures ha he sock price a = is simply 0, i.e., ~ p = 0. A = 1, a liquidiy shock x~ occurs. Boh he marke makers and he firm will aemp o accommodae he liquidiy shock. Their desire o provide liquidiy depends on hree facors: he curren price of he sock, he payoff when hey unload he posiion in he fuure, and heir risk olerance. By assuming ha he payoff nex period is ~v, we are effecively assuming ha he liquidiy providers can unload heir posiions a ~v. The uncerainy in ~v reflecs he risk hey have o bear o make he marke. Theorem 1: A = 1, he equilibrium sock price is ~ ~ * p = σ min x x v τ, () ( ) ( ) 1 M, where x = ( τ / σ ) κ 0. A = 0, he equilibrium sock price is given by M v 10

12 p 0 0 ~ ~ / / [ ~ p1 p1 p e ] Ε [ e ] = Ε (3) 1 0 where Ε [ ] denoes he expecaion a ime 0. From he soluion o he equilibrium, we 0 observe he following. In absence of any liquidiy shock, he sock price a = 1 is also zero, which reflecs he fundamenal value of he sock. Noe ha he expeced payoff of he sock is assumed o be zero. Alhough he realized payoff is risky, marke makers and he firm bear no risk in absence of any liquidiy shocks since heir iniial holdings are zero. Consequenly, he price of he sock is also zero. When here is a liquidiy shock x~, however, marke makers and he firm have o bear he risk of he sock if hey accommodae he shock. Naurally, he price has o adjus o compensae hem for he risk. The price adjusmen depends on he risk of he sock σ v, he size of he shock ~ x and he overall risk olerance of he marke. 13 When he liquidiy shock x ~ is smaller han x, he firm does no inervene and he liquidiy shock is fully absorbed by marke makers. The price is deermined by heir risk olerance. Alhough he sock price deviaes from is fundamenal, he size of he deviaion, given by ( σ / τ ) ~ x, is no large enough o rigger he firm o inervene. v M When he liquidiy shock x ~ is larger han x, however, he price deviaion becomes sufficienly large for he firm o sep in. Given ha he firm is assumed o be risk neural, i will absorb he liquidiy shock alone and he deviaion of he sock price from is fundamenal is limied a he hreshold level ( σ / τ v M ) x. The maximum deviaion is deermined by κ, he firm's inervenion cos. From he equilibrium price process, we obain several properies of he sock's reurns. For simpliciy, we consider he dollar reurns on he sock: ~ r v~ + ~ p ~ p, (4) 1 13 Please see, among ohers, Campbell, Grossman and Wang (1993) and Grossman and Miller (1988) for a more elaborae analysis of his. 11

13 n where = 1,. Le σ ( ) denoe he sock reurn variance over n periods, where n = 1,. Thus, we have 1) [ ~ ] [ ~ σ = Var r = Var r ] and σ ) = Var[ ~ r + ~ r ] ( v ( 1 ( 1 have σ ) = σ, where σ v gives he variance of he fundamenal, and. We hen σ (1) = σ + Var[ ~ ] (5) v p where Var ~ p ] denoes he shor-run price variaion due o liquidiy shocks. In general, [ Var[ ~ p ] depends on he variance of liquidiy shocks σ x, he variance of he fundamenal σ v, he risk olerance of marke makers τ M, and more imporanly he firm s cos of inervenion κ. In paricular, we have he following resul: Proposiion 1: Shor-horizon reurn variance is greaer han long-horizon or fundamenal variance. Conrolling for long-horizon or fundamenal variance, shorhorizon reurn variance increases wih he cos of inervenion κ (i.e. financing consrain), i.e., σ (1) κ > 0. Firms wih lower inervenion cos are likely o paricipae in he marke o suppor is share price. As a resul, we will see less deviaion in is sock price from is fundamenals in response o liquidiy shocks and he shor-horizon sock reurns will exhibi less variance holding fixed fundamenal variance. Given he documened persisence of financing consrains, our empirical analysis uilizes cross-secional firm variaion in he cos of inervenion. The dependen variable is naurally a firm s shor horizon variance and he independen variables are fundamenal variance and he various proxies for a firm s financing consrains. We also include oher conrols, which we deail below. The prediced relaionship from Proposiion 1 is ha all else equal, he higher a firm s financing consrain, he higher is shor-horizon variance conrolling for fundamenal variance. Since he price effecs arise from firms being able o legally execue repurchases in he firs place, in periods or regimes in which repurchases are difficul or illegal, a 1

14 firm s financing consrain under-esimaes he rue cos of inervenion and hence he relaion beween financing consrain measures and firm reurn variances will be weaker during hese periods. Hence our heory predics: Proposiion : The cross-secional relaionship beween financing consrains and reurn variances (conrolling for fundamenal variance) ough o be sronger in he period or regime in which he legal cos of doing repurchases is cheaper. As we deail below, we will es Proposiion using wo sources of exogenous variaion: legal reforms in he Unied Saes hrough ime and cross-secional variaion in legal regimes across an inernaional sample. 3. Daa Our daa on U.S. firms come from he Cener for Research in Securiy Prices (CRSP) and COMPUSTAT. From CRSP, we obain daily and monhly sock reurns, closing sock prices, shares ousanding, and share rading volume for NYSE, AMEX and NASDAQ socks. From COMPUSTAT, we obain annual informaion on a variey of accouning variables. To be included in our sample, a firm mus firs have he requisie financial daa on CRSP and COMPUSTAT. We include only common socks (CRSP iem SHRCD=10 or 11) lised on NYSE / AMEX / NASDAQ. We follow oher sudies of he U.S. marke using marke-o-book raios in excluding firms wih book value less han en million and firms wih one-digi SIC codes of 6, which are in he financialservices indusry. We will calculae long-horizon reurn variances using six-year windows and exclude socks wih less han seveny-wo monhly reurn observaions in he six-year window. Our daa on firms for he oher nine counries come from he COMPUSTAT GLOBAL daabase, which begins in From his daabase, we obain monhly closing prices, dividends, shares ousanding and rading volume, which only allow us o calculae variables such as reurn variances a monhly or lower frequencies. Moreover, we are only able o obain a subse of he accouning variables ha are available in he U.S. Namely, his daabase does no have informaion on sock repurchases nor are we 13

15 able o obain firm age. Forunaely, we do have enough daa o consruc various versions of he Kaplan-Zingales index of financing consrains. A. Reurn Variance Measures For each year, we begin in he U.S. sock marke by calculaing for each sock is cash flow variance (CVAR) according o Cohen, Polk and Vuoleenaho (006) using sixyear windows. Cash flow is measured by he logarihm of ROE - raio of clean-surplus gross earnings ( BE BE 1 + D ) o beginning-of-he-period book equiy ( BE 1 ). 14 Dividend gross D is from COMPUSTAT daa iem 1. Firm i s cash flow variance in year is calculaed using six annual daa from year o +5. This variable is denoed by CVAR i.. We hen calculae for each sock he variance of 3-year log reurns using overlapping six-year windows. For insance, firm i s 3-year reurn variance in 1963 (he firs year for his variable) is calculaed using annual daa from 1963 o Using wo hree-year non-overlapping reurns (i.e. he log reurn from he beginning of 1963 o he end of 1965, he reurn from he beginning of 1966 o he end of 1968), we calculae his 3-year reurn variance and annualize i by dividing i by hree. This variable is denoed by TVAR i. Firm i s 3-year reurn variance in 1964 is calculaed wih he same procedure using daa from 1964 o 1969, and so forh for all he oher years in our sample. The las year ha we can calculae TVAR is 000 since our daase ends in 005. For each observaion of CVAR and TVAR, we hen calculae he corresponding shorer horizon reurn variances. For insance, for firm i in 1963, we calculae he variance of daily reurns (denoed by DVAR i ), weekly reurns (denoed by WVAR i ), monhly reurns (MVAR i ), and quarerly reurns (denoed by QVAR i ), using daa from 1963 o all hese variances are calculaed using non-overlapping reurns and are 14 Book equiy BE is defined as sockholders equiy (COMPUSTAT daa iem 16) plus balance shee deferred axes (COMPUSTAT daa iem 74) and invesmen ax credi (daa iem 08) (if available), plus pos-reiremen benefi liabiliies (daa iem 330) (if available) minus he book value of preferred sock. Depending on availabiliy, we use redempion (daa iem 56), liquidaion (daa iem 10), or par value (daa iem 130) (in ha order) for he book value of preferred sock. If sockholders equiy is unavailable from COMPUSTAT, we measure sockholders equiy as common equiy (daa iem 60) plus he book value of preferred sock. If common equiy is no available, we compue sockholders equiy as he book value of asses (daa iem 6) minus oal liabiliies (daa iem 181), all from COMPUSTAT. 14

