Closed-End Fund Discounts with Informed Ownership Differential

Transcription

1 Closed-End Fund Discouns wih Informed Ownership Differenial By Gusavo Grullon Jesse H. Jones Graduae School of Managemen Rice Universiy MS 53 Houson, TX (73) (Phone) (73) (Fax) hp:// and F. Alber Wang Jesse H. Jones Graduae School of Managemen Rice Universiy MS 53 Houson, TX (73) (Phone) (73) (Fax) hp:// Firs Version: May 998 This Version: February 00 We are graeful o Bill Chrisie, Jeff Poniff, Andrei Shleifer, Richard Thaler and wo anonymous referees for insighful commens, and conference paricipans a he h Annual Conference on Financial Economics and Accouning, and he nd Texas Finance Fesival for helpful suggesions. We also hank Jeff Fleming, Dave Ikenberry and George Kanaas for helpful discussions. Raul Gonzalez provided excellen assisance wih daa collecion. We also acknowledge he help of I/B/E/S Inernaional Inc. for providing earnings forecas daa. The usual cavea applies.

2 Closed-End Fund Discouns wih Informed Ownership Differenial Absrac We develop a muli-asse rading model o examine he closed-end fund discoun. The model shows ha he discoun can arise if he qualiy of privae informaion in he underlying asses is sufficienly beer han in he fund. The model also indicaes ha a discoun (premium) can arise if he excessive volailiy of he fund dominaes (is dominaed by) he fund s diversificaion benefi. Moreover, he model predics a negaive relaion beween he discoun and he insiuional ownership differenial, as arbirageurs prefer funds wih large discouns. Using a sample of US equiy closed-end funds, we es hese predicions and find supporing evidence. JEL Code: D8, G0, G, G4 Key Words: closed-end fund discoun, asymmeric informaion, informed ownership, anomaly, asse pricing.

3 Closed-End Fund Discouns wih Informed Ownership Differenial The closed-end fund puzzle is one of he mos ineresing anomalies in finance. Unlike heir open-end brehren, closed-end funds do no allow invesors o redeem heir shares a he fund s ne asse value (henceforh NAV). Insead, closed-end funds rade publicly on he secondary markes wih a fixed number of ousanding shares. Hence, he price of a closed-end fund is subec o he supply and demand of he shares by invesors in he marke. Ofen, he price is no he same as he fund s NAV. A sysemaic deviaion of he fund price from is NAV appears o be a odds wih radiional views of he efficien markes hypohesis, which saes ha price is equal o inrinsic value. In his paper, we develop and es a simple heoreical model wih an emphasis on asymmeric informaion o examine his anomaly and o address imporan quesions associaed wih he phenomenon. For example, why do closed-end funds generally rade a discouns raher han premiums? Why do new closed-end funds and some closed-end counry funds end o rade a premiums? Why does he differenial in insiuional ownership beween he funds and he underlying asses conribue o he discoun? How does he qualiy of he privae informaion in he underlying asses affec he discoun? Earlier heoreical models explaining he closed-end fund puzzle focus on marke fricions. These marke fricions include agency coss (Boudreaux (973), Roenfeld and Tule (973), Barclay, Holderness and Poniff (993), and Coles, Suay, and Woodbury (000)), resriced socks or invesmen (Malkiel (973) and Bonser-Neal, Brauer, Neal and Whealey (990)), and axes (Malkiel (973) and Brickley, Manaser and Schallheim 3

4 (99)). Empirical suppor for hese marke fricion models is somehow limied (see Lee, Shleifer, and Thaler (990) for a review). In conras, De Long, Shleifer, Summers, and Waldmann (henceforh DSSW) (990) show ha he closed-end fund discoun can arise solely because holding he fund enails noise rader risk since fuure invesor senimen is unpredicable invesor senimen hypohesis. Lee, Shleifer, and Thaler (henceforh LST) (99) find evidence consisen wih he hypohesis based on a marke segmenaion argumen. LST posi ha insiuional invesors end o shy away from closed-end funds, presumably because hey are money managers hemselves who are relucan o delegae his funcion. This resuls in a higher concenraion of individual invesors in he fund han in he fund s underlying asses. To he exen ha individual invesors are more prone o invesor senimen, he discoun arises o compensae for he noise rader risk. In his paper, we ake a differen approach o examining he effec of he insiuional ownership differenial. We posi ha insiuional invesors and individual invesors can also differ by heir abiliies o access and/or process relevan informaion abou he asses in which hey inves. In his regard, insiuional invesors have incenive o concenrae heir invesmens in he underlying asses, in order o exploi heir informaional advanage agains individual invesors. Thus, raher han invesor senimen, his paper focuses on he informaional asymmery beween insiuional invesors and individual invesors. In his conex, he marke power of insiuional invesors depends also on he qualiy of he privae informaion hey have. To emphasize his dependence, we define informed ownership as he ownership of insiuional invesors, scaled by a proxy for he qualiy of heir privae informaion. 4

5 We develop an overlapping generaions model wih wo-period-lived invesors in he closed-end fund and in is underlying asses. Depending on he moive of rading, here are four kinds of risk-averse invesors in he markes: speculaors, indexers, arbirageurs, and liquidiy raders. Speculaors concenrae heir invesmen in individual asses, and hey are furher divided ino wo subgroups: informed and uninformed. Indexers diversify heir invesmen on heir own in he fund s underlying porfolio. Arbirageurs arbirage beween he fund and is underlying porfolio, based on he size of he curren discoun. Liquidiy raders are unclassified residual invesors in each marke and heir invesmen represens random noise. All invesors (excep liquidiy raders) are uiliy maximizers, and he equilibrium prices and demands for he fund and he underlying asses are endogenously deermined Our model shows ha he discoun can arise if he informed speculaion in he underlying asses, scaled by he qualiy of privae informaion, is sufficienly larger han he informed speculaion in he fund informed ownership hypohesis. In his case, he discoun reflecs he differenial percepion of risk beween informed (insiuional) and uninformed (individual) speculaors. The hypohesis suggess ha he discoun depends criically on he qualiy of privae informaion. In paricular, our model shows ha even if here are more insiuional invesors in a fund han in is underlying asses, he fund can sill rade a a discoun if he qualiy of privae informaion in he underlying asses is sufficienly beer. This is in sharp conras o he marke segmenaion hypohesis in LST (99), where only he insiuional ownership differenial maers. The emphasis of he effec of he qualiy of privae informaion on he discoun is a pivoal feaure ha disinguishes our papers from previous sudies in he closed-end fund lieraure. 5

