Supplemetary Appedix for Madatory Portfolio Disclosure, Stock Liquidity, ad Mutual Fud Performace This Supplemetary Appedix cosists of two sectios Sectio I provides the propositios ad their proofs about our model of iformed tradig with differet madatory disclosure frequecies Sectio II tabulates additioal results for some of the empirical tests that we coduct i the paper A Propositios I Propositios ad Proofs The followig propositio characterizes the strategies ad expected profits of the iformed trader, ad the pricig rules of the market maker I the proof of the propositio, we also show that this is the uique equilibrium whe strategies are costraied to be of the forms give i () (4) Propositio : If k >, the the equilibrium strategies ca be characterized as follows (i) There are costats α, δ,, β, Σ, γ, (4), ad the iformed trader s expected profits are give by σ z, such that the strategies satisfy () E[ π p,, p, v] = α ( v p ) + δ, for (SA) * * We defie costats μ α, for ad μ = 0, to facilitate the presetatio of results below Give Σ 0 ad σ u, the costats α,, β, Σ, γ, ad σ z solve the followig recursive equatio system: (a) If =, Σ α =, β =, = β, Σ = Σ (SA) 4 σu (b) If =, or < is ot equal to km or km for some iteger m > 0,
μ =, α =, β =, 4 ( ) 4 ( ) ( ) + μ μ+ μ μ β Σ =, Σ = Σ σu ( μ) (SA3) (c) If < is equal to km for some iteger m > 0, μ =, α =, β = 4 4 ( ) ( ) + μ μ μ Σ = β, Σ = Σ σ μ u ( ) (SA4) (d) If < is a multiple of k,, α β μ + + = =, =, μ+ 4 + ( μ+ ) 4 ( μ+ ) β Σ ( μ ) β Σ = =, Σ = Σ, γ =, σ = σ + z u σu σu ( μ+ ) ( μ+ ) (SA5) (e) I the first period, the market depth parameter is give by = μ Σ 0 ( μ) σu (SA6) (ii) The sequece of costats { μ } that appear i the recursive formulas (SA) (SA6) do ot deped o Σ 0 ad σ u, ad are uiquely determied by the followig equatios: (a) If =, the μ = 0 (b) If =, or < is ot equal to km or km for some iteger m > 0, the 0< μ < / ad 3 8( μ μ) (μ ) = 0 μ + (SA7) (c) If < is equal to km for some m > 0, the 0< < / ad μ
( μ ) μ μ μ = 3 + 8( ) ( ) 0 μ+ (SA8) (d) If < is a multiple of k, the μ = /4 (iii) I the case of full disclosure i each period (or the case of k = ), the equilibrium strategies are characterized below Deote the costats by ˆ α, ˆ δ, ˆ, ˆ β, Σ ˆ,ˆ γ, σ z ˆ (a) If =, the ˆ Σ ˆ ˆ ˆ α =, =, β =, Σ = Σ ˆ (SA9) 0 4 ˆ ˆ σ u (b) If <, the ˆ Σ ˆ α β 0 ˆ =, =, =, 4 ˆ σ ( ) ˆ u + ˆ ˆ ˆ Σ ˆ = Σ = Σ 0, γ =, σ zˆ = σ u + + (SA0) Part (i) gives the recursive formulae for the strategy parameters Part (ii) directly computes the series of key costats μ (used i the recursive formulae) through backward iductio Part (iii) for the case k = simply replicates the solutio give i Propositio 4 i Huddart, Hughes, ad Levie (00) I the special case k the above propositio reduces to the Kyle (985) model =, the equilibrium give i Propositio (i) Assume k =, that is, the iformed trader is required to disclose oce every two periods Deote the average illiquidity for the case i which the iformed trader is required to disclose every two periods by Λ = i= i ad deote the average illiquidity for the case the iformed trader is required to disclose every period by Λ ˆ ˆ = The = 3
Λ ˆ <Λ (SA) That is, more frequet disclosure leads to lower average illiquidity or higher average liquidity Furthermore, the differece Λ Λ ˆ icreases with the extet of asymmetric iformatio Σ 0 (ii) Deote the expected profits of the iformed trader i the case i which the iformed trader is required to disclose every two periods by Π ad every period by Π ˆ The Π >Π ˆ (SA) I other words, the iformed trader s profits are decreasig i the frequecy of disclosure The differece Π Π ˆ icreases with the extet of asymmetric iformatio Σ 0 (iii) If ' >, the Πˆ Π <Πˆ Π (SA3) I other words, the iformed trader s profit declie from more frequet disclosure is greater whe the total umber of periods is larger This propositio shows that market liquidity icreases as a result of more frequet disclosure Furthermore, the liquidity improvemet depeds positively o the extet of asymmetric iformatio about the uderlyig security The iformed trader, however, makes less profits due to the more frequet madatory disclosure His profit declie is greater whe iformatio asymmetry is higher or whe tradig takes loger ote that the cases k = ad k = i the propositio correspod closely to the regulatio where the madatory disclosure frequecy is icreased from semi-aual to quarterly B Proofs Proof of Propositio Part (i): We first prove (a)-(d) by iductio Case (a): Because = is the last period, the disclosure requiremet does ot chage the isider s strategy ad thus the solutio give i Theorem of Kyle (985) applies ad 4
