An empirical enquiry into the speed of information aggregation:

The case of IPOs(Joint work with Jay Dahya, Baruch College, CUNY)

Research question• How long does it take until asymmetric

information is incorporated in the price?(how many hours, days, weeks?)

• Or, how long does it take until all profit opportunities for informed investors disappear?

• What drives this ‘speed of info-aggregation’?

Theory• Kyle (1985), one insider

speed is exogenously determined– More insiders with same info (a.o. Holden and

Subrahmaniam, 1992) speed increases in the number of insiders

– More insiders with different info (Vives, 1995) speed decreases with number of insiders.

• Glosten and Milgrom (1985) with twice as many insiders, speed quadrupled (problem: what’s ‘time’?)

Empirical Work• Laboratory experiments

– Copeland and Friedman (1987, 1991)speed (and volume!) higher when info is revealed simultanously (instead of sequentially)

– Camerer and Weigelt (1991), Schnitzlein (1996) look at market mechanism

• Studies on real market data– ?– ?

A measure of information aggregation

var( ), where p v In a normal (non-event) market setting, both information v, and pricing error caused by information asymmetries are constantly renewed…

….so that in a ‘steady state’ trading process, the return volatility is constant.

Even if there’s GARCH, we should find, in non-calendar event-time, a constant cross-sectional variance.

In the ‘one-shot’ micro-microstructure models, the standard measure of information aggregation is the variance of the pricing error.

Information events, such as equity-offerings, will result in a shock in v, (v) and ().

Immediately following the event, (v) should fall back to its stationary level, while (), the parameter that has our interest, may not..

Since cov(v,) = 0, we have that (p) = (v)+()

..so that we can study the volatility process (p)(t) to study how long it takes before event-related information is aggregated in the stockprice.

The Data- 2,531 U.S. IPOs from 1993-2000

- Exclude financials, utilities, Unit-offerings, REITs etc.

- We distinguish between dot.com’s and non-dot.coms.

- And identify “stabilized” IPOs,as those firms with initial return < 2%, and had two or more of the first five trading days with closing price = offer price (Weiss, Kumar, and Seguin, 1993)

Year # IPOsaverage proceeds %-age offered average median

standard deviation dot.coms

%-age stabilized

Average first day trading turnover

1993 307 37.68 40% 14% 8% 20% 2 16% 70%

1994 240 36.11 41% 10% 5% 16% 1 23% 62%

1995 317 46.85 40% 22% 13% 30% 5 10% 81%

1996 486 48.86 33% 16% 9% 22% 16 16% 75%

1997 304 47.33 35% 15% 9% 21% 14 17% 70%

1998 188 82.13 30% 27% 12% 50% 18 13% 81%

1999 375 89.57 26% 75% 46% 96% 153 7% 146%

2000 294 88.27 23% 61% 33% 82% 74 6% 143%

Entire Sample 2,511 59.02 33% 31% 13% 57% 283 13% 93%

dot.coms 283 64.78 25% 72% 44% 91% 6% 173%

non-dot.coms 2,228 58.29 35% 26% 11% 48% 14% 69%

stabilized issues 334 51.27 40% 1% 0% 3% 17 55%

non-stabilized issues 2,177 60.21 32% 35% 17% 60% 266 85%

Initial Return

Our sample consists of all IPOs from January 1993 until December 2000 of Security Data Corporation's New Issue database that had proceeds of $ 10 million or more.Excluded are previous LBOs, Spinnoff-IPOs, offerings of "Units" of shares and warrants, American Depository Receipts or Shares (ADRs and ADSs). Also excluded are IPO-firms in the Financial services industry (Standard Industry Classification code starting with 6) and IPOs of utilities (SIC-code starting with 491 to 494). IPOs were denoted"dot.coms" if their business name ended in .com or the SDC business description contained "e-commerce", "online", "internet" or "web". Issues were considered stabilized ifthe initial return was less than 2%, and if of two or more days of the first trading week the closing price equalled the offerprice.

Table ISummary statistics of our sample

2281 on NASDAQ, 191 NYSE, 48 Amex, 1 in Boston.

How to find 2(t)?We assume the following return-generating model:

Rit - Rmt = a(t)+ it ; it N(0, it), it = (i)K(t)

Where Rmt is the return on the market portfolio.