6 In addiion, our model shows ha he discoun can arise if he price discrepancy beween he fund and is NAV is highly volaile he fund price risk. In his case, he model suggess ha he discoun arises simply as a risk premium for he excessive volailiy of he fund. Alhough fund speculaors are subec o he excess volailiy of he fund, hey enoy he diversificaion benefi provided by he fund porfolio. Thus, here is a rade-off beween he fund price risk and he diversificaion benefi in he fund. Consisen wih his inuiion, our model predics ha he discoun should be posiively relaed o he fund price risk and negaively relaed o he diversificaion benefi. Lasly, our model shows ha if invesors are nearly risk neural, hen he discoun depends only on he invesors one-period-ahead expecaion. Specifically, he discoun can arise if risk-neural invesors srongly expec ha he fund will rade a a discoun nex period a self-fulfilling prophecy. To he exen ha large premiums in exising funds may fuel boh excessive opimism and higher risk olerance, his self-fulfilling prophecy may explain he evidence ha new funds ofen ge sared when he exising funds are selling a large premiums (Weiss (989) and Peavy (990)). Our model provides several new esable implicaions for he closed-end fund discoun. Firs, i predics ha he discoun is negaively relaed o he insiuional ownership differenial, because insiuional fund arbirageurs are araced o he funds wih large discouns. Second, condiional on he insiuional ownership differenial, our model predics ha he discoun is posiively relaed o he qualiy of privae informaion in he fund s underlying asses. Third, our model predics ha he discoun is posiively relaed o he excess volailiy of he fund ne of he diversificaion benefi. 6

7 We es hese predicions using a sample of US equiy closed-end funds over he period of The empirical resuls are consisen wih he model s predicions. Firs, we find ha he discoun is indeed negaively relaed o he insiuional ownership differenial. This resul is consisen wih he noion ha insiuional arbirageurs are araced o funds wih large discouns and, o some exen, i is also consisen wih he effec of blockholding in he fund (Barclay e al. (993)). This resul, however, is inconsisen wih he marke segmenaion hypohesis (LST (99)). Second, condiional on he insiuional ownership differenial, we find ha he discoun is posiively relaed o he qualiy of privae informaion. In paricular, he discoun is larger when he uncerainy in he underlying asses rises, while he discoun is smaller when he noise in he privae signal increases. This resul suppors our informed ownership hypohesis ha he discoun reflecs he differenial percepion of risk beween he informed insiuional invesors and uninformed individual invesors. Finally, we find ha he discoun is posiively relaed o he excess volailiy of he fund, even afer conrolling for he bea risk of he consiuen asses. This resul suggess ha he discoun also reflecs a risk premium compensaing for he unique risk of he fund, which is unrelaed o he sysemaic risk of he underlying porfolio. To he exen ha he excess volailiy is due o he capricious noise rader risk, his resul is consisen wih he invesor senimen hypohesis (DSSW (990)). The paper proceeds as follows. Secion I develops he muli-asse closed-end fund model wih asymmeric informaion. Secion II examines he hree main deerminans of he discoun in he model: he self-fulfilling prophecy, he excess volailiy risk premium, and he informed ownership differenial. Secion III describes 7

8 he empirical mehodology and daa. Secion IV presens he empirical resuls. Secion V concludes. All proofs are in he Appendix. I. The Model A. The Asse Markes and Agens Consider a simple overlapping generaions model wih wo-period-lived agens who inves when young a ime and hen liquidae heir posiions o he young invesors of he nex generaion and consume heir wealh when old a ime + (Samuelson (958)). In he model, consider a closed-end fund (denoed asse f ) invesing in a porfolio of N underlying risky asses (denoed porfolio n ) wih weigh w in asse ( =,, N ). Assume ha he price of he underlying asse a ime +, denoed ~ p, +, is normally disribued wih mean m and variance σ, and he covariance beween he prices of asses i and is σ ( i, =,, N ). Thus, he ne asse value (NAV) of porfolio i n a ime +, denoed ~ p n, +, is normally disribued wih mean m n and variance σ n, such ha m N n = w m and = σ =. N N n wi w σ i i= = In a world where markes are fricionless and arbirage is cosless, he fund price a ime +, ~ p f, +, would be he same as is NAV, ~ p n, +. In his paper, we depar from such an ideal world and consider an economy under limied arbirage (Shleifer and Vishny (997)). In his conex, he fund price need no always be he same as is NAV. Le he fund price a ime + be given by ~ p ~ ~ f, + = pn, + + η, where ~ η is he price discrepancy beween he fund and is NAV and assume ha he discrepancy be normally 8

9 disribued wih mean η and variance σ η. Thus, he fund price a ime +, ~ p f, +, is normally disribued wih mean m f = m + η, and variance σ f = σ n + σ η. The random n discrepancy ~ η may be due o raional marke imperfecions or irraional invesor senimen (DSSW (990)). I is essenially an empirical issue how much he random discrepancy is due o raional or irraional facors. There are four ypes of risk-averse invesors in he N+ asse markes: speculaors, indexers, arbirageurs, and liquidiy raders. Speculaors are hose invesors who choose o concenrae heir invesmen in individual asse marke ( =,, N, f ) for speculaion purposes. They are furher divided ino wo groups: informed speculaors (denoed i) and uninformed speculaors (denoed u), depending on wheher or no hey have privae informaion abou he individual asse hey inves in. Le λ be he measure of informed speculaors in asse, while be he measure of uninformed speculaors. λ Indexers (denoed x) are hose uninformed invesors who choose o diversify heir invesmen in he underlying porfolio n. Given he measure of speculaors being uniy, le ν be he measure of indexers in each of he N underlying individual asse markes. Obviously, he fund iself, by definiion, is he primary indexer in his group. Arbirageurs (denoed a) are hose uninformed invesors who choose o arbirage beween he fund and is underlying porfolio by buying and selling he N+ asses simulaneously, given he public informaion of he curren discoun. Le δ be he measure of he arbirageurs in each asse marke. Liquidiy raders (denoed z) are residual invesors in each marke whose moives of rading canno be classified ino any of he hree ypes discussed above: speculaion, fund indexing, or arbirage. Assume ha 9