16 annualized. We repea he same procedure for 1964 using daa from 1964 o 1969 and so forh for all he oher years in he sample. For he oher nine markes during he period of , we calculae he same individual sock reurn variance measures, excep ha we are unable o calculae any daily or weekly numbers. B. Financing Consrain Proxies Our financial consrain proxies for U.S. companies are he following. The firs financing consrain proxy is REPO/VOLUME, a firm s repurchases (COMPUSTAT Iem 115 minus preferred sock reducion divided by daily dollar volume. Preferred sock reducion is from he firs difference of COMPUSTAT iem 10. We will also consider REPO/MKT, a firm s repurchases divided by marke capializaion. These wo measures follow nicely from our heory since he abiliy of a firm o sabilize is sock price depends boh on how much resources i has relaive o how many shares i migh have o sabilize. Dollar volume and marke capializaion capure he poenial size of liquidiy shocks hiing a firm. We winsorized REPO/VOLUME and REPO/MKT a 1% and 99% level. The resuls are similar when he raw REPO/VOLUME and REPO/MKT are used. Firm AGE is defined as he year ha we are considering minus he firs year ha ha firm has price daa in CRSP monhly reurns file, which sars in 195. Our hird financing consrain proxy is he KZ index. Following Lamon, Polk and Saa-Requejo (001) and Baker, Sein and Wurgler (003), we consruc he fivevariable KZ index for each firm-year as he following linear combinaion: KZ i = CF i /A i DIV i /A i C i /A i BLEV i Q i (6) where CF i /A i-1 is cash flow (Iem 14+Iem 18) over lagged asses (Iem 6); DIV i /A i-1 is cash dividends (Iem 1+Iem 19) over asses; C i /A i-1 is cash balances (Iem 1) over sar-of-he-year book asses (Iem 6); book leverage, denoed by BLEV i, which is oal deb divided by he sum of oal deb and book equiy ((Iem 9+Iem 34)/(Iem 9+Iem 34+Iem 16))---his is measured a fiscal year-end; and Tobin s Q is he marke value of equiy (price imes shares ousanding from CRSP) plus asses minus he book value of 15

17 equiy (Iem 60+Iem 74) all over asses. We winsorize he ingrediens of he index before consrucing i. We will also use a modified version of he KZ index ha differs from he original score in ha i excludes a measure of leverage and Tobin s Q: KZ3 i = CF i /A i DIV i /A i C i /A i-1 (7) KZ3 makes more sense han KZ for our purposes because highly levered firms may have higher shor-horizon volailiy for a given fundamenal volailiy if leverage raios change in a paricular manner over ime and Q may proxy for boh invesmen opporuniies and mis-pricing. To he exen ha we wan o rule ou alernaive explanaions relaed o mechanical leverage effecs and mis-pricing, we will drop leverage and Q from he KZ index. 15 I urns ou ha here is lile difference in our resuls beween using KZ3 or KZ. So we will feaure KZ3 in he main resuls and provide he resuls relaing o KZ in he robusness secion. We view he use of hese proxies as simply an effor o resric ourselves o hese previously nominaed variables, so as o avoid daa mining. The sample period is for REPO/MKT and REPO/VOLUME and is for oher US variables. For inernaional companies, he corresponding daa iem numbers from COMPUSTAT GLOBAL are he following. CF i /A i-1 is cash flow (Iem 11+Iem 3) over lagged asses (Iem 89); DIV i /A i-1 is cash dividends (Iem 36+Iem 35) over asses; C i /A i-1 is cash balances (Iem 60) over sar-of-he-year book asses (Iem 89); book leverage, denoed by BLEV i, is (Iem 106+Iem 94)/(Iem 106+Iem 94+Iem 135); and Tobin s Q is he average marke cap plus asses minus he book value of equiy (Iem 146+Iem 105) all over asses. C. Oher Variables 15 A word of warning regarding cash and leverage as proxies for financing consrains is ha consrained firms should endogenously ry o save more cash (see Almeida, Campello and Weisbach (004)) and perhaps save some deb capaciy for he fuure (hus having lower leverage). Almeida, Campello and Weisbach (004) show ha he KZ index, which loads heavily on cash and leverage, migh sor firms crosssecionally in an uninuiive way. Hence, we wan o also rely on oher, perhaps more exogenous, proxies such as firm age o make inferences. 16

18 The oher variables ha we use are very familiar and do no meri much discussion. LOGSIZE i is he log of firm i s sock-marke capializaion a he end of year. TURNOVER i is he average monhly share urnover in sock i defined as shares raded divided by shares ousanding over year. RET i is he average monhly reurn on sock i, also measured over he 1-monh period. LOGMB i is he log of firm i s marke cap a he end of year divided by is book value in year. We also use marke leverage which is denoed by MLEV i, which is he same as BLEV excep ha we replace Iem 16 wih a firm s marke capializaion a he end of ha calendar year. We can calculae hese variables for U.S. and inernaional companies. We also use exchange dummies downloaded from CRSP. D. Summary Saisics The summary saisics for he variables used in he financing consrains relaed regressions are presened in Table 1. We repor he ime series average of cross-secional means and sandard deviaions. We sar wih he saisics for he U.S. sock marke and hen repor he analogous numbers for he oher counries in urn. We firs presen he saisics for annualized reurn variances a differen horizons. The summary saisics for he oher counries are similar in magniude. We hen presen he summary saisics for our financing consrain proxies. We have checked ha hese saisics are similar o hose found in oher sudies such as Baker, Sein and Wurgler (003). Finally, we presen he summary saisics for he oher variables. 4. Empirical Resuls A. Correlaedness of Financing Consrain Proxies and Likelihood of Iniiaing Repurchase Programs We analyze he relaion beween our financing consrain proxies in Table and heir abiliy o predic repurchases. In Panel A, we calculae he conemporaneous correlaion beween he various proxies in a given year. We find ha older firms and firms wih lower values of KZ s (less consrained) are more likely o have high REPO/VOLUME or REPO/MKT values and older firms are more likely o have lower KZ scores. In oher words, hese financing consrain proxies are correlaed. Mos of 17

19 hese correlaions are saisically significan. The resuls are largely he same regardless of hese differen measures, so we plan o feaure REPO/VOLUME and leave REPO/MKT for he robusness checks. In Panel B, we focus on wha deermines (predics) wheher a firm execues repurchases. While his issue has been covered in previous papers, we jus wan o poin ou ha one can predic repurchases using pas repurchases, firm age and he KZ indices. To his end, we gaher addiional daa on which firms iniiae a sock buy-back program in a given year from he SDC Daabase, which repors for each year he firms ha have obained auhorizaion from heir board o iniiae repurchases. The SDC daa spans he period of The variable REPINITIATE i, equals one if a firm i iniiaes a repurchase program in year and zero oherwise. Abou 14.3% of firms in a given year iniiae a new repurchase program. Imporanly, we find in column (1) of Panel B ha firms wih higher values of REPO/VOLUME in year -1 are more likely o iniiae repurchase programs in year. The coefficien in fron of REPO/VOLUME is wih a -saisic of 7.7. This means ha a wo-sandard increase in REPO/VOLUME leads o an increase in he likelihood of repurchase nex year by abou 0.15 (0.0035xx1.6). Compared o he uncondiional mean probabiliy of iniiaion (which is 0.143), his is a subsanial increase in he probabiliy of iniiaion (over wice as likely). Similarly, in column (), we find ha older firms (AGE) are more likely o iniiae a repurchase program and as are lower KZ3 index value firms (less consrained) (see column (3)). These effecs are also economically sizeable (and of similar magniudes) and saisically significan. In column (4), we do a horse race beween each of hese consrain proxies and find ha each has incremenal forecasing power for repurchases nex year. Indeed, he coefficiens in fron of each of hese hree proxies are fairly similar o wha we obained when we considered each one of hem separaely (in columns (1)-(3)), excep ha he coefficien on AGE is aenuaed (now bu sill saisically significan). In Panel C, raher han using he REPINITIATE as he dependen variable, we use REPO/VOLUME. The resuls are similar. So he resuls in Panels B and C clearly show ha hese financing consrain proxies do predic he likelihood of fuure repurchases and hence verifies he premise of our empirical work. Moreover, we have also separaely 18

