Event Study and Predictability Lecture Days 4 & 5

11/9/11

1

Empirics of Financial Markets

Patrick J. Kelly, Ph.D.

Event Studies

Event Studies and Semi-Strong Form Efficiency

•  Semi-Strong Form Efficiency –  All PUBLIC information is quickly, correctly and completely

incorporated into stock prices.

•  The event study is purpose built for testing the speed of information incorporation –  If markets are efficient –  Upon the release of value relevant information –  Stock prices adjust immediate to reflect the new (surprise) value of

the firm •  The event in an event study is the release of new information that is a

surprise to the market.

© 2010 Patrick J. Kelly 3 © 2008 Patrick J. Kelly 4

Wall Street Journal September 21, 2005

Information Incorporation

© 2008 Patrick J. Kelly 5

FedEx’s Share Price July – October 2005

Sept. 21, 2005

The Seven Steps of an Event Study

1.  Event Definition –  Precision is important –  But too precise and you might miss the information release

2.  Selection Criteria –  Data availability, size, industry, liquidity characteristics, but be careful

of accidentally introducing biases •  Ex. Index delisting and choosing the Russle 1000 (oppose to S&P500)

3.  Define Normal and Abnormal returns –  Should prices change at all if the there is no surprise information in

the news release?

4.  Estimate Normal returns –  If model estimation is necessary, use the normal period for

estimation. © 2010 Patrick J. Kelly 6

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The Seven Steps of an Event Study (continued)

5.  Testing Procedure –  Testing methodology –  How to aggregate abnormal returns

6.  Empirical Results

7.  Interpretations and Conclusions –  Alternate explanations?

•  Consider….



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BHAR: Raw Rt -‐ Mkt Rt

BHAR Raw -‐ Mkt Earnings Forecast

Event Study:

•  Early event studies: –  Impact of stock splits (Dolley, 1933)

•  Associated with price increases in 2/3rd of cases

–  Ball and Brown (1968) – study of earnings announcements •  Model expected changes in earnings per share (EPS) as a naïve function of the

average change in the EPS for all other firms in the market. •  All stock were separated into two portfolios those with actual EPS:

–  Greater than the model predicted EPS –  Less than the model predicted EPS

•  They create a portfolio that


Ball and Brown (1968) PEAD

______ ____ © 2008 Patrick J. Kelly 11

Event Study: Stock Splits

•  Fama, Fisher Jensen and Roll (1969) –  Dolley’s (1933) results are puzzling

•  Why should stock prices increase merely because the stock splits?

–  Example if a stock is priced at 200 RUB per share and there is a two-for-one stock split, why should the price be any different that 100 RUB?

–  Possibilities: •  Model of expected returns is bad •  Many Stock splits are associated with increases in dividends


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FFJR 1969: Method

•  Run a simple market model regression:

–  Excluding all returns 15 months before and after the event •  Note: Typically we only use data before the event study

•  Results: –  At each time t, average across all events:

• 

–  Report for each time t the sum of up to that point: • 


titmiiti rr ,,, εβα ++=

ti,ε

N

N

i tit∑ == 1 ,εε

∑ −==

t

s stE 29ε

tε


Event Study Time Line

•  The model estimation period should include enough observations that you have decent statistical power

•  The event window should be as small as possible to increase the power of the test, but as large as needed to ensure that the real announcement is in the window

•  Use the estimates from the model estimation to calculate abnormal return over the event and post event window:


[ ]ttititi XrErAR |,,, −=Also εi,t Xt is conditioning info

Model estimation period

Event W

indow

Post-event window

t0 t1 t2 t3

Models for Normal Return

•  In other words, what is Xt?