10 all invesors have CARA uiliy and idenical coefficiens of risk aversion γ, and ha each asse ( =,, N, f ) has a fixed per capia supply π. A ime, informed speculaors of measure λ in asse marke ( =,, N, f ) receive a privae signal ~ s = ~ p + ~ e,, +, + abou he asse price a ime +, where he disurbance erm ~ e, + is assumed o be independen of he price ~ p, + and be normally disribued wih mean 0 and variance σ e. The qualiy of he privae signal may be measured inversely by he noise-o-signal raio θ such ha θ = σ / σ. The e i represenaive informed speculaor hen chooses an opimal quaniy q, o maximize his W expeced uiliy of he wealh a ime +, ~ i,, given his iniial wealh W i +, and privae signal s, a ime. The opimizaion problem is hus given by: ~ i γw ~, i i i Max E[ e s ], W W q ( ~ + where = + p p ), for =,, N, f. () q i,,, +,,, +, Solving equaion () yields he opimal demand of he informed speculaor as follows: q E( ~ p s ) p i, +,,, = γvar( ~ p, + s, ) = m + κ ( s m ) p,, γ ( κ ) σ, σ where κ =.() σ σ θ = + e + Similarly, he represenaive uninformed speculaor s opimizaion problem wihou privae informaion is given by: ~ u γw ~, u u u Max E[ e ], W W q ( ~ + where = + p p ), for =,, N, f. (3) u q,, +,,, +, Solving equaion (3) yields he opimal demand of he uninformed speculaor as follows: q E( ~ p ) p u, +,, = γvar( ~ p, + ) = m p γσ, (4) A ime, he represenaive indexer diversifies his invesmen in he underlying porfolio n. To do so, he indexer deermines he opimal weighs ( w,, w N ) for 0

11 porfolio n firs and hen chooses he opimal quaniy x q for he opimal porfolio. The opimal weighs are obained by maximizing he expeced Sharpe raio of porfolio n, based on is ex ane disribuion, denoed E( S n ). Wihou loss of generaliy, assume ha he risk-free rae is zero. Thus, he opimal weighs are given by: mn pn, mn E( p n, ) Max E( Sn ) = E( ) = σ σ ( w,, wn ) n n (5) The weighs ( w,, wn ) of porfolio n are hereby endogenously deermined, given he ex ane mean of p n,, i.e., E( p n, ), which is o be deermined in he equilibrium. Given he opimal porfolio n hus formed, he indexer chooses x q shares of he porfolio o maximize his expeced uiliy of he wealh a ime +, W ~ x +, given his iniial wealh W x. The opimizaion problem is herefore given by: ~ γw ~ x x x Max E[ e x ], W W q ( ~ + where = + p p ). (6) q x + n, + n, Solving equaion (6) yields he opimal demand of he indexer for porfolio n as follows: q E( ~ p ) p = x n, + n Var( ~, γ pn, + ) = m n p γσ n, n. (7) Like indexers, fund speculaors are also able o enoy he diversificaion benefi provided hrough heir invesmen in he fund. However, in conras o he indexers who diversify on heir own, fund speculaors face addiional fund price risk due o he random price shock, η. Thus, fixing he fund price risk, hose invesors who face relaively low ransacion coss may diversify on heir own (indexers), while hose invesors who face relaively high ransacion coss may diversify indirecly by invesing in he fund.

12 A ime, arbirageurs observe he public informaion of he curren discoun, i.e., D = pn, p f,, and rade on he be ha he discoun will rever o is expeced level nex period. To his end, hey arbirage beween he fund and is underlying porfolio by buying and selling he N+ asses simulaneously wihou shor-selling consrains. Specifically, given he expeced discoun nex period, if he fund currenly rades a a relaively large discoun (premium) o is NAV, he arbirageurs buy (sell) one share of he fund for each share of he underlying porfolio hey sell (buy). The arbirageur chooses a q shares of he fund and a q shares of he underlying porfolio o maximize his expeced uiliy of he wealh a ime +, opimizaion problem is given by: ~ a W, given his iniial wealh W a +. The ~ γw ~ a a a a Max E[ e a ], W W q ( ~ p p ) q ( ~ + where = + p p ). (8) q a + f, + f, n, + n, Solving equaion (8) yields he opimal demand of he arbirageur for he fund as follows: q p, p, + E( ~ p ~, + p, + ) = Var( ~ p ~ γ p ) a n f f n = f, + n, + pn, p f, + η D ( η) =. (9) γσ γσ η η Equaion (9) confirms ha he greaer he deviaion of he curren discoun, i.e., D = pn, p f,, from he expeced one-period-ahead level, i.e., η, he greaer he demand of he arbirageur for he fund, q a. Thus, he arbirageurs as a group indeed provide an incenive compaible marke force o miigae he closed-end fund discoun. I is worh noing ha in addiion o his group of arbirageurs, speculaors in he fund also use he public informaion of he curren discoun, D, in forming heir rading sraegies. To see his, rewrie he opimal demand of he uninformed speculaors in he fund from equaion (4) as follows: q ( m p, ) + ( D ( η)) =. This decomposiion γ ( σ + ) u n n f, n σ η

13 reveals ha he uninformed speculaors in he fund have wo bes: one ha he NAV of he underlying porfolio, p n,, would rever o is expeced one-period-ahead value, m n, and he oher ha he curren discoun, D, would rever o is expeced one-period-ahead level, η. In conras o he arbirageurs who only be on he convergence of he discoun, he fund speculaors also be on he convergence of he NAV. As a resul, he uninformed fund speculaors oal risk is augmened by he variance of he NAV, σ n. Equaion () indicaes ha he informed speculaors modify he wo bes and face a smaller oal risk han he uninformed speculaors, condiional on heir privae informaion. Therefore, boh speculaors and arbirageurs use he curren discoun o form heir rading sraegies and ogeher hey exer a naural marke force o miigae he closed-end fund discoun. Liquidiy raders invesmen represens he residual demand in each marke, unrelaed o speculaion, fund indexing, or arbirage. This group of raders includes hose invesors who diversify heir invesmen in oher porfolios han porfolio n, bu heir porfolios have some common underlying asses wih porfolio n. For example, hese oher porfolios may conain oher asses han he N underlying asses. In order o obain he primary facors driving he closed-end fund discoun, we focus our analysis on he demands and prices of he fund and he N underlying asses, while absracing from he opimizaion problems concerning hese oher asses. To his end, le he residual demand a ime in each marke ( =,, N, f ) be summarized by an exogenous, random quaniy ~ z,, such ha i is normally disribued wih mean 0 and variance σ z. In addiion, assume ha he random quaniy ~ z, be independen of all oher variables in he 3