20 checked ha hese resuls do indeed hold for he year of 87 crash, which was a paricularly relevan source of anecdoal moivaion for our work. In sum, hese findings are consisen wih he idea ha financially consrained firms are less likely o execue repurchases. B. Reurn Variance and Financing Consrains, U.S. Sock Marke We begin by looking a wheher financially consrained firms have a higher shorhorizon reurn variance conrolling for fundamenal variance (Proposiion 1). To his end, we will implemen he following cross-secional regression specificaion: STVAR i = a 0 + a 1 *CONSTRAINT i-1 + a *CVAR i + a 3 LOGSIZE i-1 + a 4 *MLEV i-1 + a 5 *LOGMB i-1 + a 6 *RET i-1 + a 7 *TURNOVER i-1 + INDUSTRYDUMMIES i-1 + EXCHANGEDUMMIES i-1 + ε i, i=1,,n (8) where STVAR i is shor-horizon reurn variance (including DVAR, WVAR, MVAR, QVAR), and CONSTRAINT is a proxy for he degree o which a firm is financing consrained (including REPO/VOLUME, AGE, and KZ3). CVAR, he variance of reurn on equiy, is a noisy measure of fundamenals. This is an imporan cavea when i comes o inerpreing our findings. We ry o deal wih his using long-horizon reurn variance bu his is no a perfec soluion eiher as we discuss below. Here, ε i sands for a generic error erm ha is uncorrelaed wih all oher independen variables. The coefficien of ineres is a 1, which capures he relaion beween financing consrains and shor-horizon reurn variance conrolling for he firm s fundamenal variance and a hos of oher firm characerisics (LOGSIZE, MLEV, LOGMB, RET, TURNOVER, INDUSTRYDUMMIES and EXCHANGEDUMMIES). 16 We hen ake he esimaes from hese annual regressions and follow Fama and MacBeh (1973) in aking heir ime series means and sandard deviaions o form our overall esimaes of he effecs of financing consrains on he shor-horizon reurn variance The indusry dummies use he Fama and French (1997) 48 indusry classificaion. 17 Insead of having TVAR on he righ hand side, one could have one of he shor-erm variances, e.g. look a how he raio of DVAR (daily variance) o WVAR (weekly variance) varies wih financing consrains. We do no expec o find much since his raio is close o one o begin wih and firms do no inervene a 19

21 In addiion o CVAR which is suggesed by heory, we include MLEV and LOGMB as conrol variables in equaion (8). While hese wo variables are hough of as financing consrain proxies in heir own righ, hey may also affec shor-horizon reurn variance for oher reasons. For insance, highly-levered firms may have a higher shorhorizon reurn variance given is fundamenal variance if a firm s deb-o-equiy raio declines over ime. And high marke-o-book companies may be more volaile because hey are growh socks. As a resul, we ake he conservaive sance in seeing o wha exen our financing consrain proxies hold up even afer conrolling for firm leverage and marke-o-book. In addiion, we include a firm s size, pas reurns and pas urnover as conrol variables. These variables are mean o pick up poenial differences in invesor senimen across firms. The resuls are presened in Table 3. The dependen variable in Panel A is DVAR, he variance of daily reurns. In column (1), he measure of financing consrain is REPO/VOLUME. Noice ha he coefficien in fron of REPO/VOLUME is negaive ( wih a -saisic of.11), which is consisen wih our model. A wo-sandard deviaion increase in REPO/VOLUME leads o a decline in shor-horizon reurn variance of ( xx1.6), which is 1% (-0.03/.47) of he cross-secion sandard deviaion of shor-horizon reurn variance. Noice ha he coefficiens on he conrol variables all come in wih expeced signs (see Chen, Hong and Sein (001)). DVAR increases wih higher fundamenal variance CVAR, firm leverage MLEV, firm marke-o-book LOGMB and sock urnover TURNOVER and decreases wih LOGSIZE and RET. The coefficiens in fron of hese variables are all saisically significan. These coefficiens do no change much as we uilize differen financing consrain proxies in columns ()-(3). The only hing o noe are ha he coefficien in fron of MLEV is no longer significan when we use he KZ3 index as financing consrain proxies. In column (), we consider our second financing consrain proxy, firm age. The coefficien in fron of AGE is negaive and saisically significan. A wo-sandard deviaion increase in firm age lowers DVAR by abou 3% as a fracion of he sandard such shor horizons. We have run hese alernae regressions and found as expeced lile effec of financing consrains in his se-up. 0

22 deviaion of DVAR. In column (3), we consider he KZ3 index in explaining DVAR. The coefficien in fron of KZ3 is posiive and saisically significan---higher KZ3 index firms, which are more financially consrained, end up wih higher reurn variance. A wo-sandard deviaion increase in KZ3 leads o an increase in DVAR ha is 4% of he sandard deviaion of DVAR. In Panel B, we re-run he same regressions bu consider reurn variances a differen horizons, from weekly reurn variance o quarerly reurn variance. We only repor he coefficien in fron of he financing consrain variables for breviy. Noice ha he signs in fron of all he financing consrains all go he righ way and he coefficiens in fron of financing consrain proxies are always saisically and economically significan. A sraighforward calculaion of economic significance in Panel B also indicaes ha he economic magniudes are roughly similar o ha of Panel A. For insance, for weekly reurn variance, he implied economic magniudes are 15% for REPO/VOLUME, 10% for AGE, and 30% for KZ3. In sum, he resuls in Table 3 srongly suppor he firs predicion of our model ha more financially consrained firms end up wih higher shor-horizon reurn variance conrolling for fundamenal variance. C. Relaions beween Financing Consrains and Variances, US Sock Marke Before and Afer Regulaory Reforms of 198 While we can conrol o some degree for firm leverage and oher covariaes, i is impossible o disinguish beween our firm inervenion effec agains oher alernaives wih his approach. As such, we urn o he firs of our wo sources of wha can arguably be deemed as exogenous variaion o beer idenify our heory: he major regulaory reform in he U.S. sock marke in 198 ha encouraged repurchases. Wihou hese variaions, we would no be able o disinguish beween our inervenion sory from a leverage alernaive for financially consrained firms having higher reurn relaive o fundamenal variance. While share repurchases had always been legal in he U.S., companies sill worried abou class-acion lawsuis accusing hem of manipulaing heir sock prices wih repurchases. The passage of he SEC 10b-18 in 198 shielded firms from such lawsuis. This law is aribued by many for he rise of share repurchases since (see, e.g., Grullon and Michaely (00)). Since he price effecs arise from firms being 1

23 able o legally execue repurchases in he firs place, in periods in which repurchases are difficul or illegal, a firm s financing consrain under-esimaes he rue cos of inervenion and hence he relaion beween financing consrain measures and firm reurn variances will be weaker during hese periods. Hence our heory suggess ha he (crosssecional) relaions beween financing consrains and reurn variances ough o be sronger afer 198 when he legal cos of doing repurchases wen down. As we alluded o in he inroducion, our idenificaion sraegy is o consider a difference-in-difference (diff-in-diff) esimae of he effec of financing consrains on shor-run variance conrolling for fundamenal variance. We firs esimae he crosssecional relaion beween consrains and variances (he firs difference) in he difficulo-repurchase regime. We ake for graned ha his relaion may no be due o our inervenion-repurchase hypohesis bu some oher sories. We hen esimae he same relaionship during he easy-o-repurchase regime (he second difference). The difference in hese wo differences is aribued o our inervenion-repurchase effec on he basis ha he oher sories such as leverage risk ough no o vary in such a manner. We are expecing a sronger relaionship in he easy-o-repurchase regime han he difficul-orepurchase regime. To see if his is he case, we ake he regression coefficiens in fron of CONSTRAINT from he annual Fama-MacBeh regressions in Table 3 and regress hese coefficiens on a consan and a dummy variable AFTER8 ha equals 1 if he year is afer 198 and zero oherwise. 18 Since higher values of REPO/VOLUME and AGE should lead o lower variance, we expec ha he coefficiens in fron of hese wo variables should become more negaive afer 198. Since higher values of KZ3 index should lead o higher variance, we expec he coefficiens in fron of KZ3 o become more posiive afer 198. The resuls are presened in Table 4. In Panel A, we repor he resuls for he variance regressions. We firs repor he resuls for he DVAR regressions, hen WVAR, and so on unil QVAR. Noice ha for REPO/VOLUME, he coefficien in fron of AFTER8 is negaive as prediced for each of hese variance regressions. In each case, 18 Our definiion of pos-198 is he firs six year window ( ) during which he dependen variables, he variances, are calculaed. We have also ried skipping from o and he resuls are largely similar.