(A6) holds ow assume that (a)-(d) holds for the (+)-th period, we will show that it also holds for the -th period Case (b): If =, or < is ot equal to km or km for some iteger m > 0, the Theorem of Kyle (985) applies to period ad we have α μ =, β = 4 ( μ ) ( μ ) Σ = β, Σ = ( β ) Σ = Σ σu ( μ) (SA4) Furthermore, because + is ot a multiple of k, cases (a)-(c) for the (+)-th period imply that α = +, ( μ ) + + = = = 4 α ( μ ) 4( μ ) α 4 μ ( μ ) + + + (SA5) Equatios (SA4) ad (SA5) complete the proof of (SA3) i case (b) Case (c): If < is equal to km for some iteger m > 0, the the isider is ot required to disclose ad Theorem of Kyle (985) also applies to period ad we have α μ =, β = 4 ( μ ) ( μ ) Σ = β, Σ = ( β ) Σ = Σ σu ( μ) (SA6) Sice + is equal to km, case (d) for the (+)-th period implies + = = = 4 α ( μ ) 4( μ ) α 4 μ ( μ ) + + + ad + + = μ + Therefore, 5
+ = + ( μ+ ) = (SA7) 4μ Equatios (SA6) ad (SA7) complete the proof of (SA4) i case (c) Case (d): If < is a multiple of k, cosider the isider s expected profits coditioal o his iformatio set i the (-)-th period, E p v v E x v p v p [ π(, ) ] = [ ( ) + α( ) + δ v] = E [ x ( v p ( x + u )) + α ( v p γ x ) + δ v] = E [( α γ ) x + ( γ α ) x ( v p ) + α ( v p ) v] + δ (SA8) * The strategy x = β ( v p ) + z with the oise term z σ implies that the ~ (0, z ) isider is idifferet amog differet values of x, therefore αγ = 0, γα = 0 This implies that γ = = = (SA9) +, 4α μ+ where i the last step we use the equatio for The breakeve coditios of the market maker are α give by cases (a)-(c) for the period (+) p = E [ v x + u ] = p + ( x + u ) * p = E [ v x ] = p + γ x * * implyig that Cov(, v x + u ) β Σ = = Var( x ) Cov(, v x ) γ = = Var( x ) + u βσ + σz + σ u β Σ βσ + σz (SA0) Equatios (SA9) ad (SA0) imply that 6
β Σ + σ = σ (SA) z u ad βσ = σ u (SA) We also have Cov (, v x ) Σ = = =Σ Σ (SA3) Var [ v x] Var [ v] γβ Var ( x) Equatios (SA) ad (SA3) imply that Σ = Σ 4 σ = Σ 4 ( μ ) σ (SA4) u + + u Recall from the (+)-period that Σ + = Σ, ( μ ) + β Σ μ Σ μ Σ = = = + + + + + + + σ u ( μ+ ) σu 4( μ+ ) σu (SA5) Pluggig ito (SA4), we obtai Σ Σ = ( ) μ + (SA6) Equatios (SA), (SA5), ad (SA6) imply that σ σ ( μ ) σ ( μ ) β = = = Σ Σ Σ u u + + u + + + ( μ ) Σ ( μ ) μ = = = 4 ( μ ) 4 ( μ ) + + + + + Σ + + + (SA7) Fially, equatios (SA8) ad (SA9) imply that α = α = = 4 ( μ ) 4 + + (SA8) Equatios (SA9), (SA), (SA6), (SA7), ad (SA8) complete the proof of (SA5) i case 7
(d) Case (e): Sice k >, cases (b) ad (c) imply that Σ β Σ0 μ Σ = β = = σ μ σ μ σ 0 u ( ) u 4 ( ) u Therefore, μ Σ = ( μ ) σ u 0 Part (ii): The proof of this part will eed the followig lemma Lemma Suppose K > 0, the there is a uique solutio μ (0,) to the followig equatio 3 8 K μ 8 μ (μ ) = 0 (SA9) Furthermore, 0< μ < / Proof of the Lemma By takig the derivative, it is easy to show that the fuctio 8μ ( μ) + f ( μ) = is icreasig for μ (0,/ ) Because f ( μ ) approaches 0 as μ 0, μ ad as μ, there is a uique μ (0,/ ) such that f ( μ ) = K, ie, (SA9) is satisfied Because f ( μ ) < 0 for μ ( /,), the above solutio is also the uique solutio i the iterval (0,) QED We proceed to prove cases (a)-(d) sequetially Case (a) is trivial as we defie μ = 0 I Case (b), =, or < is ot equal to km or km for some iteger m > 0 Applyig Part (i) Cases (a)-(c) to the periods ad (+), Σ μ = β, β =, ( ) σu μ Σ μ = β, Σ = Σ, β = ( ) ( ) + + + + + + σu μ+ + μ+ (SA30) From (SA30), we obtai 8
β = ( μ ) β + + + (SA3) μ μ+ ext, pluggig the equality β = ad β + = ( μ ) ( μ ) + + from (SA30) ito (SA3) ad reorgaizig, we obtai ( μ ) μ = μ μ + + 4( + ) (SA3) Part (i) Case (b) implies that + = 4 μ ( μ ) + (SA33) Substitutig (SA33) ito (SA3), we obtai the recursive equatio μ μ μ = 3 8( ) ( ) 0 μ + (SA34) By the secod order coditio i Kyle (985), 0 < μ < It the follows from Lemma that if 0< μ + < /, there is a uique root μ of (SA34) i (0,) such that 0< μ < /, which proves Case (b) respectively, Case (c): Applyig Part (i) Cases (c) ad (d) to the periods ad (+), Σ μ = β, β =, ( ) σu μ Σ μ = β, β =, = + + + + + σ u 4 + ( μ+ ) 4μ (SA35) Usig (SA35) ad similar algebra as i Case (b), we obtai ( μ ) μ μ μ = 3 + 8( ) ( ) 0 μ+ (SA36) The lemma ow together with iductio the implies that Case (c) holds Case (d): By Part (i) Case (a)-(d), α = =, which implies that 4 ( μ ) 4 + + 9
