Designated Market Makers for Small-Cap Stocks Is One Enough? Albert J. Menkveld Vrije Universiteit Amsterdam Presentation AMF-SEC Colloque Paris May 2007 1
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Background and Motivation Firms care about liquidity. Small-cap firms in particular, due to - high bid-ask spreads e.g. Amihud and Mendelson (1986, JFE) show that bid-ask differentials across stocks could account for 50% value differentials - Acharya and Pedersen (2005, JF) find that low liquidity coincides with high (priced) liquidity risk - Pastor and Stambaugh (2003, JPE) study size directly, show that liquidity risk is highest for small-caps and find an associated additional required return of 3.7% annually 3
Background and Motivation Firms care about liquidity. Small-cap firms in particular, due to - high bid-ask spreads e.g. Amihud and Mendelson (1986, JFE) show that bid-ask differentials across stocks could account for 50% value differentials - Acharya and Pedersen (2005, JF) find that low liquidity coincides with high (priced) liquidity risk - Pastor and Stambaugh (2003, JPE) study size directly, show that liquidity risk is highest for small-caps and find an associated additional required return of 3.7% annually Exchanges respond by (re-)introducing designated market makers (DMMs) Contemporary studies document liquidity improvement and 5% abnormal return (see Nimalendran and Petrella (2003), Venkataraman and Waisburd (2006), Anand, Tanggaard, and Weaver (2005)) 3-a
Our Contribution Thus far, markets typically feature a single DMM. Microstructure theory suggests two arguments in favor of multiple DMMs - competition (see e.g. Glosten (1989), Bernhardt and Hughson (1997), Biais, Martimort, and Rochet (2000), and Biais, Glosten, and Spatt (2005) for survey second-generation microstructure models ) - classic inventory-sharing (see Stoll (1978) and Ho and Stoll (1981, 1983), etc.) 4
Our Contribution Thus far, markets typically feature a single DMM. Microstructure theory suggests two arguments in favor of multiple DMMs - competition (see e.g. Glosten (1989), Bernhardt and Hughson (1997), Biais, Martimort, and Rochet (2000), and Biais, Glosten, and Spatt (2005) for survey second-generation microstructure models ) - classic inventory-sharing (see Stoll (1978) and Ho and Stoll (1981, 1983), etc.) We exploit the Euronext introduction of DMMs in the Dutch market to 1. study empirically whether the #DMMs that a firm hires matters for liquidity supply 2. argue exogeneity of this #DMMs and exploit it as an instrumental variable to identify causality from liquidity supply to liquidity demand (volume) and volatility 4-a
Institutional Background On October 29, 2001, Euronext introduced DMMs in the Dutch equity market. A DMM - commits to maximum spread of 4% - commits to minimum depth ofe10,0000 - does not pay trading fees - potentially receives pecuniary compensation from issuer - might be indirectly compensated through additional business e.g. seasoned offerings, banking services, etc. DMMs supply liquidity in a pure limit order market. They do not enjoy ex-post price improvement privileges (as e.g. the NYSE specialist) 5
Simple Model A maximum spread of 4% and a minimum depth ofe10,000 seem to be non-binding, but for these small-cap stocks, they can be binding. As liquidity provider you lose money for sure when the market is very volatile. Willem Meijer, SNS Securities in Financieel Dagblad 6
Simple Model A maximum spread of 4% and a minimum depth ofe10,000 seem to be non-binding, but for these small-cap stocks, they can be binding. As liquidity provider you lose money for sure when the market is very volatile. Willem Meijer, SNS Securities in Financieel Dagblad We extend a standard Ho and Stoll inventory model to capture two salient features of our institutional setting 1. two volatility regimes: in the high regime liquidity constraint is binding 2. DMMs lose money on liquidity supply but enjoy a private indirect compensation 6-a