24 he coefficien in fron of AFTER8 is saisically significan. Moreover, he economic difference is large. Imporanly, he resuls are similar for AGE and KZ3. In each and every case, he resuls are economically and saisically significan---consisen wih our hypohesis, he relaionship beween consrain and variance is much sronger afer 198. In Panel B, we repor diagnosics associaed wih hese diff-in-diff esimaes as suggesed by Berrand, Duflo and Mullainahan (00). The deails of hese diagnosics are given in he Appendix. Bu essenially, we ake he daa (cross-secional regression coefficiens from each year) and randomly shuffle hem and hen re-run he ime series regression in which we pick a break-poin (analog o he AFTER198) ha yields us he same number of observaions before and afer. In oher words, we randomly re-order he daa bu sill preend as if he coefficiens are sill in chronological sequence and run he AFTER8 regression. I is as if he AFTER8 dummy is randomly assigned. If here is rue informaion in he break using he 198 regulaory reform, regression resuls using he re-shuffled daa should be differen from hose in Panel A. Specifically, we conduc 1000 reshuffles. In each ieraion, we generae a coninuous random variable π (any coninuous disribuion will do and we choose uniform disribuion) for each year and sor years ino ascending orders of π. We hen pick a cu-off value so ha years wih π less han he cu-off value are assigned AFTER 8 = 0 and he res of years are assigned AFTER 8 = 1. The cu-off value is chosen so ha he number of years wih AFTER 8 = 1 is he same as ha in he acual esimaion. Noice ha hese pseudo-after8 regressions yield essenially a zero coefficien on average in fron of he AFTER8 dummy. The -saisics are also zero on average. This suggess ha our AFTER8 break is no spurious. Moreover, we can use he saved coefficiens from hese 1000 random shuffles and use he sandard deviaion of hese esimaes o calculae alernaive sandard errors for our coefficiens in Panel A. This is he randomizaion inference in Berrand, Duflo and Mullainahan (00). These - saisics are fairly similar o he -saisics obained in Panel A. We have also conduced addiional analyses o check he robusness of hese findings. These resuls are available on reques from he auhors. We summarize hem 3

25 here for breviy. Firs, we know ha aggregae repurchases increased dramaically direcly as a resul of he 198 regulaory change (Grullon and Michaely (00)). Hence, we could use aggregae repurchases as a proxy for he cos of doing repurchases, i.e. use aggregae repurchases (sum of all dollar repurchases across firms in each year) insead of our AFTER8 dummy in our ime series es. Indeed, his migh make sense if he aggregae level of repurchases capured he slow adopion of repurchases as an inervenion ool afer 198. Bu of course, his is no he only reason for why repurchases increased. Hence, we sill hink i is cleaner o use he AFTER8 dummy in our ime series ess. Noneheless, we ook he ime series of coefficiens in fron of financial consrain and regress hem (OLS) on a consan and he ime series of aggregae repurchases. We find ha he coefficiens in fron of REPO/VOLUME (repurchases called by volume) and AGE become more negaive as aggregae repurchases increase, while he coefficiens in fron of KZ3 become more posiive wih aggregae repurchases. These resuls are consisen wih our AFTER8 ess which show ha he inervenion effec has become sronger as repurchases have been legalized. Moreover, o he exen ha we hink ha he reforms of 198 led o an increase in repurchases, we can insrumen for aggregae repurchases using he AFTER8 dummy. The resuls are very consisen wih hose of he OLS and suppor our inervenion sory becoming more prominen afer 198. In addiion, we re-run our AFTER8 ess by conrolling for he average (crosssecional) cashflow variance (CVAR) each year. Cashflow variances are increasing over ime and migh spuriously lead o our AFTER8 findings o he exen ha hey conribue o higher price volailiy over ime. Since he cashflow variance measures are exogenous in our model, we can conrol for hem on he righ hand side of our AFTER8 ess. Our AFTER8 resuls are fairly robus o including hese conrols. We have also included as conrols he average (cross-secional) price variances each year (e.g., average of MVAR). Our resuls are similar o hose using average CVAR as a conrol. The only cavea for his exercise is ha price volailiy is a dependen variable in our regressions from which we exrac he ime series of coefficiens in fron of our consrain measures, i.e. i is an endogenous variable in our model since our model says repurchases affecs he level of price volailiy. As a resul, including price volailiy 4

26 as a conrol in our AFTER8 ess may be problemaic from an inerpreaional perspecive. D. Inernaional Evidence Bu even ou AFTER8 es has is limiaions. Namely, we canno disinguish our regulaory regime change effec from oher ime rends ha migh also be driving our AFTER8 findings. As such, we nex examine he second source of variaion associaed wih he variaion in he legal ease of repurchases across counries. Survey evidence from Kim, Schremper and Varaiya (004) on sock repurchases across he en larges sock markes, U.S., Japan, U.K., France, Germany, Canada, Ialy, he Neherlands, Swizerland and Hong Kong, sugges ha hese counries can be placed ino hree groups in erms of legal ease of repurchases: easy, medium and difficul. During he period of , he sample of our analysis, he easy group comprises of he U.S., U.K. and Canada, and he difficul group comprises of France and Germany (in which repurchases were basically illegal). 19 The oher five counries in he medium caegory are more heavily regulaed han he U.S. bu repurchases were no illegal during his period. 0 Using he same logic as for he regulaory reforms in he U.S., our heory suggess ha he prediced relaions beween financing consrains and reurn volailiy are sronger in he easy o repurchase group han in he medium difficuly group and sronger in he medium group han in he difficul o repurchase group. To es his predicion, we run a pooled regression of he en counries in our sample analogous o hose in Tables 3 and 4. In running his pooled regression, we allow he effec of each of he conrol variables o vary by counry and he effec of he financing consrain o vary by our hree groups of counries. The regression specificaion is he following: STVAR i = (d 1 *US i + d *CN i + d 3 *UK i + + d 10 *HK i ) + c 1 *CONSTRAINT i-1 *EASY i + c *CONSTRAINT i-1 *MEDIUM i + c 3 *CONSTRAINT i-1 *DIFFICULT i + CVAR i 19 Share repurchases were illegal in France and Germany unil 1998, whereas share repurchases have been legal in US, UK and Canada for a long period of ime. 0 Share repurchases became legal in Japan in 1994, in Swizerland in 199, in Hong Kong in 1991and as for Ialy and he Neherlands, share repurchases were legal by he early nineies. 5

27 *(e 1 *US i + e *CN i + e 3 *UK i + + e 10 *HK i ) + LOGSIZE i-1 *(f 1 *US i + f *CN i + f 3 *UK i + + f 10 *HK i )+ MLEV i-1 *(g 1 *US i + g *CN i + g 3 *UK i + + g 10 *HK i )+ LOGMB i- 1*(h 1 *US i + h *CN i + h 3 *UK i + + h 10 *HK i )+ RET i-1 *(k 1 *US i + k *CN i + k 3 *UK i + + k 10 *HKi)+ TURNOVER i-1 *(m 1 *US i + m *CN i + m 3 *UK i + + m 10 *HK i )+ ε i, (9) where STVAR is one of he shor-erm variance measures, US, CN, UK,, HK are counry dummies, CONSTRAINT is eiher KZ3 or KZ, EASY equals 1 when he counry is US, Canada or UK and zero oherwise, MEDIUM equals 1 when he counry is Japan, Ialy, Swizerland, Neherlands or Hong Kong and zero oherwise, DIFFICULT equals 1 when he counry is Germany or France and zero oherwise. The remaining variables are he same as from he regressions in Tables 3 and 4. 1 The -saisics are Newey-Wes (1987), hough we have also clusered sandard errors a he counry level and found similar resuls. The coefficiens for CONSTRAINT*EASY (c 1 ), CONSTRAINT*MEDIUM (c ) and CONSTRAINT*DIFFICULT (c 3 ) measure he effec of he various financing consrain variables on variance for each of hese hree groups. We hen es ha he coefficien in fron of CONSTRAINT*EASY is greaer han he coefficien in fron of CONSTRAINT*MEDIUM, which is greaer han he coefficien in fron of CONSTRAINT*DIFFICULT. The resuls are repored in Table 5. We do no have a consisen se of repurchase and firm age daa across counries bu are able o consruc he KZ measures and use he laer in our analysis. Panel A repors he resuls for variances. Noice ha for MVAR and QVAR, he effec of consrains on variance is larger in he easy group han he medium group and larger in he medium group han he difficul group. The resuls are no only economically large bu saisically significan. For insance, he coefficien for MVAR on EASYxKZ3 is compared o for MEDIUMxKZ3 compared o for DIFFICULTxKZ3. This ordering is consisen for he oher measures of 1 Indusry dummies are omied from hese regressions because indusry classificaions vary grealy by counry. 6