1.  Constant mean –  Ignores market conditions –  Often used in volume event studies

•  Usually a rolling mean of the past XX days/weeks/months

2.  Market Model (like FFJR69)

3.  Market Adjusted Model


ARi,t = ri,t !E ri,t | Xt"# $%

ri,t =!i +"irm,t +#i,t ! ARi,t = ri,t "!̂i " "̂irm,t

tmtiti rrAR ,,, −=

Notation: This slide forward

•  tMS=Model estimation period Start •  tME=Model estimation period End •  tES=Event window Start •  tEE=Event window End •  tPE=Post-event window End


Model estimation period

Event W

indow

Post-event window

tMS tME tEE tPE tES

Notation (continued)

A.  A regression the needs to be run, in the estimation period looks like this unless otherwise stated:

B.  The results of the regression from A:

C.  When using the values from B to calculate normal returns for the event or post-event period.


titmiiti rr ,,, εβα ++=

!̂i and "̂i and #̂i,t

ARi,t = ri,t !!̂i ! "̂irm,t

11/9/11

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Measuring and testing typical price response

•  If the goal is to understand how the event on average affects shareholder wealth then, average across events at each time t:

•  To then aggregate over the event window from time t1 to time t2:


ARt =1N

ARi,ti=1

N

!

CAR tES, tEE( ) = ARtt=tES

tEE

!

Test statistic for CARs with many events

•  Define the event horizon:

•  And the test statistic:

•  Where:

•  Note: this is true iif ARs are not autocorrelated and homoskedastic.


LEV = tEE ! tES +1

CAR tES, tEE( )! 2 tES, tEE( )!" #$

12

! 2 tES, tEE( ) = LEV! 2 ARt( )

Calculating Test Statistics for Event Studies in Detail

Brown and Warner (1980)

•  The traditional AR for a one period event –  Assumes no dependence in returns

•  Residuals are uncorrelated

–  Event induced variance is insignificant –  Events are not cross-sectionally correlated (at the same time)

•  From BW1980 Appendix A3 –  Notation: N events, LEst = Length of estimation window


tts =

1N

ARi,0i=1

N

!

1N

1LEst " 2

!̂i,t !!̂i,tLEstt=tMS

tME

!"

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%

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t=tMS

t=tME

!(

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12

SSE (or Residual Sum of Squares) from the estimation period LINEST in Excel can give this to you

Standard deviation of “portfolio” of events, assuming independence of the Aris.

! 2 "̂t( ) =

Test stat for CARs with many events based on BW80

•  Define the event horizon:

•  And the test statistic:

•  Where:

•  Note: this is true iif errors ( ) are not autocorrelated and homoskedastic.


LEV = tEE ! tES +1

t =CAR tES, tEE( )! 2 tES, tEE( )!" #$

12

! 2 tES, tEE( ) = LEV! 2 "̂t( )!̂t !̂t =

1N

!̂i,ti=1

N

!

Standardized Residual Method, Patel (1976)

•  Standardize the ARs/CARs before averaging –  High volatility stocks are more likely to have high ARs/CARs. The

standardization reduces their weight.


SCARi tES, tEE( ) =CARi tES, tEE( )LEV! i

2 "̂t( )!" #$12

Corrected

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ttSCARt EEESi

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11/9/11

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Ordinary Cross-sectional method

•  This test assume no cross-sectional dependence in abnormal returns, but allows for event induced changes in variance.


tts =

1N

CARi tES, tEE( )i=1

N

!

1N(N "1)

CARi "1N

CARii=1

N

!#

$%

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#

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&

'((

2

i=1

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!)

*

++

,

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.

12

Dropping (tES, tEE) to conserve space.

Standardized cross-sectional method, Boehmer et al. 1991

•  This test statistic combines the Patel and the ordinary cross-sectional t-stat. It is robust to event induced volatility changes (Boehmer, Musumeci, and Poulsen, 1991):


tBMP =

1N

SCARii=1

N

!

1N(N "1)

SCARi "1N

SCARii=1

N

!#

$%

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i=1

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12

Sign test

•  One sided (since hypothesis is that news has an effect):

•  Two sided (just in case)

•  P is the proportion of ARs or CARs which are positive.


tsign =P ! 0.5( )0.25N

tsign =P ! 0.50.25N

Non-Parametric alternate to the t-test, Corrado 1989

•  Allows for non-normal AR distributions – especially fat tails. •  Calculate normal returns for each event based on the

estimation period. (e.g. -244 to -6) •  Calculate ARi,t for the estimation and event periods. (e.g.