The parameters to be estimated are:

T ‘abnormal returns’ a(t),

N idiosyncratic standard deviations (i)

And T (event-time dependent) ‘volatility-multipliers’ K(t)

These parameters were estimated with a home-made maximum likelihood procedure.

The input for the estimation is a matrix X of NT observations where N is the number of securities and T the number of daily returns.

The likelihood of seeing X given the (2T+N) parameter vector ≡ (a(t), (i), K(t)) is:

L(X) =

N T

)K()(

))a((AR

))K((12

TN22

2ti,

21

e2π ti

t

ti

I want to minimize the -log of this:

-logL =

N

1

T

122

2,

21 ))(K)(Clog(

)(K)())(aAR(

)π2log(2

TNi t

ti titit

day a(t ) (%) K(t ) a(t ) K(t ) a(t ) K(t ) a(t ) (%) K(t ) a(t ) (%) K(t )

2 1.27 ** 1.39 ** 0.73 * 1.25 * 4.07 ** 2.25 ** 1.44 ** 1.50 ** -0.52 0.68 **3 0.82 * 1.18 * 0.65 * 1.19 1.01 1.47 ** 0.87 * 1.27 ** -0.49 0.66 **4 0.52 * 1.11 * 0.45 0.99 -0.15 1.36 * 0.57 * 1.14 * -0.83 * 0.69 **5 0.22 1.02 -0.08 0.95 1.86 * 1.27 0.22 1.05 -0.20 0.76 *6 -0.03 0.99 -0.03 0.97 -0.16 0.94 -0.04 0.98 -0.08 0.957 -0.10 1.00 0.01 0.94 -0.33 0.86 -0.11 0.99 0.02 0.998 -0.13 1.03 0.02 0.96 0.49 0.90 -0.07 0.99 -0.19 1.209 -0.19 1.04 -0.24 0.96 0.37 0.84 -0.10 0.95 -0.53 1.41 **

10 0.13 0.99 0.13 0.94 0.03 0.96 0.25 0.94 -0.62 1.34 **11 0.23 1.02 0.24 0.91 -0.02 0.96 0.25 0.95 -0.06 1.28 *12 -0.15 0.99 -0.02 0.88 -0.41 0.81 -0.08 0.94 -0.17 1.1313 -0.23 0.99 -0.14 0.93 0.46 0.79 -0.13 0.94 -0.42 1.1514 -0.16 0.98 0.02 0.98 -0.35 0.87 -0.11 0.98 -0.08 0.9715 0.04 0.96 0.25 0.93 -0.10 0.81 0.11 0.94 -0.09 1.0116 0.17 0.98 0.01 0.97 1.01 0.89 0.26 0.95 -0.05 1.0717 0.06 1.03 0.08 1.02 0.47 0.88 0.20 1.04 -0.21 0.9118 -0.24 1.03 -0.17 1.08 0.14 1.07 -0.14 1.06 0.03 1.0519 -0.01 1.02 0.11 1.04 0.07 0.99 0.10 1.06 0.15 1.0220 0.13 1.02 0.18 1.08 0.22 0.91 0.17 1.04 0.30 0.87

40 0.38 0.98 -0.17 1.00 0.52 1.07 -0.06 0.99 -0.12 0.9660 0.02 0.98 0.09 0.97 -0.36 1.04 0.01 0.98 0.08 1.0180 0.28 1.01 0.26 1.04 0.27 0.89 0.28 1.01 -0.12 1.04

100 0.12 1.03 0.08 1.02 0.29 1.10 0.08 1.04 0.25 0.97

Table IV

Average (i ) = 0.54 Average (i ) = 0.46Entire sample

Average (i ) = 0.41Stabilized IPOs

For the first 100 days of public trading the daily returns were collected from the CRSP tapes. A cross-sectional Maximum Likelihood method was used to simultaneouslyestimate the abnormal returns with respect to the equally-weighted NYSE-AMEX-NASDAQ returns, a(t ), the firm-specific volatilities, (i ), and the event-day specificvolatility multipliers, K(t ). The procedure was carried out for each subsample separately, so that the abnormal returns and event-day specific volatility factors of the entiresample are not necessarily the exact weighted average of the abnormal returns of the subsamples. The table displays only the average (i ) of the subsamples and the first 20a(t )'s and K(t )'s. The MLE procedure also provides significance levels. We used ** and * to denote statistical significance at the 1% and 5% levels with respect to a(t ) =0% and K(t ) = 1.