28 variances. In Panel C below, we find ha his ordering is in fac saisically significan. The resuls for he KZ are given in Panel B. They are similar o hose of KZ3. In Panel C, we repor he upper-bound on he p-value for esing he inequaliies regarding he effec of financing consrains on variances: c 1 > c > c 3. For boh KZ3 and KZ, he prediced inequaliy is saisically significan. In sum, we conclude ha he inernaional evidence is srongly supporive of our second predicion. Finally, in Panel D, we firs randomly reshuffle each counry ino he EASY, MEDIUM and DIFFICULT groups so ha he oal number of counries in each group equals ha in Panels A and B and hen run he regression specificaion in Panels A and B on he reshuffled daa reshuffles are repeaed. Panel D repors he average coefficiens and average Newey-Wes -saisics of EASY x CONSTRAINT, MEDIUM x CONSTRAINT and DIFFICULT x CONSTRAINT in he regressions using he reshuffled daa. Wha we expec is he coefficiens in fron of he various consrain measures for each group o be roughly he same, i.e. we should no see he ordering in he size of he coefficiens across he hree groups of counries as we have in Panels A and B. Indeed, noice ha he coefficien for CONSTRAINT is posiively significan on average across he EASY, MEDIUM and DIFFICULT groups. More imporanly, he coefficiens are roughly he same size across he hree groups of counries (wih he coefficien in he MEDIUM group being slighly larger han he res and he coefficien in he coefficien in he DIFFICULT groups slighly smaller han he res). Since he MEDIUM group has he mos counries and he DIFFICULT group he leas, his means he U.S., U.K. and Canada are now more likely o be in he MEDIUM group and leas likely o be in he DIFFICULT group across he 1000 simulaions. This would explain he sligh differences in coefficiens. The imporan hing o noe is ha he ordering of EASY > MEDIUM > DIFFICULT found in Panels A and B are absen on average using shuffled daa which suggess he findings in Panels A and B are genuinely due o he cu according o ease-of-repurchase. Also repored is he fracion of reshuffles such ha he differences in he coefficien of consrain beween EASY and MEDIUM group and The upper-bound on he p-value is derived in he following manner. Le p denoe he p-value of he join es ha c 1 > c > c 3, which is defined as p=1-prob(c 1 > c and c > c 3 ). The p-value can be rewrien as: p=1-[prob(c 1 > c ) + Prob(c > c 3 )-Prob(c 1 > c or c > c 3 )]=[1- Prob(c 1 > c )]+[1- Prob(c > c 3 )]-1+ Prob(c 1 > c or c > c 3 ). Since Prob(c 1 > c or c > c 3 )-1 is always less han zero, i follows ha p 1-Prob(c 1 > c ) +1- Prob(c > c 3 ). 7

29 beween MEDIUM and DIFFICULT group are larger han hose in panel A and B. This occurs in only less han.5% of he reshuffles which is in line wih he p-values compued in Panel C. E. Robusness Checks In his secion, we perform a number of robusness checks. We begin by aking he baseline regression specificaion in Table 3 and consider a number of permuaions. Firs, here is he worry ha he sandard errors from he Fama-MacBeh regressions are no appropriae. So raher han esimaing i using Fama-MacBeh mehodology, we run a pooled regression and cluser he sandard errors by boh firm and ime as in Thompson (006). The righ hand side variables are he same as in Table 3 excep wih he addiion of year dummies. The resuls are repored in Panel A. They are similar o hose in Table 3 and he -saisics are if anyhing larger. This alleviaes any concerns regarding saisical inference for our resuls. Indeed, we have also re-calculaed he sandard errors for our cross-counry regressions using boh clusering by counry and Thompson sandard errors and our resuls are sill significan. These resuls are available on reques from he auhors. Nex, in Panel B, we work wih log of he variances raher han he level of he variances hemselves. In oher words, we ake he logs of DVAR, WVAR, MVAR, QVAR, and CVAR and hen re-run he regressions using logs of variances everywhere here is a level for he variances. Working wih logs can alleviae concerns abou ouliers and gives us a sense of robusness o funcional forms. The resuls are similar o hose in Table 3. In Panel C, we use hree-year sock reurn variance insead of he cashflow variance (CVAR) as a conrol. The resuls are also similar o hose in Table 3. In Panel D, we look a he behavior of he wo oher measures of financing consrains, REPO/MKT insead of REPO/VOLUME and KZ insead of KZ3. For breviy, we only repor he resuls analogous o hose in Table 4, which looks a he relaionship beween hese consrain measures and variance before and afer he regulaory reforms of 198. The resuls are largely similar o hose in Table 4. 8

30 In Panels E and F, we apply he robusness checks using he log specificaion and replacing CVAR wih TVAR o he inernaional regression specificaion of Table 5. Again, he resuls are similar and very robus. F. Reurn Skewness and Financing Consrains, U.S. Sock Marke In sum, our inernaional evidence helps buress he AFTER8 evidence and hese wo findings in sum srongly disinguish our inervenion hypohesis from oher alernaives. Here, we ry o make our case even sronger by esing an addiional predicion regarding reurn skewness and financial consrains. Under he assumpion ha repurchases are more likely o be affeced by financing consrains as opposed o issuances (e.g., κ = in he model), we ge an addiional esable implicaion, which is ha financially unconsrained firms should have more posiively skewed reurns. Before presening our resuls, we noe ha he reasonableness of his assumpion depends on horizons. A shor horizons, i would be difficul for firms o sabilize equiy prices using issuances. In conras, firms wih more capaciy o repurchase shares quickly afer a marke crash (e.g. crash of 1987) should have more posiively skewed shorhorizon reurns. A long horizons, when here is poenially buil up demand for a sock, even financially consrained firms can issue equiy o ake advanage of high prices. And so we would no expec here o be any skewness implicaions a long horizons. This is an ineresing empirical quesion and confirmaion of a relaion beween reurn skewness and financial consrains would furher help make our case. We have he following resul: Proposiion 3: Reurn skewness is higher for less financially consrained firms. Also, his relaion should be sronger afer 198 han before. To es his proposiion, we firs define and consruc daily skewness measures. We focus our analysis on daily reurn skewness since we know from exising work (see, e.g., Chen, Hong and Sein (1998)) ha here is lile skewness in reurns a longer horizons because of he law of large numbers. Following Chen, Hong and Sein (001), our measure of daily reurn skewness, which we denoe DSKEW i, is calculaed by aking he sample analog o he hird 9

31 momen of daily (raw) reurns, and dividing i by he sample analog o he sandard deviaion of daily reurns raised o he hird power. These daily reurns are, more precisely, acually log changes in price and dividend. We use log changes as opposed o simple daily percenage reurns because hey allow for a naural benchmark if sock reurns were lognormally disribued, hen an DSKEW measure based on log changes should have a mean of zero. Scaling he raw hird momen by he sandard deviaion cubed allows for comparisons across socks wih differen variances; his is he usual normalizaion for skewness saisics. 3 We nex look a wheher financially consrained firms also have less posiively skewed reurns (Proposiion 3). To his end, we will implemen he following crosssecional regression specificaion from Chen, Hong and Sein (001): DSKEW i = b 0 + b 1 *CONSTRAINT i-1 + b *LOGSIZE i-1 + b 3 MLEV i-1 + b 4 *LOGMB i-1 + b 5 *RET i-1 + b 6 *TURNOVER i-1 + INDUSTRYDUMMIES i-1 + EXCHANGEDUMMIES i-1 + ε i, i=1,,n (10) where CONSTRAINT is a proxy for he degree o which a firm is financing consrained. Here, ε i again sands for a generic error erm ha is uncorrelaed wih all oher independen variables. The coefficien of ineres is b 1, which capures he relaion beween financing consrains and reurn skewness conrolling for a hos of oher firm characerisics (MLEV, LOGSIZE, LOGMB, RET, TURNOVER, INDUSTRYDUMMIES, and EXCHANGEDUMMIES). The specificaion in (10) is similar o ha of Chen, Hong and Sein (001) excep for he financing consrain proxies. 4 We hen ake he esimaes from hese annual regressions and follow Fama and MacBeh (1973) in aking heir ime series means and sandard deviaions o form our overall esimaes of he effecs of financing consrains on shor-horizon reurn skewness. The resuls are presened in Table 7. The dependen variable in Panel A is DSKEW, he skewness of daily reurns. In column (1), he measure of financing 3 See, e.g., Greene (1993). 4 We have also ried adding lagged skewness as a conrol variable as in Chen, Hong and Sein and find ha he resuls are unchanged. So we say wih he more parsimonious specificaion above. We have also included firm volailiy conrols and he resuls are similar o hose repored here. 30