14 model. I is worh noing ha he sochasic liquidiy rading serves effecively as camouflage in he markes, prevening prices from fully revealing (Kyle (985)). B. The Equilibrium Given he demand of each ype of agen and he corresponding measure in each marke, he marke clearing condiion for each of he N underlying asses is given by: i u x a λ q~ + ( λ ) q ~ + ν w q ~ δ w q ~ + ~,, z, = π, for =,, N (0) In conras, he marke clearing condiion for he fund f is given by: λ i λ u a f q ~ f + ( f ) q ~ f + δ q ~ + ~ z f = π. (),,, Noe ha he arbirageurs inves in all N+ asses according o heir arbirage deal by buying ~ q a shares of he fund and selling w q ~ shares of asse for all =,, N a simulaneously. In conras, he indexers diversify heir invesmen in he N underlying asses by buying w q ~ shares of asse for all =,, N. Since boh he arbirage deal x and he index invesmen depend on prices across markes, he N+ equilibrium prices, p,, p, p, N, f,, are obained by solving all N+ marke clearing condiions in equaions (0)-() simulaneously. The equilibrium prices are shown in Theorem below: Theorem. The equilibrium prices, p ( =,, N ) and p, are given by, f, p, = d, + [( b ( + g ) g b ) d f, ( b + g ( bf )) d ( bg g ( bf + b )) mn ], () h p f, = [( + b + g ) d f, bf ( d + gmn )], (3) h where ~ ( )( ~ d = m + c s m ) b η + γc σ ( ~ z π ), for k =,, N, f (4) k, k k k, k k k k k, 4

15 N N N (5) d = w d, b = w b, g = w g, and h = b + ( b )( + g), f = = = b δw c σ c f f w c = b f = δ σ ν σ,, g =, c =, and c f = (6) σ σ σ λ n λ η η f + + θ θ f Given he equilibrium prices in Theorem, we can now calculae he curren NAV of he fund, p n,, and he expeced Sharpe raio, E( S n ), as shown in Corollary below: Corollary. Given he variables b, g, h, bf, c f and c ( =,,N ) in (5)-(6), he NAV of he fund, p n,, and he expeced Sharpe raio, E( S n ), are as follows: N p = w p ( bd ( b )( d = + + gm )) (7) n,, f, f n = h m E( p ) γπ E S bc b c w where w w N N N n n, ( n ) = = ( fσ f + ( f ) σ ), σ n = i σ i. σ n hσ n = i= = (8) The expeced Sharpe raio, E( S n ), depends on he ex-ane asse variance and covariance, σ ( i, =,, N ), he fund price shock, σ η, he noise-o-signal raio, i θ k ( k =,, N, f ), and he measures of he informed speculaors, λ k ( k =,, N, f ), of he indexers, ν, and of he arbirageurs, δ, respecively, in asse markes. All of hese parameers are available o he indexers a ime, when hey deermine he opimal weigh allocaion ( w,, w N ) for porfolio n as shown in equaion (5). Thus, he opimal weighs are endogenously deermined as par of he equilibrium. II. The Deerminans of he Closed-End Fund Discoun 5

16 Given he equilibrium prices of he fund, p f,, and is NAV, p n,, in (3) and (7), respecively, we can calculae he uncondiional expeced discoun in equilibrium such ha E( D ) = E( p n, ) E( p f, ). Moreover, we are able o idenify he key deerminans for he discoun as shown in Proposiion below: Proposiion. The uncondiional expeced discoun is given by N ( g)( n ) w E( D γπ + σ + σ η σ ) = η + [ ], where h b ( g)( bf ). h λ = + + f λ (9) = + + θ θ The expeced discoun is posiive if f (i) he one-period-ahead expeced discoun is sufficienly large ( η >> 0 ), or (ii) he fund price risk is sufficienly large (σ = σ + σ >> σ ), or N f n η w = (iii) he informed ownership in he underlying asses is sufficienly larger han in he fund λ λ f ( >> ). θ θ f We discuss he hree deerminans of he discoun in Proposiion as follows. A. The Self-fulfilling Prophecy Firs, if he one-period-ahead expeced discoun, i.e., E ( p, p, ) = η, is n + f + posiive and dominaes he second erm in equaion (9), hen he uncondiional expeced discoun will be posiive. This can happen if invesors risk aversion coefficien is close o zero, i.e., γ 0. In oher words, if invesors are nearly risk-neural and expec a posiive discoun nex period, hen i can become a self-fulfilling prophecy. On he oher hand, such a self-fulfilling prophecy also implies ha closed-end funds can rade a a 6

17 premium if he invesors srongly expec so. This may parially accoun for he empirical observaion ha new funds ofen ge sared when he exising funds are selling a premiums (Weiss (989), Peavy (990), and LST (99)). This may also explain he premiums in some closed-end counry funds a a ime when invesors are overly opimisic abou heir invesmen in he funds (LST (990)). B. The Risk Premium for he Excess Volailiy of he Fund Second, if invesors risk aversion coefficien γ is no rivial, hen he discoun also depends on he second erm, which is essenially a risk premium. In paricular, if invesors one-period-ahead expecaions are unbiased in he sense ha hey do no expec eiher a discoun or a premium nex period, i.e., η = 0, hen he discoun can sill arise if he risk premium is large. This is cerainly a more ineresing case on which our paper focuses in wha follows. In his case, he discoun can emerge if he variance of he fund price is sufficienly larger han he weighed-average variance of he underlying asses, N f n η w = i.e., σ = σ + σ >> σ (see equaion (9)). In oher words, he excess volailiy of he fund can generae he discoun. A closer look a his relaion reveals ha his resul depends on a rade-off beween he fund price risk and he diversificaion benefi by invesing in he fund. To see his, he diversificaion benefi implies ha he porfolio s variance is less han he weighed-average variance of he underlying asses, i.e., σ N n w < = σ. The diversificaion effec can be measured by he reducion of he N variance in he porfolio, i.e., w σ σ n. Bu, invesing in he fund also enails = addiional fund price risk, i.e., σ η. Thus, he condiion ha he variance of he fund price 7