Average (i ) = 0.78

Post-IPO abnormal returns and volatilities

non-dot.coms dot.coms Non-stabilized IPOsAverage (i ) = 0.57

day a(t ) (%) K(t ) a(t ) K(t ) a(t ) K(t )a(t ) (%) K(t )a(t ) (%) K(t )

2 1.27 ** 1.39 **0.73 * 1.25 * 4.07 ** 2.25 **1.44 ** 1.50 **-0.52 0.68 **3 0.82 * 1.18 * 0.65 * 1.01 1.47 **0.87 * 1.27 **-0.49 0.66 **4 0.52 * 1.11 * 0.45 -0.15 1.36 * 0.57 * 1.14 *-0.83 * 0.69 **5 0.22 -0.08 1.86 * 0.22 -0.20 0.76 *6 -0.03 -0.03 -0.16 -0.04 -0.087 -0.10 0.01 -0.33 -0.11 0.028 -0.13 0.02 0.49 -0.07 -0.199 -0.19 -0.24 0.37 -0.10 -0.53 1.41 **

10 0.13 0.13 0.03 0.25 -0.62 1.34 **11 0.23 0.24 -0.02 0.25 -0.06 1.28 *12 -0.15 -0.02 -0.41 -0.08 -0.1713 -0.23 -0.14 0.46 -0.13 -0.4214 -0.16 0.02 -0.35 -0.11 -0.0815 0.04 0.25 -0.10 0.11 -0.0916 0.17 0.01 1.01 0.26 -0.0517 0.06 0.08 0.47 0.20 -0.2118 -0.24 -0.17 0.14 -0.14 0.03

Av. (i ) = 0.54 Av. (i ) = 0.46Entire sample

Av. (i ) = 0.41Stabilized IPOs

Av. (i ) = 0.78non-dot.coms dot.coms Non-stabilized

Av. (i ) = 0.57

A look at the abnormal returns

Figure 3Daily Cumulated Abnormal Returns

Daily abnormal returns were estimated not with a maximum likelihood estimation procedure thattakes into account the heteroskedasticity of the return-errors. The returns were cumulated for100 days. Note that for each subsample (stabilized and unstabilized issues, dot.coms and non-dot.coms) a separate estimation procedure was carried out, so that the abnormal returns of theentire sample is not necessarily the exact weighted average of the abnormal returns of thesubsamples.

-6.0

-3.0

0.0

3.0

6.0

1 11 21 31 41 51 61 71 81 91

-3

0

3

6

9

12

15

1 11 21 31 41 51 61 71 81 91Cum

ulat

ed A

bnor

mal

Ret

urn

(%)

dot.coms Non-dot.coms All

Volatility as a function of event-time

daya(t ) (%) K(t ) a(t ) K(t ) a(t ) K(t )a(t ) (%) K(t )a(t ) (%) K(t )

2 ** 1.39 ** * 1.25 * ** 2.25 ** ** 1.50 ** 0.68 **3 * 1.18 * * 1.19 1.47 ** * 1.27 ** 0.66 **4 * 1.11 * 0.99 1.36 * * 1.14 * * 0.69 **5 1.02 0.95 * 1.27 1.05 0.76 *6 0.99 0.97 0.94 0.98 0.957 1.00 0.94 0.86 0.99 0.998 1.03 0.96 0.90 0.99 1.209 1.04 0.96 0.84 0.95 1.41 **

10 0.99 0.94 0.96 0.94 1.34 **11 1.02 0.91 0.96 0.95 1.28 *12 0.99 0.88 0.81 0.94 1.1313 0.99 0.93 0.79 0.94 1.1514 0.98 0.98 0.87 0.98 0.9715 0.96 0.93 0.81 0.94 1.0116 0.98 0.97 0.89 0.95 1.0717 1.03 1.02 0.88 1.04 0.9118 1.03 1.08 1.07 1.06 1.0519 1.02 1.04 0.99 1.06 1.0220 1.02 1.08 0.91 1.04 0.87

Av. (i ) = 0.54 Av. (i ) = 0.46Entire sample

Av. (i ) = 0.41Stabilized IPOs

Av. (i ) = 0.78non-dot.coms dot.coms Non-stabilized

Av. (i ) = 0.57

Figure 4Event-day Specific Volatility Multipliers

Daily abnormal returns, firm-specific volatilities and event-day volatility multipliers were estimatedwith a maximum likelihood estimation procedure The graphs display the 'volatility multipliers', theevent-day specific factor with which the securities' return standard deviations are multiplied to getlikelihood maximizing standard deviations.