32 consrain is REPO/VOLUME. The coefficien in fron of REPO/VOLUME is of he righ sign (0.0014) and saisically significan (wih a -saisic of 3.43). A wo-sandard deviaion movemen in REPO/VOLUME leads o an increase in firm reurn skewness ha is abou 7.4% of he sandard deviaion of DSKEW (which in our sample is 0.8). Moreover, he coefficiens on he conrol variables all come in wih expeced signs as found in Chen, Hong and Sein (001): DSKEW becomes more negaive wih firm size, firm leverage, firm marke-o-book LOGMB, pas reurns RET and sock urnover. In column (), we consider our second financing consrain proxy, firm age. The coefficien in fron of AGE is posiive and of he righ sign and bu is imprecisely measured. However, a wo-sandard deviaion increase in firm age increases DSKEW by abou 4.% as a fracion of he sandard deviaion of DSKEW, which is comparable o he economic effec from REPO/VOLUME. In column (3), we look a he effec of KZ3 on DSKEW. The coefficien is of he righ sign ( ) and saisically significan (wih a -saisic of.47). The economic effec is a sizeable implied movemen in DSKEW of 7.3% as a fracion of he sandard deviaion of DSKEW. In sum, he evidence is in suppor of Proposiion 3. All he coefficiens are of he prediced sign and have ineresing economic effecs hough one of our hree measures is imprecisely measured. This is perhaps no oo surprising given ha skewness is nooriously difficul o measure. In Panel B, we perform he same AFTER8 es now for skewness insead of volailiy. The logic is he same: o he exen ha repurchases were easier afer 198, we should expec our prediced relaionships o be sronger afer 198 han before. This is indeed wha we find. For all hree financing consrain measures, he relaionship beween financing consrains and reurn skewness is much sronger afer 198. This difference is saisically significan for wo of he hree measures (REPO/VOLUME and KZ3). We hink ha Panel B srongly suppors Proposiion 3 and buresses our firm inervenion hypohesis. 5. Conclusion 31

33 Moivaed by subsanial evidence ha firms are buyers-of-las resor for heir own socks, we develop a model o explore he effecs of such firm inervenion on sock reurns. Our model generaes wo key predicions. Those wih more abiliy o repurchase shares should prices drop far below fundamenal value (less financially consrained ones) should have lower shor-horizon reurn variance han oher firms conrolling for fundamenal variance. Second, his relaion is sronger in regimes in which i is legally easier o conduc repurchases. Using sandard proxies for financing consrains such as firm payou raios, firm age and he Kaplan-Zingales index, we find srong suppor for boh of hese predicions. There is an analogy of firms being buyers of las resor for heir own socks o cenral banks being lenders of las resor for heir economies. Moreover, we may be under-appreciaing he macroeconomic significance of coordinaed firm inervenion as winessed by he evens of he Crash of 1987 and he evens of Sepember 11. As such, here can also be heoreical inquires ino he role of such firm inervenion along he lines of he vas lieraure on lenders of las resor. Much more work can be done on he opic of firms as buyers of las resor for heir own sock and firm inervenion in markes more generally. 3

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37 Appendix Soluion o Equilibrium We firs solve for he equilibrium a dae 1 and 0 recursively. Le θ M and θ F denoe he sock holding a dae 1. The opimizaion problem of a marke maker is given by ~ ~ θm ( vv p1 )/ τm max E 1 [ e ]. θm The soluion is θ ( / )( ~ M = τ M σ v p1). The opimizaion problem of he firm is given by ~ ~ θ F ( vv p1 ) / τ F max E 1 [ e ]. θ F 0 The soluion is ( τ ~ ~ F / σ v )( p1 κ), p1 < κ θ F = 0, oherwise The marke clearing condiion requires ha µθ M + θ ~ F = x which leads o he equilibrium price: σ v + x x ~ ~ κ ( ~ τ x x M τ ), F p1 = σ v ~ x ~ τ x < x M, where x = ( τ M / σ v ) κ. In he limi of τ F, we have ~ ~ σ v τ x, x x M ( ) min( ~ 1, p = = σ x x ). ~, ~ v τ σ M v τ x x < x M Now le us consider he equilibrium a dae 0. Only marke makers are presen hen. Le θ M 0 denoe a marke maker's sock holding a dae 0. His opimizaion problem is ~ 1 ( ~ θ M 0 ( p1 p0 ) / τ M p1 ) σ max v E 0 e. θm 0 Since θ M 0 = 0 in equilibrium, from he opimaliy condiion for θ M 0 we obain Equaion (3) for he equilibrium sock price a 0. Proof of Proposiion 1 Wihou loss of generaliy, we se σ x = 1. Le mk denoe he k -h momen of ~ p 1 : [ ~ ] ( 1) ( k k k / ) [{ min ( ~ k m k E p = σ, *)} 1 v τ M E x x ]. Give ha ~ x is a sandard normal, we have 36

38 and m m 1 = = dm1 [1 N( x*)], dx * = 1 e π x* 1 x n( x) dx + x* x *[1 N ( x*)] x* x * n( x) dx dm x *[1 N( x*)], dx * = dx * v dκ = σ / τ M. ~ r is given by ( ) ). The variance of reurn 1 [ ~ [ ~ σ (1) Var r1 ] = Var v1 + p1] = σ v + σ v / τ M ( m m We have dσ (1) = ( σ v / τ M ) [1 N( x*)]( x * + m1 ) 0. dκ Since σ ) = σ, Proposiion 1 follows. ( v Proof of Proposiion 3 Le s denoe he skewness of he sock reurn. The skewness of reurn ~ r = v~ + ~ p p is [( ~ [ ~ 3 ] [( ~ [ ~ 3 3 r E r ]) = E p E p ]) ] = m3 3mm1 1. s E m Then, i is easy o show ha ds = 3[1 N( κ)][( κ + m1 ) ( m m1 )]. dκ For κ =, m 3 = 0 and ds / dk < 0. Thus, for κ sufficienly large, s is posiive and decreases wih κ as saed in Proposiion

39 Randomized inference for US. We wan o es he null hypohesis ha he AFTER8 effec c 1 is 0 in ˆ β = c0 + c1 AFTER8 + η The dummy AFTER8 (1 if he year of he cross-secional regression is afer 198 and 0 oherwise) is assumed o be independen of η. βˆ is he coefficien in fron of consrain in he cross-secional regression of year, STVAR = X β + ε STVAR is a vecor of reurn variances for various socks, X is a marix of regressors. The Newey-Wes (1987) -saisics in he Panel A of Table 4 allows for auo-correlaions of finie lags for η. The persisence in volailiy can imply η is auo-correlaed a all lags. This can arise for example if ε = φ + ω The vecor φ capures a persisen shock o he reurn variances of differen socks. ω is ' ' assumed o be i.i.d. across ime. In his case, leing ( ) coefficien ˆ β = β + M ( φ + ω ) M 1 = X X X, he linear regression ( φ + ω ) = c0 + c1 AFTER8 + M This creaes persisence a all lags. Such persisence, ogeher wih he cross-secional correlaion of volailiy, is difficul o deal wih using ypical mehods of inference. We use a randomized inference procedure o calculae an alernaive -saisic robus o such persisence. To begin, noice ha under he null of = 1 0 ˆ β = c 0 + M φ + ω has he same marginal disribuion across year as long as M is saionary. Furher, leing and denoe he firs and las years in he sample, he join disribuion of ( ˆ β, ˆ β ˆ + 1,..., β ) remains he same if he ime indices are reshuffled as long as he join disribuion of ( M, M + 1,..., M ) remains he same afer reshuffling of he years. This includes bu is no resriced o he case where M is i.i.d. or highly persisen (e.g., M = m + ξ where ξ is i.i.d. across ime). As a resul, if we reshuffle he ime index, he resuling esimaor of c 1 will have he same disribuion as he esimaor using he unshuffled daa under he null, as long as he number of years wih AFTER 8 being 0 or 1 equal ha in he un-shuffled daa. If we conduc a simulaion by randomly shuffling years, he resuling esimaor c 1 using shuffled daa will race ou he disribuion of he c, ( ) esimaor using he un-shuffled daa. We will use he sandard deviaion of he c 1 esimaes using shuffled daa o calculae an alernaive -saisic valid in small samples ha is robus o severe auo-correlaion of sock reurn variances ˆ ˆ c1 = Sd. Dev. ( unshuffled daa) ( cˆ ( shuffled daa) ) 1 38