18 is sufficienly greaer han he weighed-average variance of he underlying asses, i.e., N n η w = σ + σ >> σ, is saisfied only if he fund price risk dominaes he diversificaion N benefi, i.e., σ >> w σ σ. On he oher hand, he rade-off implies ha he fund η = n can rade a a premium, on average, if he diversificaion benefi dominaes he fund price risk, i.e., σ << σ σ η N w = n. We may use he raio of he variance of he fund price over he weighed-average variance of he underlying asses, i.e., σ f N w =, as he measure of he rade-off beween σ he wo opposie effecs. Risk-averse invesors demand less of he fund when he fund price risk increases and/or when he diversificaion benefi in he fund decreases. Such a fall in demand can lead o he discoun of he fund. Thus, he discoun should be posiively relaed o his rade-off raio. By equaion (9), he raio may be modified furher by a muliplier + g, such ha he modified raio is given by ( + g) σ f N = w σ. By equaions (5)-(6), he consan g is given by g N ν c w σ = = σ n < ν. Recall ha ν is he measure of he indexers who diversify on heir own in he underlying asses, raher han diversifying hrough he fund. The relaive diversificaion benefi in he fund should decline as he measure of he indexers ν increases. As a resul, he discoun should increase, ceeris paribus. This 8

19 inuiion is capured in he modified rade-off raio, since he raio rises wih he measure ν and his, in urn, leads o a greaer discoun. Recall also ha he fund iself is he primary indexer in his group. Hence, fixing he capial of he fund, he measure ν should be negaively relaed o he number of he underlying asses in he fund, N. Thus, he fund may miigae he discoun by invesing in a well-diversified porfolio. In paricular, if he fund is sufficienly well-diversified, i.e., N and ν 0, hen he modified raio reduces o he basic rade-off raio, i.e., ( + g) σ f σ n + σ η, and N w σ w σ = = moreover he porfolio risk reduces o is sysemaic componen, i.e., σ β σ, where β n is he bea of he underlying porfolio n and σ m is he marke risk. n n m The fund price risk effec may explain he empirical evidence ha open-ending announcemens end o generae posiive abnormal reurns for he closed-end funds (Brauer (984) and Brickley and Schallheim (985)). I is also consisen wih he claim ha he source of he gain is he discoun eliminaion associaed wih he marke revising he probabiliy of open-ending (Brauer (988)). To see his, noe ha afer an openending announcemen, he closed-end fund price ends o converge o is NAV. The magniude of he adusmen rises wih he likelihood of being open-ended evenually. The more likely he open-ending even will ake place, he more rapidly he magniude of he fund price shock, σ η, will shrink in he process. By equaion (9), his adusmen will lead o a smaller discoun, hus rendering a posiive abnormal reurn o he closedend fund. Brauer (984) shows ha he funds wih large discouns are more likely o be arges of open-ending. Thus, he fund price risk effec may also accoun for he evidence 9

20 ha a porfolio of he discoun-weighed closed-end funds ends o generae abnormal reurns (Thompson (978) and Poniff (995)). The diversificaion effec may explain he empirical finding ha closed-end counry funds end o rade a large premiums, paricularly for hose counries wih greaer invesmen resricions (Bonser-Neal, Brauer, Neal, and Whealey (990)). This is so because he more difficul i is o inves and diversify direcly in a foreign marke, he greaer is he diversificaion benefi ha may be gained by invesing indirecly in a closed-end fund argeed a ha counry. On he oher hand, i is relaively easier for invesors in he U.S. marke o diversify on heir own. This should reduce he relaive diversificaion benefi in domesic closed-end funds, and, as a resul, should lead o a greaer discoun, ceeris paribus, in comparison o foreign closed-end funds. C. The Informed Ownership Hypohesis Proposiion also shows ha boh he presence of informed invesors, λ, and he qualiy of privae informaion, / θ, play a criical role in explaining he closed-end fund discoun. Define informed ownership in marke k by λ k θ k for k =,, N, f, which is he ownership of informed invesors in marke k, scaled by he qualiy of heir privae informaion. This measure highlighs he fac ha he marke power of he informed invesors depends no only on heir ownership in he marke bu also on he qualiy of heir privae informaion. Proposiion (iii) indicaes ha he discoun can arise when he informed ownership in he underlying asses is sufficienly larger han in he fund, i.e., λ θ λ f >>. We call his new explanaion for he discoun informed ownership θ f hypohesis, which emphasizes he role of he qualiy of privae informaion. 0

21 The economic raionale behind he informed ownership hypohesis is relaed o he differenial percepion of risk beween he informed and uninformed invesors. To see his, noe ha risk-averse invesors will no accep a fair game. They require addiional risk premium o compensae for heir risky invesmen. As a resul, he price hey are willing o pay for a risky invesmen is less han is expeced liquidaion value. The exen o which risk-averse invesors shed price o compensae for risky invesmen increases wih he perceived risk of he invesmen. Informed invesors wih privae informaion have a lower perceived risk of he same risky invesmen han uninformed invesors do. This is so because he condiional variance of he risky invesmen, given he privae informaion, is smaller han he uncondiional variance. The condiional variance measures he perceived risk of he informed invesors, whereas he uncondiional variance measures ha of he uninformed invesors. Hence, he informed invesors price shedding is smaller han he uninformed invesors, ceeris paribus. The marke price is essenially he ownership-weighed average price of wha he informed and uninformed invesors are willing o pay. Consequenly, a sufficienly larger informed ownership in a fund s underlying asses han in he fund iself will lead o a discoun. In his paper, we ake he view ha insiuional invesors and individual invesors may differ in heir abiliy o access or process relevan informaion abou he asses hey inves. In paricular, we associae insiuional invesors wih he informed invesors in our model and individual invesors wih he uninformed. In his conex, he informed ownership hypohesis implies ha a discoun can arise when he produc of he presence of insiuional invesors in he underlying asses and he qualiy of heir privae informaion is sufficienly larger han ha in he fund, i.e., λ λ f >>. This implies ha θ θ f