0.40

0.70

1.00

1.30

1.60

1 6 11 16 21 26 31 36 41 46

0.5

1.0

1.5

2.0

2.5

1 6 11 16 21 26 31 36 41 46

vola

tility

-mul

tiplie

r

dot.coms non-dot.coms

0.40

0.70

1.00

1.30

1.60

1 6 11 16 21 26 31 36 41 46event-time (days)

vola

tility

mul

tiplie

r

stabilized non-stabilized

0.5

1.0

1.5

2.0

2.5

1 6 11 16 21 26 31 36 41 46

How long does it take before the ex-ante dispersed information is aggregated in the stock price?

Not long! It takes about 3-4 days

A bit longer for dot.com firms

Q: What drives this fast information aggregation?

day

1 80.78 % 69.09 % 173.40 % 84.67 % 54.69 %2 18.22 12.38 64.56 19.38 10.523 10.17 6.95 35.72 10.85 5.614 7.22 5.55 20.52 7.58 4.835 6.33 4.95 17.27 6.59 4.606 5.59 4.29 15.90 5.86 3.827 4.78 3.77 12.81 4.99 3.388 4.17 3.50 9.44 4.35 2.929 3.98 3.32 9.24 4.16 2.77

10 3.66 3.06 8.47 3.83 2.5411 3.71 3.19 8.00 3.89 2.6512 3.31 2.99 5.99 3.51 2.1113 3.34 2.98 6.39 3.51 2.3214 3.25 2.91 6.11 3.39 2.4715 3.27 2.89 6.43 3.43 2.3416 3.30 2.97 5.98 3.32 2.2317 3.25 2.89 6.17 3.64 2.3218 3.26 2.91 6.08 3.80 2.6019 3.33 3.01 5.94 4.23 2.6820 3.23 2.89 6.01 3.59 2.74

40 3.19 2.85 5.96 3.61 2.2160 3.18 2.79 6.39 3.65 2.4380 3.26 2.85 6.56 3.67 2.36

100 3.27 2.91 6.25 3.79 2.62

stabilized IPOs

Post-IPO trading turnoverTable II

For the first 100 days of public trading the daily trading volumes (#-shares) were collected from the CRSPtapes. The daily volumes were divided by the total number of shares offered (excluding the greenshoe-option)to obtain the turnovers. IPOs were denoted "dot.coms" if their business name ended in ".com" or the SDCbusiness description contained "e-commerce", "online", "internet" or "web". Issues were considered stabilizedif the initial return was less than 2% and if on two or more days of the first trading week the closing priceequalled the offerprice.

Entire sample non-dot.coms dot.coms non-stabilized IPOs

0

10

20

30

40

50

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96event-time (days)

Tur

nove

r (%

)

non-dot.coms dot.coms non-stabilized stabilized

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Volume over time

day

1 2.73 % 2.85 % 1.78 % 2.74 % 2.62 %2 2.77 2.88 1.91 2.79 2.653 2.84 2.95 1.98 2.84 2.844 2.88 2.99 1.96 2.87 2.945 2.89 3.00 2.02 2.88 2.956 2.92 3.06 1.97 2.92 3.037 2.97 3.07 2.14 2.94 3.148 3.02 3.13 2.12 2.98 3.279 3.04 3.14 2.20 3.00 3.31

10 3.05 3.16 2.13 3.01 3.3111 3.07 3.19 2.13 3.02 3.4012 3.08 3.19 2.18 3.01 3.5013 3.10 3.23 2.27 3.05 3.5814 3.11 3.24 2.31 3.08 3.5715 3.16 3.28 2.23 3.09 3.6216 3.18 3.29 2.25 3.11 3.6017 3.20 3.29 2.30 3.13 3.5618 3.23 3.35 2.32 3.17 3.6319 3.22 3.32 2.34 3.15 3.6220 3.23 3.35 2.27 3.15 3.72

Table IIIPost-IPO Bid/Ask spreads

For the first 100 days of public trading the daily closing bid and ask quotes were collected from the CRSP tapes.The differences between bid and ask were divided by the mid quote to obtain relative spreads. IPOs weredenoted 'dot.coms' if their business name ended in ".com" or the SDC business description contained "e-commerce", "online", "internet" or "web". Issues were considered stabilized if the initial return was less than2%, and if of two or more days of the first trading week the closing price equalled the offerprice.