μ = α = /4 Part (iii): This is simply a replicatio of the solutio for the case of disclosure i every period give i Propositio 4 of HHL We refer the reader to HHL for the proof QED Proof of Propositio Sice is proportioal to Σ 0, the aggregate illiquidity fuctio Λ σ u = = is proportioal to Σ 0σ u, ad so is the aggregate illiquidity i the full-disclosure case Λ ˆ Therefore, if (A5) is true, the decrease i illiquidity Λ Λ ˆ, or improvemet i liquidity is proportioal to Σ 0σ u, ad is thus icreasig i Σ 0 We ext proceed to prove (SA) To facilitate the proof, we explicitly idicate the total umber of periods i our otatios below, such as usig μ, = μ,, = We will also assume that Σ σ u 0 =, sice it is just a ormalizig costat i (SA) We first show the followig lemma that is useful for our proof Lemma i) μk,, k =,,, is decreasig with k ii) For 4, iii) For ay 0 k, Proof of Lemma m, + m, > m+, + m+,, if m (SA37) k+, + +, + k,, 0 ˆ > (SA38) ˆ ˆ > (SA39) ˆ k+, + +, + k,, Part i): Defie vi = μ i +, the recursive formula (SA8) implies that
( vi ) f ( v i + ) = v i (SA40) where 8 x ( x) f ( x) = We also have vk (0,/ ) Therefore x 8 vi+ ( vi+ ) ( vi) 8 vi ( vi) f ( vi + ) = = > = f( vi ) v v v i+ i i Sice f ( ) is icreasig for x (0,/ ), v i is icreasig i i ad thus μk is decreasig i k Part ii): We have + m + m 4 μm + 4 μm = 4 μm ( μm+ ) = 4 μm+ ( μm+ ) m+ + m+ + + 4μm+ 4 μ m+ (SA4) μm+ We kow that f ( μm ) = ad the fuctio μ m+ + 4x y = 6 x( x) satisfies ( x) f( y) <, if /> x> 036 Therefore, the icreasig property of the fuctio f implies x that μ + 4μ >, if > 036 m+ m μm+ 6 μm+ ( μm+ ) (SA4) Pluggig (SA4) ito (SA4), we have + + m m m+ m+ >, if μ > 036 m+ (SA43) Sice m, Part i) ad the fact that μ 3 = v = 0387 > 036 imply that μ m + > 036 ad thus (SA37) holds Part iii): First, ote that by the recursive formulas i Propositio,
= = = k, k, k 3, 4μ k 4μ k 4 μ k 3( μ k ) / k / k μ =, = m= 4 μm ( μm ) 4μ m= 4 μm ( μm ) / v / = i= / k4 vi( vi) Therefore, = = k+, + = k, /+ /+ / v /+ 4 v ( v ) v v /+ v 4 v ( v ) / /+ /+ 4 v/+ ( v/+ ) v 4 v ( v ) /+ /+ / = > ( v /)( v /+ ) + ( )( ) ( + ) ( + ) ˆ = > = ( + )( + 3) + ˆ +, +, Where we used the fact that v i i, which is easily verified usig the recursive formula i (SA40) ad the icreasig property of the fuctio f This proves (SA38) (SA39) ow follows from (SA38) ad the recursive relatios k, = 4μ, = 4v k k k k, ad k+, + 4vk k+, + = This completes the proof of the lemma QED Give the lemma, we will prove (SA) usig iductio o the umber of periods I the case =, usig the recursive formulas i Propositio, it is easy to obtai that + = 046 + 0 46 > ˆ = 0707,,, We will ext show the followig equatios hold for ay 4, For = 4, we have ˆ 3, +,,, + ˆ,,, (SA44)
+ = 0388 + 05 > ˆ,4,4, 3,4 4,4, = 05 + = 0345 + 03 > ˆ = 05 ow suppose (SA44) hold for Equatio (SA38) from Lemma the imply that + + ˆ ˆ, +, + 3,, +, +, + + ˆ ˆ +, + +, +,, +, +, Thus (SA44) also hold for + Combig (SA44) ad (SA37), we see that / Λ = ( + ) ( + ) + ( + ) m, m, 3,,,, m= ˆ ˆ, =Λ (SA45) This completes the proof of (SA) (ii) We shall first show that the expected profits of the iformed trader i period for the cases k = ad k = are give by E[ π ] = σ, E[ ˆ π ] = ˆ σ,, (SA46) Ideed, i the case where the iformed trader is required to disclose every period (k = ), Propositio 4 of HHL shows that the expected profit is give by σu ˆ ˆ E[ ˆ π ] = Σ 0 / = σ u I the case where the iformed trader is oly required to disclose every two periods (k = ), if = or is ot a multiple of, the by (), (), (SA), ad (SA5), the expected profit is Ex [ ( v p )] = E[ β ( v p )( v p ( β ( v p ) + u ))] * * * = β ( β ) Σ = β Σ = σ u If < is a multiple of, the by (), (), ad (SA5), Ex [ ( v p )] = E[( β ( v p ) + z )( v p ( β ( v p ) + z + u ))] * * * 3 μ = β ( β ) Σ σ = β Σ σ + z u 4( μ+ ) ( μ+ ) 3 μ = σ σ ( μ ) ( ) = σ u + u u + μ+ 3