22 he insiuional ownership differenial by iself may no generae he discoun if he qualiy of heir privae informaion is sufficienly poor. This dependence on he qualiy of privae informaion disinguishes our informed ownership hypohesis from he invesor senimen hypohesis, which suggess ha he insiuional ownership differenial alone, i.e., λ >> λ f, should lead o he discoun (DSSW (990) and LST (99)). This disincion is especially imporan for considering he impac of fund arbirageurs who are essenially uninformed insiuional invesors. In his case, while he presence of he arbirageurs adds o he insiuional ownership in he fund, i does no increase he corresponding informed ownership. Fund arbirageurs rade on he be ha he unusually large curren discoun should rever o is expeced level nex period. Hence, a greaer discoun should arac more arbirageurs o he fund, and his, in urn, leads o a smaller insiuional ownership differenial beween he underlying asses and he fund. This implies a negaive relaion beween he curren discoun and he insiuional ownership differenial. This negaive relaion is conrary o he predicion of he invesor senimen hypohesis, bu no o our informed ownership hypohesis since he arbirageurs are essenially uninformed. This negaive relaion is consisen wih he opimizaion behavior of he arbirageurs considered in our model (see equaion (9)). D. The Comparaive Analysis on he Closed-End Fund Discoun In his subsecion, we invesigae he conribuion of invesor ype o he discoun. To do so, we examine several comparaive saics based on he uncondiional expeced discoun in equaion (9) and show he resuls in Proposiion below.

23 Proposiion. Given equaion (9), he conribuion of each ype of invesor o he discoun is summarized as follows: (i) Holding consan he informed ownership in he fund, he discoun rises wih he informed ownership in he underlying asses, i.e., E( D ) λ θ > 0. (ii) The discoun rises wih he measure of he indexers, i.e., E( D ) ν > 0. (iii) The discoun falls wih he measure of he arbirageurs, i.e., E( D ) δ < 0. E( D ) (iv) The discoun is unrelaed o he amoun of liquidiy rading, i.e., σ z = 0. Proposiion (i) esablishes he informed ownership hypohesis in a formal way. This resul highlighs he role of asymmeric informaion as a unique feaure ha disinguishes our model from he previous models in he lieraure in explaining he discoun. Therefore, his hypohesis provides a new esable implicaion for he discoun, which we invesigae empirically in grea deail in he laer par of his paper. Proposiion (ii) saes ha he larger he number of invesors who can diversify on heir own, he greaer is he discoun. This happens because if invesors can diversify on heir own, heir demands for he fund will decline for diversificaion purposes. The reduced demand for he fund should, in urn, lead o a greaer discoun. This resul may explain he empirical evidence ha he U.S. domesic closed-end funds end o have a larger discoun han do foreign funds. This is so presumably because i is easier for invesors o diversify on heir own in he U.S. marke han in he foreign marke. 3

24 Proposiion (iii) highlighs he effec of he fund arbirage on he expeced discoun. Specifically, he proposiion predics a negaive relaion beween arbirage aciviy and he expeced discoun. This is so because he group of arbirageurs represens a naural marke force ha consanly bridges he gap beween he fund price and he NAV of is underlying porfolio. Fixing he curren discoun, he expeced discoun is herefore negaively relaed o he presence of he arbirageurs in he marke. Proposiion (iv) indicaes ha he exogenous liquidiy rading, σ z, bears no consequence for he discoun. However, as menioned previously, he liquidiy rading serves effecively as camouflage for informed rading, hus prevening prices from being fully revealed in our model under asymmeric informaion. III. Empirical Mehodology and Daa A. Empirical Model As menioned before, our heoreical model provides several new esable implicaions. Our empirical analysis focuses on wheher he discoun is posiively relaed o () he informed ownership differenial and () he excess volailiy of he fund, ne of he diversificaion benefi. The posiive relaion beween he discoun and he informed ownership differenial (informed ownership hypohesis) is a previously unexamined predicion ha highlighs he effec of asymmeric informaion and disinguishes our paper from he previous sudies in he lieraure. This new hypohesis suggess ha he discoun should be posiively relaed o he qualiy of privae informaion in he underlying asses. We 4

25 es his predicion empirically wih a focus on he effec of he qualiy of privae informaion. Since privae informaion is more relevan for he underlying asses han for he funds hemselves, he degree of informed ownership differenial across closed-end funds is driven primarily by he differences of informed ownership in heir underlying asses. Thus, our empirical analysis focuses on he differences of he informed ownership in he underlying asses, λ = λ σ. To his end, we use he differenial in insiuional θ σ e ownership beween he underlying asses and he fund as he proxy for λ, and use he signal-o-noise raio of he underlying asses, σ, as he measure for he qualiy of σ privae informaion. Observe ha he signal-o-noise raio, σ, has wo componens: he amoun of σ uncerainy in he underlying asses, σ, and he amoun of uncerainy in he privae signal, σ e. Since he signal-o-noise raio is increasing in σ and decreasing in σ e, he informed ownership hypohesis implies ha he discoun should be posiively relaed o he ineracion variable λ σ and negaively relaed o he ineracion variable λ σ The posiive relaion beween he discoun and he excess volailiy of he fund, ne of he diversificaion benefi, highlighs he ne effec of he fund price risk. In paricular, he discoun is posiively relaed o he excess volailiy of he fund and negaively relaed o he diversificaion benefi in he fund. Following our discussion in Secion II.B., we use he raio of he variance of he fund price over he weighed-average e e e. 5