Entire sample non-dot.coms dot.coms non-stabilized IPOs stabilized IPOs

789

101112131415161718192021

3.22%3.22%

Figure 2

Bid/Ask spread over time

Relative Bid/Ask spreads (Closing Ask minus Closing Bid divided by average(Ask, Bid) are given for the first100 days of public trading of stabilized issues, non-stabilized issues, Internet IPOs and non-Internet IPOs.

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

1 11 21 31 41 51 61 71 81 91

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

1 11 21 31 41 51 61 71 81 91Event-time (days)

Bid

/Ask

spre

ad (%

)

dot.coms non-dot.coms

789

101112131415161718192021

3.22%3.22%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

1 11 21 31 41 51 61 71 81 91

Bid/

Ask

spre

ad (%

)

stabilized not stabilized

Stabilized and Non-stabilized IPOs

Ellul and Pagano (337 British IPOs between 1998 and 2000)

The low B/A spreads can be explained by the huge volumes.

Ellul and Pagano also document high turnover (first week 13%* vs. 3.5% stationary; U.S.: first day 80% vs. 3.5% stationary)

Why do British marketmakers charge high spreads if volume is so high?

Adverse selection!

There’s a high probability of trading with an informed agent. Ellul & Pagano find high adverse selection which gradually decreases.

We also did a bid/ask spread decomposition (using the methodology of Madhavan, et al. (1997)),

And find that in our data there’s a low adverse selection component (which gradually increases)

Coeff. Std. Err. Coeff. Std. Err. (cent) (%) Coeff. Std. Err. Coeff. Std. Err. (cent) (%)

1 5,723,656 0.42 0.01 8.52 0.01 17.86 4.66 4,001,700 0.38 0.01 8.25 0.01 17.26 4.39

2 1,470,345 0.86 0.01 8.63 0.02 18.98 9.05 1,260,018 0.59 0.01 8.26 0.02 17.71 6.65

3 744,679 1.21 0.02 8.51 0.03 19.44 12.43 596,134 0.94 0.02 8.42 0.03 18.71 10.01

4 611,082 1.33 0.02 8.66 0.04 19.97 13.31 417,586 1.12 0.02 8.21 0.04 18.66 11.96

5 508,094 1.55 0.02 8.67 0.04 20.45 15.18 406,537 1.16 0.02 8.46 0.04 19.24 12.10

6 421,932 1.66 0.03 8.62 0.04 20.56 16.15 368,872 1.25 0.03 7.81 0.04 18.13 13.80

7 338,074 2.06 0.03 8.35 0.05 20.82 19.81 316,711 1.44 0.03 8.30 0.04 19.49 14.81

8 309,987 2.07 0.03 8.17 0.05 20.48 20.20 284,518 1.53 0.03 8.24 0.05 19.53 15.64

9 320,223 2.03 0.03 8.33 0.05 20.72 19.59 280,320 1.44 0.03 7.87 0.04 18.61 15.44

10 292,239 2.14 0.03 8.00 0.05 20.28 21.11 268,837 1.52 0.03 7.69 0.05 18.42 16.50

11 255,505 2.29 0.04 7.70 0.05 19.98 22.96 286,266 1.41 0.03 8.05 0.05 18.92 14.89

12 236,290 2.31 0.04 7.46 0.06 19.54 23.64 273,746 1.62 0.04 8.01 0.05 19.27 16.80

13 232,863 2.55 0.04 7.51 0.06 20.12 25.35 249,929 1.72 0.04 8.59 0.05 20.63 16.70

14 240,601 2.33 0.04 7.53 0.06 19.72 23.63 260,885 1.54 0.03 8.09 0.05 19.26 16.02