-244 to +5) •  Rank all ARs from 1 to Lest+LEv (Smallest to Largest)

–  Break ties by assigning each tied observation the average rank


Ki,t = rank(ARi,t )

Corrado, 1989


tCorrado =

1N

Ki,0 !12(LEst + LEv )+

12

"

#$%

&'i=1

N

(

1LEst + LEv

1N

Ki,t !12(LEst + LEv )+

12

"

#$%

&'i=1

N

()

*+

,

-.

2

t=tMS

tEE

("

#$$

%

&''

12

CAR test statistics: event time clustering

•  The CAR test statistic assumes that ARs are independent. If there is event time clustering, this assumption is violated. –  Clustering is when event windows overlap

•  Calculate portfolio returns for all firms with overlapping events.

•  Use normal period portfolio return variance as an estimate of variance –  Might be biased downward if events affect volatility.

•  Scale up normal period variance by the cross-section (cross-event) increase in volatility during the event.

•  Or use Corrado (1989) non-parametric test.


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Long Horizon Event Studies

•  Previous slide shows that tests with long event windows have low power.

•  Risk Adjustment –  smaller errors compound over time, becoming large –  AR very sensitive to model choice. Which is correct?

•  Other problems: cross-correlation and skewness, see Kothari and Warner, 2004

•  Alternate adjustment: –  Characteristic matching, then BHAR

•  Otherwise similar non-event firms •  Investable, low turnover strategy

–  Calendar time portfolios, then Jensen’s alpha •  More….


Calendar Time Approach

•  Create portfolios of all firms which experience the event over T months –  T is the number of months you measure abnormal return for one

event

•  Each month create an equally or value weighted portfolio of all firms experiencing the event in the previous T months.

•  Regress the time series on a factor model –  Alpha is your average monthly abnormal return.

•  Problem is events are time-period specific, it might be better to weight the calendar months by the number of events (see Fama, 1998 and Kothari and Warner, 2004).


What makes for better tests 48

Table 2 General characterization of properties of event study test methods.

Length of Event Window Criterion

Short (< 12 months) Long (12 months or more)

Specification Good Poor/Moderate

Power when abnormal performance is:

Concentrated in event window

High Low

Not concentrated in event window

Low Low

Sensitivity of test statistic specification to assumptions about the return generating process:

Expected returns, unconditional on event

Low High

Cross-sectional and time-series dependence of sample abnormal returns

Low/Moderate Moderate/High

Variance of abnormal returns, conditional on event

High High

Sensitivity of power to:

Sample size High High

Firm characteristics (e.g., size, industry)

High High


What makes for better tests


48







High Low


Low Low



Low High




High High




High High

48







High Low


Low Low



Low High




High High




High High

Power of Event Study, by volatility and horizon 50

Figure 1: Power of event study test statistic when abnormal return is 10%

0.00

0.40

0.80

1.20

0 20 40 60 80 100 120 140 160 180 200

Sample Size (N)

Powe

r

One Day Interval

One Month Interval

Six Month Interval

Figure 2a: Power of event study for firms in the lowest volatility decile.

0.00

0.40

0.80

1.20

0 20 40 60 80 100 120 140 160 180 200

Sample Size (N)

Powe

r

Abnormal Return 1%Abnormal Return 5%


Power of Event Study, by volatility and horizon


50

Figure 1: Power of event study test statistic when abnormal return is 10%

0.00

0.40

0.80

1.20

0 20 40 60 80 100 120 140 160 180 200

Sample Size (N)

Powe

r

One Day Interval

One Month Interval

Six Month Interval

Figure 2a: Power of event study for firms in the lowest volatility decile.

0.00

0.40

0.80

1.20

0 20 40 60 80 100 120 140 160 180 200

Sample Size (N)

Powe

r

Abnormal Return 1%Abnormal Return 5%

Documents

Event Study and Predictability Lecture Days 4 & 5