26 variance of he underlying asses, σ f N w =, as he measure of he rade-off beween he σ wo opposie effecs. In order o es he wo main predicions of our model while conrolling for oher possible explanaions, we consider he following economeric model: DISCOUNT i = β 0 + β DIFFIOi + β DIFFIO i x VWVOLi + β3 DIFFIO i x PNOISEi + β 4 VOLRATIO i + β5 BETAi + β 6 EXPRATIOi + β 7 PBLOCKi + β8 EXPRATIOix PBLOCK i + β9 INVPRICEi + β0 PSTOCKi + γ 8 D(8) i + + γ 97 D(97) i + ε i, (0) where DISCOUNT i is he difference beween he NAV and he price for fund i a ime, expressed as a percenage of he fund price: (NAV-PRICE)/PRICE. For simpliciy, we suppress he subscrip i as we discuss each regressor in wha follows. The variable DIFFIO is he differenial in insiuional ownership beween he underlying asses and he fund, i.e., DIFFIO = VWIOA IOF, where VWIOA is he value-weighed average of he fracion of insiuional ownership (excluding he fund s ownership) in he fund s underlying common socks and IOF is he fracion of insiuional ownership in he fund. As discussed previously, insiuional arbirageurs may be araced o he funds wih large discouns, hence DIFFIO is, o some exen, deermined endogenously. In his case, he OLS esimaors are likely o be biased because DIFFIO will be conemporaneously correlaed wih he error erm in Equaion (0). In his paper, we use an insrumenal variable approach o solve his poenial economeric problem. To his end, we firs regress DIFFIO on several (exogenous) insrumenal variables ha migh explain he level of DIFFIO. Specifically, we esimae he following regression: 6

27 DIFFIOi = ψ + ψ VWIOA i + ϕf() i + + ϕ 34F(34) i + φ 8D(8) i + + φ 97D(97) i + ξ i 0, () where VWIOA is he value-weighed average of he fracion of insiuional ownership (excluding he fund s ownership) in he fund s underlying common socks, F(k) is dummy variable for fund k (k =,, 34), and D(y) is dummy variable for year y (y = 8,,97). Since i is reasonable o assume ha he insiuional ownership in he fund s underlying asses is exogenously deermined, we use VWIOA as an insrumenal variable in (). We hen use DIFFIO, he prediced value of DIFFIO from Equaion (), as a proxy for he differenial in insiuional ownership in he esimaion of Equaion (0). Since DIFFIO should be uncorrelaed wih he error erm in Equaion (0), he esimaed values of he coefficiens should be unbiased. Our model suggess ha he fund arbirage aciviy leads o a posiive associaion beween he discoun and he insiuional ownership of he fund. This implies ha he coefficien of DIFFIO, β, should be negaive. In addiion, a large block ownership in he fund can also lead o a small DIFFIO. Thus, finding a negaive coefficien for DIFFIO would also be consisen wih he agency argumen in Barclay e al. (993). On he oher hand, he marke segmenaion hypohesis (LST (99)) argues ha a higher concenraion of individual invesors in he fund, hus a larger insiuional ownership differenial, should lead o a larger discoun. This hypohesis implies ha he coefficien of DIFFIO, β, should be posiive. The variable VWVOL is our proxy for he amoun of uncerainy in he underlying asses, σ. For robusness, we consider wo alernaive proxies: VWVOL() and VWVOL(), where he former [laer] proxy is he value-weighed average of he 7

28 sandard deviaions of he underlying asses [excess] reurns esimaed over he 50 days before he end of he calendar year. We muliply hese proxies by he fracion of common socks in he fund s porfolio. We do his o ake ino accoun he fac ha he res of he fund s holdings (i.e., fixed income and cash equivalen securiies) have an informed-ownership close o zero. The ineracion variable DIFFIO x VWVOL is he proxy for λ σ. According o our informed ownership hypohesis, he coefficien of he ineracion variable DIFFIO x VWVOL, β, should be posiive. The raionale is ha he larger he uncerainy in he underlying asses, he greaer he informed ownership differenial, and consequenly, he greaer he discoun. PNOISE is he proxy for he amoun of uncerainy in he privae signal, σ e. Following exising lieraure, we assume ha he error and he dispersion of analyss earnings forecass measure he magniude of he noise in he privae signal (Fried and Givoly (98) and Givoly and Lakonishok (988)). Analyss collec non-public informaion abou fuure earnings and reveal i o he marke hrough heir forecass. The precision of hese forecass may reflec he qualiy of privae informaion. Tha is, he higher he precision of analyss earnings forecass (e.g., he smaller he variance of he error and he dispersion), he smaller he noise in he privae signal. In his paper we consider hree differen proxies for he noise of analyss earnings forecass. Firs, we use he value-weighed average of he sandard deviaions of analyss earnings forecass (VWDISPER). Second, we use he value-weighed average of he sandard deviaions of analyss earnings forecas errors (VWSTDFOR). Third, we use he value-weighed average of he mean absolue deviaions of analyss earnings forecas errors (VWMADFOR). As in he case of VWVOL, we muliply hese proxies by he fracion of 8

29 common socks in he fund s porfolio o ake ino accoun he fac ha he res of he fund s holdings (i.e., fixed income and cash equivalen securiies) have an informed- ownership close o zero. The ineracion variable DIFFIO x PNOISE is he surrogae for λ σ. According o our informed ownership hypohesis, he coefficien of he e ineracion variable DIFFIO x PNOISE, β 3, should be negaive. The raionale is ha he poorer he qualiy of he privae signal, he smaller he informed ownership differenial, and consequenly, he smaller he closed-end fund discoun. VOLRATIO is he proxy for he rade-off raio beween he fund price risk and he diversificaion benefi, i.e., σ f N w =. We calculae he proxy as he raio of he σ variance of he fund reurns esimaed over he 50 days before he end of he calendar year over he value-weighed average of he variance of he underlying common sock reurns esimaed over he same ime period. We muliply he value-weighed average of he variance of he underlying common socks by he fracion of common socks in he fund s porfolio o ake ino accoun he fac ha he res of he fund s holdings (i.e., fixed income and cash equivalen securiies) have a low level of uncerainy. Our model indicaes ha he larger he fund price risk or he smaller he diversificaion benefi is (hence he larger he value of VOLRATIO), he greaer he discoun should be. This implies ha he coefficien of VOLRATIO, β 4, should be posiive. Finding evidence ha he discoun is posiively relaed o he rade-off variable, VOLRATIO, would be consisen wih he hypohesis ha he discoun represens he risk premium for he excess volailiy of he fund ne of he diversificaion effec. To conrol for he poenial effec of he sysemaic risk of he underlying porfolio on he discoun, we also include 9