Therefore, (SA46) always hold Combiig part (i) ad (SA46), we obtai the desired result o total expected profits, ˆ [ ] ˆ = E π σu = Λ σu > Λσu = Π = = Π = As the expected profits are proportioal to the aggregate illiquidity, by part (i), the differece Π ˆ Π decreases with Σ 0 (iii) We shall show for ay, Π ˆ Π <Π ˆ Π (SA47) + + If this is true, the (A7) follows by iductio Because of (SA46), this is equivalet to Λ ˆ Λ <Λ ˆ Λ (SA48) + + The case = ca be directly verified usig the expressios of s calculated i (i) ext we show (SA48) holds for ay 4 From (SA38) ad (SA39) i Lemma, we have ˆ + > + (SA49) +, + i+, + i+, + ( i, i, ), i / ˆ, From (SA37) ad iductio, it is easy to show that Usig (SA49) ad (SA50),, + +, + > i+, + + i+, +, i / (SA50) / Λ Λ ˆ = ( + ) ( + ) ˆ + + i+, + i+, + +, + i= 0 / + ˆ +, + (,, ) ( ) ˆ i + i + +, + ˆ i=, / + ˆ ˆ,, ( ˆ + + + ˆ + + i, + + i, ), = ( Λ Λ) ˆ ˆ i=,, + = = + ( Λ ˆ ) ˆ Λ > Λ Λ QED 4
II Additioal Tables for Robustess Checks I this sectio, we preset results that are omitted from the mai text of the paper for the sake of brevity SAI Aalysis of the 985 Regulatio Chage This table presets results for tests o stock liquidity ad fud performace coducted usig December 985 as aother evet moth I the year of 985, the SEC chaged the frequecy of disclosure required for mutual fuds from a quarterly frequecy to a semi-aual frequecy We repeat our aalyses i Pael A of Table III ad Pael B of Table VII of the paper ad preset the results i this table SAII Tests Cotrollig for the Chage i Mutual Fud Owership This table presets the results of regressios of the chage i stock liquidity o Mutual Fud Owership ad the chage i mutual fud owership It is possible that mutual fud tradig chages aroud the regulatio chage Icludig the chage i mutual fud owership i the regressios helps cotrol for this possibility We fid our results o the impact of the regulatio chage o stock liquidity are robust to the iclusio of this variable SAIII-IV Tests usig Abormal Owership These two tables preset results usig abormal mutual fud owership as the mai idepedet variable i our tests It is possible that mutual fud owership of stocks is related to the stock characteristics To cotrol for this possibility, we use employ a two-stage procedure I the first stage, we regress mutual fud owership o both stock characteristics ad a lagged liquidity variable We defie the residual from this regressio as Abormal Mutual Fud Owership I the secod stage, we regress the chage i stock liquidity o Abormal Mutual Fud Owership ad other cotrol variables Table SAIII shows that our results i Pael B of Table II ad Pael D of Table III i the paper are robust to this specificatio Further, the results i Table SAIV show that our fidigs o o-mf Owership ad Hedge Fud Owership are also robust to this two-stage procedure 5
SAV Fud Subsample Tests usig Alterative Performace Measures This table reports results from our fud subsample tests i which we use alterative measures of fud performace Specifically, we classify iformed fuds usig Liquidity-adjusted DGTW (Rspread) ad the impatiet tradig measure of Da, Gao, ad Jagaatha (0) Liquidity-adjusted DGTW (Rspread) is aalogous to Liquidity-adjusted DGTW i the paper (stocks sorted usig Rspread istead of Amihud whe formig the DGTW bechmark portfolios) Our results usig these alterative measures are qualitatively similar to those preseted i Table V i the paper SAVI Tests of the Log-Ru Impact of the Regulatio Chage Our model predicts that the regulatio chage has a permaet impact o both stock liquidity ad the iformed trader s profits To test these predictios, we estimate regressios as i equatios (9) ad (3) of the paper but use three-year cumulative chages i liquidity ad performace as our depedet variables We fid that, as show i Pael A of this table, the impact of Mutual Fud Owership o stock liquidity persists after three years Further, the declie top performig mutual fuds experiece is cocetrated i the year after the regulatio chage ad does ot revert i subsequet years (see Pael B of Table SAVI) These fidigs support our model s predictios about the permaet impact of a icrease i madatory portfolio disclosure frequecy SAVII Tests usig Chages i Mutual Fud Characteristics I this table, we preset results usig chages i mutual fud characteristics as the idepedet variables i regressios estimated usig equatio (3) of the paper It is possible that top mutual fuds themselves experieced chages aroud the SEC rule chage i 004; such chages i fud characteristics, rather tha the regulatio chage, may explai the performace deterioratio i top fuds Our results o fud performace i this table rules out such a possibility 6