Simple Model Consider the market for a risky asset with end-of-period liquidation value v NID(0, σ i ). We propose a five-stage game. WLOG, we consider the sell-side of liquidity supply: 1. N potential DMMs consider entry. If they enter, they enjoy private benefit C i and commit to ask price cap A 2. the volatility regime is learned: σ h with probability p h, normal volatility otherwise 3. liquidity is supplied by those who entered 4. a liquidity trader sends market buy of (deterministic) size Q 5. payoffs are realized 7
We find Simple Model 1. multiple Nash equilibria, unique sequential one, assume n DMMs enter 8
We find Simple Model 1. multiple Nash equilibria, unique sequential one, assume n DMMs enter 2. that a higher #DMMs leads to a lower expected ask: E[A ] = (1 p h ) φ n + p h A with φ Qσ 2 γ 8-a
We find Simple Model 1. multiple Nash equilibria, unique sequential one, assume n DMMs enter 2. that a higher #DMMs leads to a lower expected ask: E[A ] = (1 p h ) φ n + p h A with φ Qσ 2 γ 3. that a higher #DMMs reduces transitory volatility: E[A ] = E[A ] + I φ n Q 8-b
We find Simple Model 1. multiple Nash equilibria, unique sequential one, assume n DMMs enter 2. that a higher #DMMs leads to a lower expected ask: E[A ] = (1 p h ) φ n + p h A with φ Qσ 2 γ 3. that a higher #DMMs reduces transitory volatility: E[A ] = E[A ] + I φ n Q Relevance of the model for our setting - the competitive equilibrium is most likely implemented in limit order market (see Biais, Foucault, and Salanié (1998)) 8-c
We find Simple Model 1. multiple Nash equilibria, unique sequential one, assume n DMMs enter 2. that a higher #DMMs leads to a lower expected ask: E[A ] = (1 p h ) φ n + p h A with φ Qσ 2 γ 3. that a higher #DMMs reduces transitory volatility: E[A ] = E[A ] + I φ n Q Relevance of the model for our setting - the competitive equilibrium is most likely implemented in limit order market (see Biais, Foucault, and Salanié (1998)) - a private indirect compensation drives the entry as evident from (i) press coverage, (ii) interviews with DMM firms, and (iii) a Granger causality analysis using volume and volatility 8-d
Data and Methodology DMMs are introduced for 74 small-caps. Based on Euronext data, we define for each of the first 20 months - average #DMMs - average of time-weighted (intraday) quoted spread - volume - volatility of daily midquote returns - average market cap (fixed across time) 9
Data and Methodology DMMs are introduced for 74 small-caps. Based on Euronext data, we define for each of the first 20 months - average #DMMs - average of time-weighted (intraday) quoted spread - volume - volatility of daily midquote returns - average market cap (fixed across time) We use standard panel data econometrics (and robust standard errors) - simple OLS, OLS between, OLS within - use #DMMs as instrumental variable in Hausman/Taylor and Arrelano/Bond/Bover GMM approach 9-a
Hausman-Taylor and ABB GMM The general model takes the form: y it = x 1,itβ 1 + x 2,iβ 2 + λ t + η i + v it We follow two strategies to maximize the power of the instrumental variable. 10
Hausman-Taylor and ABB GMM The general model takes the form: y it = x 1,itβ 1 + x 2,iβ 2 + λ t + η i + v it We follow two strategies to maximize the power of the instrumental variable. 1. Hausman and Taylor (1981) propose strategy that allows each time-varying instrumental variable to instrument for a time-varying as well as a time-invariant endogenous variable through decomposition into two orthogonal components: z i = 1 20 20 t=1 z i,t z i,t = z i,t z i In its most elementary form, the approach assumes (i) no time effect, (ii) v it to be i.i.d. and (iii) η i to be i.i.d. and (iv) both are mutually independent and independent of any of the explanatory variables. 10-a
Hausman-Taylor and ABB GMM (ctd) 2. Arellano and Bond (1991) and Arellano and Bover (1995) propose two-stage GMM that generalizes Hausman-Taylor. For group i, we define: y i = W i δ + ιη i + v i where W contains x 1,it, x 2,i, and a time-dummy, δ is the associated parameter vector, ι is a Tx1 vector of ones, and v i is the vector with error terms. Let Z i contain the instrumental variables i.e. Z i [ιz i z i ] The GMM estimator now takes the form: ( ˆδ = ( W iz i )A N ( ) 1( Z iw i ) W iz i )A N ( i i i i ( 1 ) A N = Z N ih i Z i i 11 Z iy i )