15 294,440 2.06 0.03 7.82 0.05 19.77 20.87 246,476 1.60 0.04 7.56 0.05 18.33 17.50

16 322,511 1.97 0.03 7.65 0.05 19.25 20.51 247,763 1.69 0.04 7.76 0.05 18.90 17.90

17 330,453 2.00 0.03 7.79 0.05 19.57 20.42 305,614 1.53 0.03 7.81 0.05 18.68 16.38

18 366,438 1.95 0.03 7.96 0.05 19.83 19.65 391,753 1.32 0.03 8.14 0.04 18.91 13.92

19 351,997 1.90 0.03 8.00 0.05 19.80 19.21 385,254 1.11 0.02 7.85 0.04 17.92 12.43

20 386,613 1.57 0.03 7.98 0.04 19.10 16.44 411,868 1.05 0.02 8.09 0.04 18.28 11.52

21 305,193 1.79 0.03 8.00 0.05 19.59 18.31 355,617 1.19 0.03 7.59 0.04 17.56 13.51

22 293,654 1.82 0.03 8.02 0.05 19.69 18.50 271,976 1.42 0.03 7.90 0.05 18.63 15.19

23 254,858 1.99 0.04 7.27 0.05 18.51 21.45 231,302 1.65 0.04 7.96 0.05 19.22 17.16

24 238,759 2.19 0.04 7.55 0.06 19.49 22.51 250,811 1.55 0.03 8.14 0.05 19.38 15.98

25 236,611 2.14 0.04 7.01 0.05 18.31 23.41 242,826 1.65 0.03 8.63 0.05 20.56 16.03

26 256,131 2.14 0.04 8.13 0.05 20.54 20.86 215,765 1.68 0.04 8.89 0.06 21.13 15.88

27 239,830 2.36 0.05 8.28 0.06 21.29 22.16 192,379 1.85 0.04 8.41 0.06 20.54 18.06

28 213,322 2.65 0.05 7.78 0.06 20.88 25.43 192,681 1.88 0.04 8.15 0.06 20.07 18.72

29 195,052 2.67 0.05 7.90 0.06 21.15 25.24 168,598 2.02 0.04 8.10 0.06 20.25 19.9730 202,701 2.51 0.05 7.75 0.06 20.51 24.45 157,435 2.16 0.05 7.88 0.06 20.08 21.54

19.87 19.55 19.08 14.91

Implied Traded Spread

Proportion of Adverse Selection

Cost

For a subsample of 392 dotcom and 246 non-dotcom companies that went public in 1999 and 2000, we estimated the parameters in the spread decomposition model of Madhavan, Richardson, and Roomans (1997) for the first 30 trading days after the IPO date. The No. of Obs. is the number of the trades of the combined sample. Trades are matched with the eligible BBO quotes at least 1 second earlier. is the estimated adverse selection cost per share. is the fixed cost per share. The implied traded spread is .The proportion of of the bid ask spread that attributed to adverse selection is .

Table VSpread decomposition for non-dotcom and dotcom companies

Fixed Cost per share

(cent)

Average

Implied Traded Spread

Proportion of Adverse Selection

Cost

No. of Obs.

Adverse Selection Cost per share

(cent)

Non-Dotcom Companies (392 Companies) Dotcom Companies (246 Companies)

Day No. of Obs.

Adverse Selection Cost per share

(cent)

Fixed Cost per share

(cent)̂ ̂ ̂ ̂

)ˆˆ(2 )ˆˆ/(ˆ Non-dotcoms Dotcoms

(%) (%)