SAVIII Full Period Time-series Placebo Tests excludig Crisis Periods This table presets results aalogous to those preseted i Table IX of the paper We exclude kow crisis years (998, 000, ad 00) from our placebo period to esure that our results are ot drive by these years We cotiue to fid the differece i the performace drop for top madatory ad top volutary fuds is statistically larger i May 004 compared to the 994-006 placebo period after excludig the crisis years 7
Table SAI Impact of the 985 Regulatio Chage o Stock Liquidity ad Fud Performace This table presets results related to the 985 regulatio chage Pael A presets regressios of the chage i liquidity aroud December 985 o Mutual Fud Owership, o-mf Owership, ad the lagged stock characteristic variables we use i Pael B of Table II of the paper The last two rows report the differeces betwee the coefficiets of Mutual Fud Owership ad o-mf Owership ad the p-values from the F-tests of the differeces Pael B presets regressios of the chage i mutual fud performace o a idicator variable equal to oe if the fud was i the top quartile of a give performace measure ad zero otherwise, ad the fud characteristics we use i Pael B of Table VII i the paper Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level, ad t-statistics are reported below the coefficiets Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level respectively Pael A: 985 Liquidity Aalysis () () VARIABLES ΔAmihud ΔRspread MF Owership 0453-004 (039) (-4) o-mf Owership -058*** -065*** (-36) (-35) Mometum -0484*** -039*** (-895) (-980) Book-to-Market 0067*** -0037** (30) (-0) Size -093*** -0*** (-5) (-040) Lagged Liquidity -04*** -046*** (-976) (-46) Costat -0860*** -078*** (-678) (-60) Observatios,386,386 Adj R-squared 054 0496 Differece (MF o-mf) 07-08388 p-value (Differece) 0547 0349 8
Pael B: 985 Performace Aalysis VARIABLES () () (3) 4-factor Alpha 5-factor Alpha DGTW 4-factor Alpha -095 (-40) 5-factor Alpha -057 (-39) DGTW -009 (-096) Log(TA) 056* 0069 0066 () (6) (69) Turover 0044 00-00 (035) (40) (-06) Expese Ratio 45559 955 0339 (9) (038) () Costat -83-05 -054 (-80) (-0) (-46) Observatios Adjusted R-squared 048 0367 0049 9
Table SAII Impact of Madatory Portfolio Disclosure o Stock Liquidity: Regressios Icludig the Chage i Mutual Fud Owership This table reports the regressio results of the chages i stock liquidity variables aroud May 004 o the mutual fud owership ad other cotrol variables as i Pael B of Table II of the paper We augmet these regressios by icludig ΔMutual Fud Owership as a additioal cotrol variable The idepedet variables are the averages of the variables i Pael A of Table II i the year prior to May 004 Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level ad t-statistics are reported below the coefficiets i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level, respectively VARIABLES () () (3) (4) ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Mutual Fud Owership -94*** -088*** -46*** -966*** (-049) (-364) (-453) (-73) ΔMutual Fud Owership -48*** -3460*** -36*** -546*** (-979) (-75) (-30) (-759) Mometum -006*** -00*** -09*** -005*** (-64) (-064) (-74) (-74) Book-to-Market -03*** -0049*** -009* -036*** (-9) (-334) (88) (-647) Size -053*** -09*** -038*** -005*** (-46) (-60) (-04) (-575) Lagged Liquidity -033*** -07*** -078*** -08*** (-45) (-87) (-679) (-885) Costat -37*** -036*** -0457*** -035*** (-306) (-833) (-035) (-83) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 075 073 099 00 0
Table SAIII Impact of Madatory Portfolio Disclosure o Stock Liquidity: Base Regressios Usig Abormal Owership This table reports the results of a two-stage regressio procedure I the first stage, we regress the aggregate mutual fud owership o Mometum, Size, Book-to-Market, ad the correspodig lagged liquidity variable We defie Abormal MF Owership as the residual of this first-stage regressio We the regress the chage i stock liquidity aroud May 004 o this abormal owership variable ad other cotrol variables as i Pael B of Table II of the paper Paels A ad C report the results of the first-stage aalysis i 004 ad the placebo period i 006, respectively Paels B ad D report the secod-stage regressios i 004 ad 006, respectively Pael E reports the differeces betwee the coefficiets o abormal mutual fud owership i 004 ad 006 ad the p-values from F-tests Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level ad