40 Such randomized inference is robus o oher ypes of auo-correlaions. For example, ε = σ φ + ω where he i.i.d. variable σ capures he ime variaion of he sensiiviy of ε o he persisen variable φ. This can arise if he marke incorporaes informaion in φ differenly a differen poins in ime as in Hong, Sein and Yu (006). One can easily verify ha he previous analysis holds under his seup. Similarly, he randomized inference allows he regressor o have ime-varying sensiiviy o is persisen componen, e.g. M = σ m + ξ. The randomized inference also holds in he special case when φ = 0 (no persisence) which reduces o he randomized inference mehod in Berrand, Duflo and Mullainahan (00). To generae re-shuffled years in he simulaion, we generae a coninuous random variable π (any coninuous disribuion will do and we choose uniform disribuion) for each year and sor years ino ascending orders of π. We hen pick a cu-off value so ha years wih π less han he cu-off value are assigned AFTER 8 = 0 and he res of years are assigned AFTER 8 = 1. The cu-off value is chosen so ha he number of years wih AFTER 8 = 1 is he same as ha in he acual esimaion reshuffles are repeaed and we use he sandard deviaion of he 1000 esimaes from he reshuffled daa as an alernaive measure of he sandard error for he acual esimae. Randomized inference - Inernaional evidence We conduc a simulaion of 1000 ieraions. In each ieraion, we randomly reshuffle he 10 counries ino he EASY, MEDIUM, and DIFFICULT groups such ha he number of counries in each group coincides wih ha in he acual esimaion (3 counries in EASY group, 5 counries in MEDIUM group and counries in DIFFICULT group). Specifically, we generae a coninuous random variable π (any coninuous disribuion will do and we chose uniform disribuion) for each counry and sor counries ino ascending orders of π. The firs 3 counries are classified as EASY, he nex 5 counries are classified as MEDIUM, and he las counries are classified as DIFFICULT. We hen run he pooled inernaional regression using he randomly assigned ease-ofrepurchase groups. We calculae he fracion of simulaion oucomes in which c1 c and c c3 exceed hose in he acual esimaion. 39

41 Table 1: Summary Saisics This able repors various ime-series averages of cross-secional means and sandard deviaions. Reurn variances a various horizons include DVAR (daily), WVAR (weekly), MVAR (monhly), QVAR (quarerly) and TVAR (hree-year). CVAR is he cash-flow variance. REPO/VOLUME is firm repurchases o daily dollar rading volume. REPO/MKT is firm repurchases o marke capializaion. AGE is he number of years a sock has price daa in CRSP monhly file which sars in 195. KZ is he Kaplan-Zingales index of financing consrains and KZ3 is he KZ index ne of book leverage and firm marke-o-book raio. LOGSIZE is log marke capializaion. TURNOVER is monhly urnover. RET is average monhly reurn in a year. LOGMB is log marke-o-book raio. MLEV is marke leverage. US daa are from for REPO/VOLUME and REPO/MKT and from for oher variables. All oher counries are from US UK Canada Germany France Mean Sd Dev Mean Sd Dev Mean Sd Dev Mean Sd Dev Mean Sd Dev Annualized reurn variance DVAR WVAR MVAR QVAR TVAR CVAR Financing consrain measure REPO/VOLUME REPO/MKT AGE KZ KZ Oher LOGSIZE TURNOVER RET LOGMB MLEV

42 Japan Ialy Swizerland Neherland HongKong Mean Sd Dev Mean Sd Dev Mean Sd Dev Mean Sd Dev Mean Sd Dev Annualized reurn variance DVAR WVAR MVAR QVAR TVAR CVAR Financing consrain measure REPO/VOLUME REPO/MKT AGE KZ KZ Oher LOGSIZE TURNOVER RET LOGMB MLEV

43 Table : Correlaedness of Financing Consrain Proxies, U.S. Sock Marke This able repors he resuls of he correlaion of he various financing consrain proxies. Panel A repors he imeseries average of he cross-secional correlaion marix for he five financing consrain proxies, along wih he Newey- Wes (1987) -saisics in he parenheses. Panel B repors he resuls of Fama-MacBeh regressions of REPINITIATE (a dummy variable ha equals 1 if a firm iniiaed a repurchase program in a given year and zero oherwise) on previous year values of REPO/VOLUME, AGE and KZ3. Panel C repors he resuls of Fama-MacBeh regression of REPO/VOLUME on previous year values of REPO/VOLUME, AGE and KZ3. The regressions in panels B-C include Fama-French (1997) indusry dummies. Newey-Wes (1987) -saisics are in he parenheses. Panel A: Correlaion marix REPO/VOLUME REPO/MKT AGE KZ3 KZ REPO/VOLUME 1 REPO/MKT 0.77 (95.74) 1 AGE (1.96) (9.63) 1 KZ (1.10) (0.36) (11.11) 1 KZ (3.45) (1.95) (13.6) (14.77) 1 Panel B: Dependen Variable is indicaor of share repurchase auhorizaion (REPINITIATE) REPO/VOLUME REPINITIATE (1) REPINITIATE () REPINITIATE (3) REPINITIATE (4) (7.7) (6.91) AGE (10.65) (8.16) KZ (30.9) (18.11) Consan (4.06) (3.61) (3.99) (3.0) Panel C: Dependen Variable is firm repurchases o daily dollar rading volume (REPO/VOLUME) REPO/VOLUME (1) REPO/VOLUME () REPO/VOLUME (3) REPO/VOLUME (4) REPO/VOLUME (6.17) (5.3) AGE (1.66) (0.33) KZ (0.69) (0.4) Consan (.68) (.48) (.47) (.9) 4

44 Table 3: Sock Reurn Variance and Financing Consrain, U.S. Sock Marke This able repors he Fama-MacBeh regression resuls of reurn variances a various horizons on financing consrain measures. Reurn variances a various horizons include DVAR (daily), WVAR (weekly), MVAR (monhly) and QVAR (quarerly). CONSTRAINT is given by he following hree financing consrain proxies. REPO/VOLUME is firm repurchases o daily dollar rading volume. AGE is he number of years a sock has price daa in CRSP monhly file which sars in 195. KZ3 is he Kaplan-Zingales index of financing consrains ne of book leverage and firm marke-o-book raio. CVAR is cash-flow variance. LOGSIZE is log marke capializaion. MLEV is marke leverage. LOGMB is log marke-o-book raio. RET is average monhly reurn in a year. TURNOVER is monhly urnover. The regressions include Fama-French (1997) indusry dummies and exchange dummies for NASDAQ and AMEX. The sample period is for REPO/VOLUME and for AGE and KZ3. Newey-Wes (1987) -saisics are in he parenheses. Panel A: Dependen variable is daily reurn variance (DVAR) REPO/VOLUME (1) AGE () KZ3 (3) CONSTRAINT (.11) (.38) (7.91) CVAR (1.38) (9.98) (9.0) LOGSIZE (4.01) (3.37) (3.5) MLEV (.77) (3.) (0.65) LOGMB (.31) (3.7) (3.65) RET (5.4) (5.67) (6.49) TURNOVER (.75) (3.16) (3.13) Panel B: Coefficien in fron of CONSTRAINT from regressions in which he dependen variables are weekly reurn variance (WVAR), monhly reurn variance (MVAR), and quarerly reurn variance (QVAR) REPO/VOLUME (1) AGE () KZ3 (3) WVAR (.18) (.7) (9.68) MVAR (.13) (.6) (8.58) QVAR (.0) (3.33) (11.78) 43

45 Table 4: The Relaion beween Reurn Variances and Financing Consrains in he U.S. Sock Marke, Before and Afer he Regulaory Reforms of 198 Panel A of his able repors he resuls of a ime-series regression using he coefficiens in fron of CONSTRAINT from he annual cross-secional regressions in Table 3. These coefficiens are regressed on a consan and a dummy variable AFTER8 ha equals one if he year of he cross-secional regression is afer 198 and zero oherwise. Newey-Wes (1987) -saisics wih welve lags are in parenheses. In Panel B, he AFTER8 dummy is firs randomly assigned o be 0 or 1 so ha he oal number of years wih AFTER8=1 equals ha in panel A and hen run he regression specificaion in panel A. This reshuffle of he AFTER8 dummy is repeaed 1000 imes. Panel B repors he average of he regression coefficien in fron of AFTER8 and he average of is Newey-Wes -saisics across he 1000 reshuffles. Also repored in panel B is an alernaive -saisics of he AFTER8 esimae in panel A using he sandard deviaion of he 1000 esimaes in he regressions of reshuffled daa o measure he sandard error. Panel A. US sock marke before and afer he regulaory reforms of 198 Panel B. Randomized Inference REPO/VOLUME (1) AGE () KZ3 (3) DVAR Consan (5.36) (1.01) (6.60) AFTER (.71) (1.99) (3.8) WVAR Consan (11.58) (3.10) (7.31) AFTER (.39) (.8) (3.4) MVAR Consan (8.61) (3.79) (7.3) AFTER (.31) (.59) (3.31) QVAR Consan (6.03) (7.00) (6.91) AFTER (.44) (.58) (.1) REPO/VOLUME (1) DVAR Average AFTER8.70E E Average (AFTER8) AFTER8 in Panel A / Sd Dev(AFTER8) (.85) (.19) (3.91) WVAR Average AFTER8 1.78E E E-05 Average (AFTER8) AFTER8 in Panel A / Sd Dev(AFTER8) (.71) (3.9) (3.84) MVAR Average AFTER8 1.89E E-06.13E-05 Average (AFTER8) AFTER8 in Panel A / Sd Dev(AFTER8) (.76) (3.78) (3.79) QVAR Average AFTER8 8.34E E E-06 Average (AFTER8) AFTER8 in Panel A / Sd Dev(AFTER8) (.8) (3.5) (.33) AGE () KZ3 (3) 44