Summary Statistics Mean St. Dev. St. Dev. Between a St. Dev. Within b #DMM 3.12 1.44 1.33 0.57 Market Capitalization (ebln) 0.37 0.37 0.37 0.00 #Trades per Day 59.57 84.70 79.67 28.73 Daily Volume (emln) 0.57 0.85 0.76 0.38 Quoted Spread (%) 1.33 1.17 0.95 0.68 Volatility Daily Midquote Returns (σ) 2.31 1.64 0.98 1.32 Autocorrelation Daily Midquote Returns -0.04 0.24 0.09 0.22 Price (e) 15.86 12.05 11.18 4.48 #Observations (N*T) 74*20 a : Based on the time means i.e. x i = 1 T T t=1 x i,t. b : Based on the deviations from time means i.e. x i,t = x i,t x i. 12
Does #DMMs Impact Bid-Ask Spread? Without Instrumental Variables (A) OLS (B) OLS between (C) OLS within (D) HT/ GLS With IVs (E) ABB/ GMM #DMM -0.65** -0.70** -0.51* -0.50** -0.56** (-3.41) (-3.57) (-1.64) (-2.08) (-2.37) (#DMM) 2 0.05** 0.05** 0.06* 0.06* 0.05** (2.46) (2.54) (1.73) (1.64) (2.19) Market Cap -0.94** -0.92** -4.78-2.86* (-3.64) (-3.69) (-0.52) (-1.88) N*T 74*20 74*1 74*20 74*20 74*20 R 2 0.27 0.41 0.02 a : Based on the time means i.e. x i = 1 T T t=1 x i,t. */**: Significant at a 90/95% level. 13
Does #DMMs Impact Bid-Ask Spread? 2.00 OLS ABB GMM 1.75 1.50 1.25 1.00 0.75 0.50 0.25 1 2 3 4 5 6 7 8 14
Does the Bid-Ask Spread impact Volume? Without Instrumental Variables (A) OLS (B) OLS between (C) OLS within (D) HT/ GLS With IVs (E) ABB/ GMM Quoted Spread -0.13** -0.16** -0.08* -0.15-0.17 (-2.46) (-2.40) (-1.66) (-0.90) (-0.55) Market Cap 1.43** 1.39** 1.90 1.65 (7.19) (7.14) (0.86) (0.60) Intercept 0.21** 0.27** 0.06 0.12 (2.04) (2.14) (0.06) (0.10) N*T 74*20 74*1 74*20 74*20 74*20 R 2 0.48 0.60 0.02 a : Based on the time means i.e. x i = 1 T T t=1 x i,t. */**: Significant at a 90/95% level. 15
Does the Bid-Ask Spread impact Volatility? Without Instrumental Variables (A) OLS (B) OLS between (C) OLS within (D) HT/ GLS With IVs (E) ABB/ GMM Quoted Spread 0.72** 0.68** 0.78** 0.89* 0.73** (12.65) (6.27) (10.54) (1.63) (2.83) Market Cap 0.16 0.12 4.84 4.07 (0.65) (0.45) (0.59) (1.40) Intercept 1.28** 1.35** -0.68-0.06 (8.20) (5.94) (-0.19) (-0.05) N*T 74*20 74*1 74*20 74*20 74*20 R 2 0.25 0.41 0.17 a : Based on the time means i.e. x i = 1 T T t=1 x i,t. */**: Significant at a 90/95% level. 16
Does the B-A Spread impact Autocorrelation? We regress first-order autocorrelation in midquote returns on the bid-ask spread to identify whether low spreads reduce transitory volatility: Without Instrumental Variables (A) OLS (B) OLS between (C) OLS within With IVs (E) ABB/ GMM Quoted Spread -0.02** -0.04** 0.01-0.11** (-3.37) (-3.07) (0.66) (-3.31) Intercept -0.01 0.01 0.04 (-0.65) (0.62) (0.77) N*T 74*20 74*1 74*20 74*20 a : Based on the time means i.e. x i = 1 T T t=1 x i,t. */**: Significant at a 90/95% level. 17
Conclusions As of 10/29/01, Euronext allows Dutch small-caps to hire DMMs to guarantee a minimum liquidity supply. Interestingly, the #DMMs that a firm hires seems to be dominated by factors other than trading conditions, e.g. seasoned equity offerings, banking services, etc. We study a panel of 74 firms that hire up to 8 DMMs in the first 20 months after the introduction. We find: 18
Conclusions As of 10/29/01, Euronext allows Dutch small-caps to hire DMMs to guarantee a minimum liquidity supply. Interestingly, the #DMMs that a firm hires seems to be dominated by factors other than trading conditions, e.g. seasoned equity offerings, banking services, etc. We study a panel of 74 firms that hire up to 8 DMMs in the first 20 months after the introduction. We find: 1. The quoted spread decreases in the #DMMs with diminishing marginal effect (2% for 1 DMM to 1% for 8 DMMs). This is consistent with (i) competition among DMMs and (ii) risk-sharing. 2. We use the exogenous #DMMs as IV and find that a lower spread does not create additional volume, but does reduce (transitory) volatility. 18-a
Designated Market Makers for Small-Cap Stocks Is One Enough? Albert J. Menkveld Vrije Universiteit Amsterdam ajmenkveld@feweb.vu.nl 19
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