t-statistics are reported below the coefficiets i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level, respectively Pael A First-Stage Aalysis i 004 VARIABLES X = Amihud X = Rspread Depedet Variable: MF Owership () () (3) (4) X = Size-weighted Rspread X = Effective Spread Mometum -000** 0004*** 0005*** 0006*** (-53) (58) (547) (79) Book-to-Market 0004*** 000 000* -000* (355) (60) (7) (-8) Size -000*** 000*** 000*** 00*** (-599) (330) (45) (639) Liquidity (X) -0056*** -007*** -009*** -006*** (-3508) (-638) (-880) (-839) Costat -0330*** -00*** -008*** -0070*** (-403) (-909) (-39) (-303) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 0547 0449 0458 045
Pael B: Secod-Stage Regressios i 004 VARIABLES () () (3) (4) ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Abormal MF Owership -085*** -795*** -00*** -459*** (-77) (-96) (-94) (-883) Mometum -008*** -07*** -046*** -040*** (-804) (-80) (-396) (-99) Book-to-Market -033*** -0055*** -0036** -09*** (-93) (-370) (-35) (-64) Size -039*** -043*** -065*** -0068*** (-34) (-94) (-46) (-764) Lagged Liquidity -077*** -074*** -0*** -0077*** (-56) (-046) (-359) (-594) Costat -0795*** -060*** -006*** -04*** (-087) (-40) (-54) (-559) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 0087 037 065 00586 Pael C: First-Stage Aalysis i 006 Depedet Variable: MF Owership () (3) (4) (5) VARIABLES X = Amihud X = Rspread X = Size-weighted Rspread X = Effective Spread Mometum -0004** 0009*** 0008*** 0009*** (-) (470) (466) (490) Book-to-Market 000-000 -0003* -0007*** (079) (-59) (-90) (-48) Size -00*** -00*** -0008*** -00*** (-767) (-093) (-93) (-088) Liquidity (X) -0059*** -005*** -0054*** -0049*** (-386) (-3639) (-3954) (-370) Costat -0344*** -034*** -066*** -036*** (-4643) (-464) (-5065) (-476) Observatios 4,467 4,467 4,467 4,467 Adj R-squared 053 057 0536 058
Pael D: Secod-Stage Regressios i 006 VARIABLES () () (3) (4) ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Abormal MF Owership -055*** -069*** -0639*** -0575*** (-499) (-667) (-680) (-644) Mometum -06*** -07*** -030*** -087*** (-084) (-566) (-748) (-633) Book-to-Market -0036** -0038*** -00-007 (-4) (-73) (-43) (-9) Size -007*** -04*** -09*** -0090*** (-736) (-48) (-98) (-84) Lagged Liquidity -0085*** -07*** -056*** -08*** (-650) (-079) (-47) (-589) Costat -0439*** -0395*** -048*** -080*** (-635) (-337) (-445) (-540) Observatios 4,467 4,466 4,466 4,466 Adj R-squared 005 06 07 047 Pael E: Differeces i the Coefficiets o Abormal Mutual Fud Owership (Paels B ad D) () () (3) (4) VARIABLES ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Diff of Coefficiets (004-006) -090* -66*** -46*** -0884** Test of Differeces (p-value) 0059 <000 <000 <000 3
Table SAIV Impact of Madatory Portfolio Disclosure o Stock Liquidity: Cross-sectioal Placebo Regressios Usig Abormal Owership This table reports the results of a two-stage regressio procedure I the first stage, we regress the aggregate mutual fud (or o-mutual fud or hedge fud) owership o Mometum, Size, Book-to-Market, ad the correspodig lagged liquidity variable We defie Abormal MF Owership (or Abormal o-mf Owership or Abormal Hedge Fud Owership) as the residual of the first-stage regressio We the regress the chage i stock liquidity aroud May 004 o this abormal owership variable ad other cotrol variables as i Pael B of Table II of the paper Paels A ad C report the results of the first-stage aalysis i 004 for o-mf Owership ad Hedge Fud Owership, respectively Paels B ad D report the secod-stage regressios i which we compare Abormal MF Owership with Abormal o-mf Owership ad Abormal Hedge Fud Owership, respectively The last two rows i Paels B ad D compare the coefficiets o abormal mutual fud owership ad the correspodig abormal istitutioal owership variable ad the p-values from F-tests Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level ad t-statistics are reported below the coefficiets i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level, respectively Pael A First-Stage Aalysis for o-mf Istitutios VARIABLES Depedet Variable: o-mf Owership () () (3) (4) X = Amihud X = Rspread X = Size-weighted Rspread X = Effective Spread Mometum -005*** -000*** -000*** -0007*** (-44) (-504) (-503) (-34) Book-to-Market 003*** 004*** 005*** 007*** (845) (69) (636) (437) Size -009*** 0047*** 0045*** 0035*** (-875) (370) (446) (87) Liquidity (X) -0*** -003*** -0037*** -0040*** (-767) (-737) (-99) (-90) Costat -073*** -07*** -087*** -05*** (-337) (-8) (-96) (-3) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 057 0483 0487 05 4