46 Table 5: Relaion Beween Reurn Variances and Financing Consrains, Inernaional Evidence This able repors he resuls of pooled regressions of reurn variances on financing consrain measures KZ3 and KZ using all sock markes during he period of These regressions are analogous o hose in Table 3 and Table 4 excep ha he regressions are pooled and we allow he effec of each of he conrol variables (LOGSIZE, TURNOVER, RET, LOGMB, MLEV) o vary by counry (US, Canada, UK, Germany, France, Japan, Ialy, Swizerland, Neherlands, Hong Kong) and he effec of he financing consrain variables (KZ3 and KZ) o vary by ease-of-repurchase counry groups (EASY which includes US, Canada and UK, DIFFICULT which includes Germany and France, and MEDIUM which includes he remaining counries). The regressions include counry and year dummies. We only repor he coefficiens in fron of EASY x CONSTRAINT, MEDIUM x CONSTRAINT and DIFFICULT x CONSTRAINT. Panel A repors he resuls for KZ3 and B repors he resuls for KZ. Newey-Wes (1987) -saisics are repored in he parenheses. Panel C repors he upper bound of he p-value of he join es ha he coefficien in fron of EASY x CONSTRAINT is greaer han he coefficien in fron of MEDIUM x CONSTRAINT is greaer han he coefficien in fron of DIFFICULT x CONSTRAINT. Panel D firs randomly reshuffles each counry ino he EASY, MEDIUM and DIFFICULT groups so ha he oal number of counries in each group equals ha in panel A and B and hen run he regression specificaion in panel A and B on he reshuffled daa reshuffles are repeaed. Panel D repors he average coefficiens and average Newey-Wes -saisics of EASY x CONSTRAINT, MEDIUM x CONSTRAINT and DIFFICULT x CONSTRAINT in he regressions using he reshuffled daa. Also repored is he fracion of reshuffles such ha he differences in he coefficiens of consrain beween EASY and MEDIUM group and beween MEDIUM and DIFFICULT group are larger han hose in Panels A and B. Panel A: Resuls for KZ3 MVAR (1) QVAR () EASY x KZ (7.30) (6.8) MEDIUM x KZ (1.57) (1.07) DIFFICULT x KZ (1.8) (1.96) Panel B: Resuls for KZ MVAR (1) QVAR () EASY x KZ (8.31) (7.91) MEDIUM x KZ (1.61) (1.11) DIFFICULT x KZ (1.66) (1.86) Panel C: Upper bound of he p-value of he join es ha he financing consrain effec is sronger in easier o repurchase counries MVAR (1) QVAR () KZ KZ

47 Panel D. Randomized Inference MVAR (1) QVAR () KZ3 Average coef (EASY x KZ3) Average coef (MEDIUM x KZ3) Average coef (DIFFICULT x KZ3) Average (EASY x KZ3) Average (MEDIUM x KZ3) Average (DIFFICULT x KZ3) Fracion EASY-MED>Panel A & MED-DIFF>Panel A KZ Average coef (EASY x KZ) Average coef (MEDIUM x KZ) Average coef (DIFFICULT x KZ) Average (EASY x KZ) Average (MEDIUM x KZ) Average (DIFFICULT x KZ) Fracion EASY-MED>Panel A & MED-DIFF>Panel A

48 Table 6: Robusness Checks This able repors various robusness check resuls. Panel A repors he pooled regression analog o he resuls in Table 3 wih he excepion of including year dummies in he regression. The sample period is for REPO/VOLUME, is for AGE and KZ3. The coefficiens in fron of CONSTRAINT in hese pooled regressions are repored in Panel A. The -saisics in he parenheses are adjused for heeroskedasiciy and correlaion using Thompson (006). Panel B and Panel E repea he regressions in Table 3 and Table 5 using he log insead of he level of he cash-flow variance CVAR and sock reurn variances. Panel C and panel F repea he regressions in Table 3 and Table 5, excep ha he cash flow variance is replaced by hree-year sock reurn variance. Panel D repeas he regression in Panel A of Table 4 using REPO/MKT and KZ as proxies of consrain. Panel A. Coefficien in fron of CONSTRAINT in pooled regressions of sock reurn variance on financing consrain Panel B. Log specificaion Panel C. Three-year variance REPO/VOLUME (1) AGE () KZ3 (3) DVAR (3.95) (0.94) (11.6) WVAR (4.03) (3.8) (15.1) MVAR (3.94) (4.4) (13.86) QVAR (3.80) (4.8) (13.38) REPO/VOLUME (1) AGE () KZ3 (3) DVAR (3.09) (3.60) (17.68) WVAR (.91) (3.77) (0.) MVAR (.83) (4.08) (18.96) QVAR (.84) (5.10) (19.31) REPO/VOLUME (1) AGE () KZ3 (3) DVAR (.05) (1.3) (8.10) WVAR (.14) (.44) (9.17) MVAR (.06) (.59) (7.35) QVAR (.1) (3.45) (9.7) Panel D. US sock marke before and afer he regulaory reforms of 198 (REPO/MKT and KZ) REPO/MKT (1) KZ () DVAR Consan (3.46) (6.40) AFTER (.84) (4.18) 47

49 Panel E. Inernaional evidence Log specificaion WVAR Consan (8.46) (7.09) AFTER (.61) (.91) MVAR Consan (5.4) (7.6) AFTER (.65) (.99) QVAR Consan (4.9) (6.74) AFTER (3.08) (.00) MVAR (1) QVAR () KZ3 EASYxKZ (1.86) (1.48) MEDIUMxKZ (1.07) (0.9) DIFFICULTxKZ (3.35) (3.45) KZ EASYxKZ (13.60) (13.5) MEDIUMxKZ (1.06) (0.8) DIFFICULTxKZ (.91) (.94) Panel F. Inernaional evidence Three-year variance MVAR (1) QVAR () KZ3 EASYxKZ (6.77) (6.06) MEDIUMxKZ (3.1) (.7) DIFFICULTxKZ (1.87) (.14) KZ EASYxKZ (7.78) (7.13) MEDIUMxKZ (3.3) (.73) DIFFICULTxKZ (1.70) (.05) 48

50 Table 7: Sock Reurn Skewness and Financing Consrain, U.S. Sock Marke Panel A of his able repors he Fama-MacBeh regression resuls of daily sock reurn skewness on financing consrain measures. CONSTRAINT is given by he following hree financing consrain proxies. REPO/VOLUME is firm repurchases o daily dollar rading volume. AGE is he number of years a sock has price daa in CRSP monhly file which sars in 195. KZ3 is he Kaplan-Zingales index of financing consrains ne of book leverage and firm marke-o-book raio. LOGSIZE is log marke capializaion. MLEV is marke leverage. LOGMB is log marke-obook raio. RET is average monhly reurn in a year. TURNOVER is monhly urnover. The regressions include Fama- French (1997) indusry dummies and exchange dummies for NASDAQ and AMEX. The sample period is for REPO/VOLUME and for AGE and KZ3. Newey-Wes (1987) -saisics are in he parenheses. Panel B of his able repors he resuls of a ime-series regression using he coefficiens in fron of CONSTRAINT in Panel A. These coefficiens are regressed on a consan and a dummy variable AFTER8 ha equals one if he year of he crosssecional regression is afer 198 and zero oherwise. Newey-Wes (1987) -saisics wih welve lags are in parenheses. Panel A: Reurn skewness and financing consrain REPO/VOLUME (1) AGE () KZ3 (3) CONSTRAINT (3.43) (0.76) (.47) LOGSIZE (6.1) (4.80) (4.75) MLEV (4.51) (.88) (0.18) LOGMB (.11) (3.67) (3.07) RET (6.35) (8.40) (6.0) TURNOVER (3.57) (.77) (3.14) Panel B: US sock marke before and afer he regulaory reforms of 198 REPO/VOLUME (1) AGE () KZ3 (3) DSKEW Consan (.94) (0.87) (.38) AFTER (.15) (0.36) (.84) 49