A Dynamic Intraday Measure of the Probability of Informed Trading and

Firm-Specific Return Variation

Sanders Chang, Lenisa Chang, F. Albert Wang

University of Dayton and University of Cincinnati

Motivation The role of information in asset prices Two types of traders: informed vs.

uninformed (Kyle 1985, Black 1986, Campbell et al. 1993)

Existing Probability of informed trading (PIN) measures based on a sequential trade model (Easley et al. 1997, 2002)

But, PIN measures static info trading over a very long macro horizon (1 month to 1 year)

PIN Measure (Easley et al. 1997, 2002) The likelihood function for a single trading

day

Maximum likelihood estimation over T days

PIN Measure The probability of informed trading

One must aggregate very fine intraday data (5-min intervals) within the trading day across multiple days

T The variation and info content of intraday

trades is diluted, or even lost in such a macro horizon

Twofold Aim of the Study Develop a dynamic intraday version of PIN

(i.e., DPIN) for informed trading at high frequencies: 15-minute intervals throughout the trading day

Examine the relationship between private information (measured by DPIN) and firm-specific return variation to validate Roll’s (1988) conjecture

Data (1993-2008) Intraday transaction data come from the

Trades and Quotes (TAQ) database Share code, shares outstanding, etc. are

from the Center for Research in Security Prices (CRSP)

NYSE stocks with at least 250 trades per month, excluding foreign firms, ETF, CEF, and REIT

Each trading day divided into 26 (15-min) intervals.

A total of 14,405,663 firm-interval observations

Herding vs. Contrarian Trades The unexpected return of 15-min interval from

residual

Calculate # of buy (NB), sell (NS), total trades (NT) for each interval based on Lee and Ready (1991)

Contrarian (herding) trades are to buy (sell) in presence of negative unexpected returns or to sell (buy) in presence of unexpected positive returns

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Rationales behind DPIN Uninformed trading is associated with

negative serial correlation in stock returns, while informed trading has no correlation (Campbell et al 1993)

Unexpected returns exhibit significant negative serial correlation for herding trades while no serial correlation for contrarian trades (Aramov et al 2006)

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Baseline DPIN Measure Contrarian trades are closely akin to

informed trades and herding trades are a good representation of uninformed trades (Aramov et al 2006)

The dynamic probability of informed trading (DPIN) during any given 15-minute interval is obtained by calculating the proportion of contrarian trades taking place during that interval

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Distribution of DPIN_BASETable 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

The DPIN_BASE measure yields adequate cross-sectional variation across stocks

0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73

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5

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Percent

DPIN

DPIN with Disposition Effect The disposition effect suggests that

uninformed investors will be less willing to sell shares following price declines because of loss aversion

is an indicator variable that takes on the value of unity if the cumulative return over the last ten intervals is negative and zero otherwise

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Distribution of DPIN_DISPTable 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

DPIN_DISP distribution mimics that of DPIN_BASE, but with slightly less than half the mean and median

0.075 0.090 0.105 0.120 0.135 0.150 0.165 0.180 0.195 0.210 0.225 0.240 0.255 0.270 0.285 0.300 0.315 0.330 0.345 0.360 0.375 0.390 0.405

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5

10

15

20

25

30Percent

DPIN_DISP

DPIN with Size Effect Informed traders are more likely to submit

larger orders (Easley and O'Hara 1987)

is a "large trades" indicator variable that equals 1 if the trade size for stock i over interval j is larger than the stock's median interval trade size over the same trading day, and zero otherwise

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Distribution of DPIN_SIZETable 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

DPIN_SIZE distribution mimics that of PIN (Easley et al. 2002) with similar mean, median, left skew, and long right tail

0.135 0.150 0.165 0.180 0.195 0.210 0.225 0.240 0.255 0.270 0.285 0.300 0.315 0.330 0.345 0.360 0.375 0.390 0.405 0.420 0.435 0.450 0.465 0.480 0.495

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DPIN_SIZE_Med

DIPN_SIZE vs. PIN (Easley et al. 1997, 2002)

Informed traders are more likely to submit large orders given information event (Easley et al. 1987)

By construction, DIPN_SIZE implicitly assumes information event occurs only with large orders

DIPN_SIZE is closest to the PIN of Easley et al. (1997, 2002) partly because Size may serve as a proxy for the occurrence of the information event

Yearly DPIN: Summary Statistics

Measure MeanMedia

n STD Min Max           

DPINBASE 0.458 0.455 0.036 0.274 0.733           DPINDISP 0.215 0.215 0.029 0.073 0.401           DPINSIZE 0.231 0.227 0.027 0.133 0.500

           

Table 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

The means and medians of the refined DPINs are quite close to the PIN measure of Easley et al. (2002): 0.191 and 0.185

Yearly Cross-Sectional Average DPIN over Time

Yearly C-S average DPINs mimic that of PIN (Easley et al. 2002) with little year-to-year variation or with much stability over time

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1993 1995 1997 1999 2001 2003 2005 2007

Year

DPI

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DPIN_BASE

DPIN_DISP

DPIN_SIZE

Intraday DPIN and Firm Characteristics

Table 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

Stocks with higher DPIN are more opaque as they are associated with much smaller firm size, lower volume, and higher illiquidity

Measure High/LowNo.