Pael B Secod Stage Regressios for Abormal o-mf Owership VARIABLES () () (3) (4) ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Abormal MF Owership -0636*** -30*** -56*** -057*** (-59) (-766) (-860) (-58) Abormal o-mf Owership -08*** -0447*** -0494*** -0400*** (-395) (-664) (-693) (-493) Mometum -008*** -07*** -046*** -040*** (-806) (-84) (-400) (-993) Book-to-Market -033*** -0055*** -0036** -08*** (-96) (-37) (-36) (-66) Size -039*** -043*** -065*** -0068*** (-35) (-94) (-469) (-769) Lagged Liquidity -077*** -073*** -0*** -0077*** (-55) (-049) (-37) (-595) Costat -0795*** -060*** -006*** -04*** (-086) (-40) (-53) (-56) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 0086 046 074 0063 Diff of Coeffs (MF - o-mf) -0408*** -0855*** -068*** -0657*** Test of Differece (p-value) 007 <000 <000 004 5
Pael C First-Stage Aalysis for Hedge Fuds VARIABLES Depedet Variable: HF Owership () () (3) (4) X = Amihud X = Rspread X = Size-weighted Rspread X = Effective Spread Mometum -0005*** 000* 000* 0004*** (-379) (89) (9) (308) Book-to-Market 0009*** 0005** 0005** 000 (369) () (3) (076) Size -003*** 0006*** 0005*** 000 (-64) (55) (478) (095) Liquidity (X) -0059*** -005*** -008*** -008*** (-345) (-60) (-805) (-350) Costat -079*** -007*** -005*** -0007 (-79) (-99) (-43) (-54) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 090 00934 00985 00 6
Pael D Secod Stage Regressios for Abormal HF Owership VARIABLES () () (3) (4) ΔAmihud ΔRspread ΔSize-weighted Rspread ΔEff Spread Abormal MF Owership -070*** -008-69*** -05*** (-69) (-099) (-99) (-704) Abormal HF Owership -033*** -08-088*** -0590*** (-367) (-43) (-803) (-479) Mometum -008*** -0083*** -046*** -040*** (-806) (-9) (-49) (-996) Book-to-Market -033*** -05*** -0036** -08*** (-94) (-835) (-37) (-66) Size -039*** -0073*** -065*** -0068*** (-34) (-08) (-477) (-767) Lagged Liquidity -077*** -00*** -0*** -0077*** (-55) (-9) (-373) (-594) Costat -0795*** -049*** -006*** -04*** (-085) (-7) (-54) (-560) Observatios 4,635 4,634 4,634 4,634 Adj R-squared 00855 048 077 0069 Diff of Coeffs (MF - HF) -0407** -0679*** -08*** -065*** Test of Differece (p-value) 000 000 00004 0009 7
Table SAV Impact of Madatory Portfolio Disclosure o Stock Liquidity: Subsamples of Mutual Fuds This table reports the regressio results of the chages i stock liquidity o mutual fud owership of top- ad o-top-performig fuds The depedet variables are the chages i the liquidity variables after May 004 All regressios iclude cotrols for lagged stock liquidity ad other stock characteristics as i Pael B of Table II i the paper The last two rows report the differeces betwee the coefficiets of the owership of top-quartile ad o-top-quartile fuds ad the p-values from the F-tests of the differeces Liquidity-adjusted DGTW (Rspread) is calculated by augmetig size, book-to-market, ad mometum with stock liquidity (usig Rspread) i the characteristics used to form the DGTW bechmark portfolios Da, Gao, ad Jagaatha DGTW is the impatiet tradig measure of Da, Gao ad Jagaatha (0) Paels A ad B report the results whe fuds are separated based o whether or ot they are i the top quartile of these performace measures for the prior year Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level, ad t-statistics are reported below the coefficiets i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level respectively Pael A: Liquidity-Adjusted DGTW (Rspread) () () (3) (4) ΔSize-Weighted ΔEff ΔAmihud ΔRspread VARIABLES Rspread Spread Top Fud Owership -0009*** -00040*** -00045*** -00033*** (-597) (-0) (-097) (-68) o-top Fud Owership -00006** -000*** -0007*** -0007*** (-5) (-634) (-73) (-387) Differece (Top o-top) 4,635 4,634 4,634 4,634 p-value (diff) 0087 063 095 00696 Pael B: Da, Gao, ad Jagaatha (0) () () (3) (4) ΔSize-Weighted ΔEff ΔAmihud ΔRspread VARIABLES Rspread Spread Top Fud Owership -0004*** -00039*** -00043*** -00033*** (-44) (-939) (-974) (-63) o-top Fud Owership -000*** -0004*** -0003*** -0009*** (-449) (-797) (-948) (-486) Differece (Top o-top) 4,635 4,634 4,634 4,634 p-value (diff) 00876 069 00 007 8