30 he value-weighed average of he marke beas of he underlying asses, BETA, in our regressions. BETA is also muliplied by he fracion of common socks in he fund s porfolio. We use EXPRATIO o conrol for he effec of poenial agency problems on he closed-end fund discoun. EXPRATIO is he oal annual operaing expenses scaled by he fund s oal ne asse value. If he discoun is relaed o he poenial dead-weigh loss of he managemen expenses of he fund, we should expec he coefficien of EXPRATIO, β 6, o be posiive (Malkiel (977)). We also conrol for he effec of sock ownership concenraion on he closed-end fund discoun because here is evidence ha managers use blockholdings o derive privae benefis and avoid poenial akeover aemps (Barclay e al. (993)). The raionale behind his argumen is ha managers who exrac privae benefis from he fund enrench hemselves by concenraing shares among friendly blockholders. Thus, funds wih a large fracion of blockholders should rade a a larger discoun han do oher funds. In his paper we use PBLOCK as proxy for he level of blockholding in he fund. PBLOCK is he fracion of shares of he closed-end fund held by blockholders, where a blockholder is defined as an invesor holding more han 5% of he shares of he closedend fund. PBLOCK includes he ownership of insiders bu excludes he ownership of hosile blockholders. Following Barclay e al. (993), we also examine he effec of he ineracion variable EXPRATIO x PBLOCK on he closed-end fund discoun o see wheher he discoun is more sensiive o he expense raio when managers are more enrenched. The managemen enrenchmen argumen implies ha he coefficien of 30

31 PBLOCK, β 7, and he coefficien of he ineracion variable EXPRATIO x PBLOCK, β 8, are boh posiive. Since cross-secional differences in closed-end fund discouns may be relaed o differences in he liquidiy or ransacion coss of he fund sock, we use INVPRICE as proxy for marke liquidiy (Poniff (996)). INVPRICE is divided by he marke price per share of he closed-end fund a he end of he year. This variable should conrol for he effec of liquidiy on he discoun because rading coss are negaively relaed o he price of he sock. The reason for his is ha relaive bid-ask spreads are higher for lowprice socks. In general, we should expec a posiive correlaion beween INVPRICE and he closed-end fund discoun, hus a posiive value for β 9. PSTOCK is he oal marke value of all common socks in he fund s porfolio scaled by he fund s oal ne asse value. The res of he fund s holding are mainly fixed income and cash equivalen securiies. Since hese securiies are relaively easier o hedge han socks, we may use PSTOCK as a proxy for he poenial effec of cosly arbirage on he closed-end fund. Poniff (996) argues ha closed-end fund discouns should be posiively relaed o he coss of arbirage because he incenive o eliminae he difference beween he fund s ne asse value and he fund s price declines wih hese coss. Thus, he cos of arbirage argumen implies ha he coefficien of PSTOCK, β 0, should be posiive. Finally, we employ year dummies D(y) o conrol for any ime-series rend in he closed-end fund discoun for years from 98 o 997. B. Esimaion Mehodology Because we are using panel daa in our esimaions, he assumpions of he OLS model are likely o be violaed. Thus, we esimae a variance-componens model as in 3

32 Barclay e al. (993) o address his economeric issue. We assume ha he error in Equaion (0) has wo componens: one ha varies across funds and over ime, µ, and anoher ha varies across funds bu is consan over ime, α. Assuming ha hese componens are uncorrelaed wih he regressors in Equaion (0), we can use he wosep GLS procedure in Hsiao (986) o esimae he parameers of his model. In he firs sep we obain esimaes of he variances of µ and α using he following esimaors: y y β ' x x T i i i i σ µ = () i i i and σ α ' σ = yi β xi M T µ i, (3) i where y i is he DISCOUNT for fund i a ime, x i is a vecor conaining all he regressors in Equaion (0) for fund i a ime, T i is he number of years ha fund i appears in he sample, M is he number of funds in he sample, y = ( yi ) / Ti, and i x = ( xi ) / Ti. Equaion () is esimaed using only funds ha appear in he sample for i i more han one year. The vecor β in Equaion () is he vecor of esimaed coefficiens from he regression of yi yi on xi xi. The vecor β in Equaion (3) is he vecor of esimaed coefficiens from he regression of y i on x i. Using hese esimaes of he variances of µ and α, we ransform our original daa using he following funcions: ~ y i = -/ y ( σ + σ ) if T = i µ α / (y [ σ / ( σ + T σ ) ] y ) / σ if T > i µ µ i α i µ i i i (4) 3

33 and ~ x i = -/ x ( σ + σ ) if T = i µ α / (x [ σ / ( σ + T σ ) ] x ) / σ if T > i µ µ i α i µ i i (5) In he second sep we esimae he parameers of Equaion (0) applying OLS o his ransformed daa. To examine how he esimaed parameers of Equaion (0) change when we use he wo-sep GLS procedure, we also esimae he parameers of his equaion applying OLS o he original daa. C. Daa An iniial lis of closed-end funds is obained from he CDA/Wiesenberger s Invesmen Companies Yearbook. From his iniial lis, we idenify all closed-end funds ha are classified under he following invesmen obecives: (i) aggressive growh, (ii) equiy income, (iii) growh - domesic, (iv) growh and curren income, (v) mid capializaion, (vi) S&P 500 Index, (vii) small capializaion, (viii) balanced allocaion domesic, (ix) asse allocaion, (x) energy/naural resources, (xi) financial services, (xii) healh care/bioechnology, (xiii) echnology/communicaions, and (xiv) uiliies. We focus on hese invesmen obecives because we are only ineresed in hose funds ha inves primarily in US common socks. The reason for his is ha we need o gaher financial informaion (i.e., sock reurns and analyss earnings forecass) on he underlying asses of he closed-end funds, which in many cases i is only available for domesic common socks. This consrain dramaically reduces he number of funds in our sample because we exclude foreign funds as well as fixed income funds. To be included in he final sample, each closed-end fund mus saisfy he following crieria: (i) he fund is publicly raded for a leas one year over he period 33