Firms SizeIlliquidi

ty Volume           

DPINBASE High 1,899 819,299 7.051 103,740  Low 2,306 5,448,227 0.760 591,708           DPINDISP High 2,046 1,265,812 6.094 162,587  Low 2,159 5,340,255 1.241 569,050           DPINSIZE High 1,721 534,357 7.715 67,367  Low 2,484 5,313,942 0.751 581,898

           

Intraday DPIN: Summary Statistics

The STDs are much higher and the medians for the two refined DPINs are zero, hence no information events for many intervals

Measure Mean Median STD 25th % 75th %

DPINBASE 0.447 0.431 0.297 0.250 0.600

DPINDISP 0.212 0.000 0.301 0.000 0.417

DPINSIZE 0.222 0.000 0.289 0.000 0.429           

The U-shaped Intraday DPIN for large size

The U-shaped intraday pattern is consistent with the clustering of uninformed trading and the corresponding strategic informed trading (Kyle 1985, Admati and Pfleiderer 1988)

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DPIN_SIZE

The Inverse U-shaped DPIN for Small Size

Table 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

Stealth trading: informed traders break up large orders into a series of small trades to hide their information (Barclay and Warner 1993, Chakravarty 2001, Alexander and Peterson 2007)

DPIN_SMALL

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Is DPIN a Good Proxy for Informed Trading?

The yearly DPIN is consistent with the prior literature of informed trading as it closely mimics the PIN measure of Easley et al. (2002)

The intraday DPIN is closely associated with firm characteristics in terms of the degree of opaqueness

The intraday DPIN captures strategic informed trading: a U-shaped pattern for large trades (Wood et al. 1985, Jain and Joh 1988) and an inverse U-shaped pattern for small trades (Blau et al. 2009)

Firm-Specific Return Variation (FSRV) A daily market model regression (e.g., Roll

1988, Durnev et al. 2004, 2005, and Chen et al. 2007)

The R-squared statistic from the regression:

FSRV measures the unexplained daily variation in a firm’s return after market returns

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Empirical Tests Fama-MacBeth (1973) Regression with a

total of N = 4,191 stocks and T = 3,994 days in regressions

Regression on first-differenced data to remove firm fixed effects and lower persistence in the data

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Can DPIN Explain FSRV?Table 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

  FSRV FSRV FSRVDPINBASE 0.558***      (28.55)     DPINBASE, t-1 0.467***      (24.29)    DPINDISP   0.270***      (16.91)  DPINDISP,t-1   0.093***      (7.64)  DPINSIZE     0.640***

      (21.63)DPINSIZE,t-1     0.569***      (21.90)Wald 1411.5*** 343.24*** 947.39***

DPIN and its lag are jointly significant at the 1% level

Informed trading causes firm-specific return variation – Roll √

Can DPIN Explain FSRV (Cont’d)?Table 1: Summary statistics for DPIN measures and firm characteristics(a) Yearly cross-sectional DPIN across all years(b) DPIN and firm characteristics

∆DPIN and its lag are jointly significant at the 1% level

Informed trading causes firm-specific return variation – Roll √

  ∆FSRV ∆FSRV ∆FSRV∆DPINBASE 0.150***      (8.31)    ∆DPINBASE, t-1 0.054***      (2.99)    ∆DPINDISP   0.194***      (11.07)  ∆DPINDISP,t-1   0.033*      (1.77)  ∆DPINSIZE     0.145***

      (5.32)∆DPINSIZE,t-1     0.072***      (2.72)Wald 77.87*** 125.79*** 34.61***

Robustness Check Equally weighted and valued weighted

market model to measure FSRV Fama-MacBeth regressions on time-

demeaned data (Skoulakis 2008) to eliminate firm fixed effects

Reverse causality by regressing DPIN on FSRV

All robustness checks render support to our main finding: Informed trading causes firm-specific return variation, and not vice versa

Conclusion Construct a dynamic PIN measure that is

easy to implement, compared to the existing static PIN measure (Easley et al. 1997, 2002)

The intraday DPIN captures strategic informed trading: a U-shaped pattern for large trades and an inverse U-shaped pattern for small trades

Use DPIN to examine the empirical link between private info and firm-specific return variation (FSRV)

Confirm Roll’s (1988) conjecture that FSRV is driven by private info, and not vice versa