Table SAVI Log-Ru Impact of the Regulatio Chage o Liquidity ad Fud Performace This table reports results related to the log-ru impact of the regulatio chage o stock liquidity ad fud performace Pael A cotais regressios of chages i stock liquidity o Mutual Fud Owership, o-mf Owership ad the stock-level cotrol variables as i Table II of the paper Pael B cotais regressios of chages i mutual fud performace o a top fud idicator variable ad the fud-level cotrols as i Table VII of the paper The first colum i each table presets the results where the depedet variable is the oe-year chage i liquidity or performace, while the secod colum presets the results where the depedet variable is the three-year chage i liquidity or performace The third colum presets the differeces betwee coefficiets i the first ad secod colum Stadard errors are adjusted for heteroskedasticity ad clustered at the stock level ad t-statistics are reported below the coefficiets i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level, respectively Pael A Stock Liquidity Short-Term Chage i Y Log-Term Chage i Y Log-Term Short-Term VARIABLES Y = Amihud Diff (MF - o-mf) -0408** -0474-0067 (56) (53) (-00) Y = Rspread Diff (MF - o-mf) -0855*** -87*** -043 (45) (404) (-9) Y = Size-Weighted Rspread Diff (MF - o-mf) -068*** -30*** -033 (504) (40) (-064) Y = Effective Spread Diff (MF - o-mf) -0657*** -0774** -07 (69) (5) (-030) 9
Pael B Fud Performace Short-Term Log-Term Log-Term VARIABLES Chage i Y Chage i Y Short-Term Y = 4-factor Alpha Top Y -00*** -04*** -003 (-650) (-606) (-38) Y = 5-factor Alpha Top Y -0089*** -009*** -000** (-49) (-504) (-05) Y = DGTW-adj Retur Top Y -043*** -06*** -009 (-98) (-67) (-8) Y = Liquidity-adjusted DGTW Top Y -0068*** -0075*** -0007 (-3) (-507) (-64) 30
Table SAVII Impact of Disclosure Regulatio o Mutual Fud Performace: Chages o Chages Regressios This table reports results of multivariate regressios of chages i fud performace after 004 o lagged fud performace ad chages i fud characteristics I all regressios, we cotrol for chages i fud characteristics, icludig ΔLog(TA), ΔTurover, ΔFlow, ΔExpese Ratio, ad ΔLoad All variables are defied as i Table VII of the paper Stadard errors are adjusted for heteroskedasticity ad clustered at the fud level, ad t-statistics are reported i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level respectively () () (3) (4) VARIABLES 4-factor Alpha 5-factor Alpha DGTW Liquidity-adj DGTW Top 4-factor Alpha -003*** (-678) Top 5-factor Alpha -0087*** (-353) Top DGTW -05*** (-89) Top Liquidity-Adj DGTW -0067*** (-57) ΔLog(TA) 0004-006** 008*** 0005 (058) (-0) (369) (56) ΔTurover -0005-0006 00** -0000 (-088) (-5) (00) (-006) ΔFlow 05** 0036 0048-0040* (56) (070) (09) (-70) ΔExpese Ratio 006-0866 95 69 (00) (-038) (080) (53) ΔLoad -0006-0007 -000 0007 (-09) (-033) (-007) (074) Costat 0040*** 0033*** 007*** 009*** (3) (969) (69) () Observatios,3,3,7,7 Adjusted R-squared 0 057 03 0305 3
Table SAVIII Impact o Mutual Fud Performace: Full Placebo Periods Excludig Crisis Periods This table compares the regressio results of the chages i fud performace for the matched samples of madatory ad volutary fuds (see Table IV of the paper) i a two-year period aroud the SEC disclosure regulatio i 004 with the same regressios coducted for placebo periods costructed usig each placebo moth i the period of 994-006 (excludig 004 ad the kow crisis years of 998, 000, ad 00) The idepedet variables i the placebo tests are the lagged variables All performace variables are aualized I all regressios, we cotrol for Log(TA), Turover, Flow, Expese Ratio, ad Load Paels A ad B report results for the samples matched usig Models ad i Table IV of the paper, respectively Stadard errors are adjusted for heteroskedasticity ad clustered at the fud level, ad t-statistics are reported i paretheses Coefficiets marked with ***, **, ad * are sigificat at the %, 5%, ad 0% level 4-factor Alpha 5-factor Alpha DGTW Liq-adj DGTW Pael A Madatory ad Volutary Fuds Matched by Model Mad - Vol (May 004) -00-004 -006-0047 Mad - Vol (Mea over placebo periods) -006-003 -00-000 Quad diff (May 004 - Placebo period) -0005-000 -0048*** -0046*** t-statistic (-097) (-04) (-83) (-666) Pael B Madatory ad Volutary Fuds Matched by Model Mad - Vol (May 004) -0030-004 -004-0040 Mad - Vol (Mea over placebo periods) -003-000 -0009-0007 Quad diff (May 004 - Placebo period) -007*** -004** -003*** -0033*** t-statistic (-353) (-4) (-994) (-5) 3