1 4.66 4.39

2 9.05 6.65

3 12.43 10.01

4 13.31 11.96

5 15.18 12.10

6 16.15 13.80

7 19.81 14.81

8 20.20 15.64

9 19.59 15.44

10 21.11 16.50

12 23.64 16.80

14 23.63 16.02

16 20.51 17.90

18 19.65 13.92

20 16.44 11.52

22 18.50 15.19

24 22.51 15.98

26 20.86 15.88

28 25.43 18.7230 24.45 21.54

Proportion of Adverse Selection Cost

Day

Non-dotcoms Dotcoms

266,722 175,675

133,066 83,791

92,564 59,673

81,335 49,943

77,129 49,191

68,142 50,904

66,972 46,905

62,617 44,499

62,732 43,281

61,692 44,358

60,401 48,093

55,835 43,854

47,760 44,737

47,278 36,315

48,406 28,394

59,665 37,635

74,385 48,837

76,439 62,210

89,513 72,12094,527 88,716

Number of Informed trades

Informed trading over time

0

50

100

150

200

250

300

0 5 10 15 20 25 30days after IPO

num

ber

of in

form

ed

trad

es

0

5

10

15

20

25

30

%-a

ge o

f inf

orm

ed

trad

es

Non-dotcoms (trades) Dotcoms (trades) Non-dotcoms (%-age) Dotcoms (%-age)

Interpretation:In both the U.S. and the U.K. informed trading is abnormally high and decreasing.

In the U.S. there is much more uninformed trading.

Because in the U.S. the proportion of informed trading is lower than stationary, informed traders in the U.S. are not constraint by low liquidity.

Thanks to spectacular volumes of uninformed trading on U.S. stock exchanges, information is aggregated fast.

In the U.K., informed traders are constraint by low liquidity, information aggregation is slow.

How long does it take until stationarity sets in?

S.E.

Model 1: turnover = t+, 99.23 4.08

-1.36 0.017

Switching date = x x 11.79 1.23

Model 2: turnover = + 3.28 0.024

Model 1: spread = t+, 2.65 0.021

0.079 0.032

Switching date = x x 18.46 5.41

Model 2: spread = + 3.35 0.030

Model 1: spread = t+, 1.32 0.038

-0.28 0.037

Switching date = x x 3.84 0.94

Model 2: spread = + 1.00 0.00

A maximum likelihood procedure was used to simultaneously estimate, for the turnover, Bid/Ask spread, and the volatility multiplier K(t ), the coefficients ofmodel 1, model 2 and the switching date x . In the graphs both models are depicted with a bold line, the actual observations with asterisks, and the confidenceinterval for the switching date with a dotted line.

Panel A: non-dot.com IPOs

dating the switch to stationarity

Volatility

Trading volume

Bid/Ask spread

0

5

10

15

20

1 6 11 16 21 26 31 36

Turn

over

(%)

1.6

1.8

2

2.2

2.4

2.6

1 6 11 16 21 26 31 36

Bid

/Ask

Spr

ead

(%)

0.6

1.2

1.8

2.4

1 6 11 16 21 26 31 36

event-time (days)

Vola

tility

-mul

tiplie

r

0

5

10

15

20

1 6 11 16 21 26 31 36

Turn

over

(%)

2.6

2.8

3

3.2

3.4

3.6

1 6 11 16 21 26 31 36

Bid

/Ask

Spr

ead

(%)

0.6

0.9

1.2

1.5

1 6 11 16 21 26 31 36

event-time (days)

Vola

tility

-mul

tiplie

r

Initial return subsamples

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40

event-time

annu

aliz

ed s

igm

a

Overpriced

Stabilized

2-6% underpriced

Thin lines gives the average i within the sampleBold lines gives the K(t) multiplied with the ave(i)

0.25

0.5

0.75

1

1.25

1.5

1 4 7 10 13 16 19 22 25 28 31 34 37 40

event time

annu

aliz

ed s

igm

aUP 6-14.99%

UP 15-50%

UP > 50%

No difference except the average i.

For the sizzling hot IPOs, the time to full aggregation may be a bit longer..

Speed and underwriter prestige

0.4

0.5

0.6

0.7

0.8

0.9

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

days after IPO

annu

aliz

ed s

igm

a

CMRrank<8.5

CMRank>8.5

Average i of IPOs floated by prestigious underwriters is higherInformation aggregation for IPOs with prestigeous underwriters is quicker

To do:

How does speed of information aggregation depend on

Volume, Size, %-age offered, syndicate-size

Plan1: Split sample in two based on the above. Then do the MLE again to find the K(t)’s

Plan 2: “MLE-regression”: Estimate the parameters in:

ARi,t = Ri,t - Rbm,t = a(t)+ i,t, i,t N(0, i,t)

i,t = (i)(K(t)+(t)·V(t,i))

or i,t = (i)(K(t)+(t)·UP(i))

Do exactly the same for British data. Compare fixed price offerings vs. bookbuilt offerings.