Event study Event study analysisanalysis

Lecture 5Lecture 5

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PlanPlan

Up to now:Up to now:– Low-frequency analysis of return Low-frequency analysis of return

predictabilitypredictability– Search for a stable relationship between Search for a stable relationship between

stock returns and publicly available stock returns and publicly available variablesvariables

Today:Today:– High-frequency analysis of changes in High-frequency analysis of changes in

security prices in response to security prices in response to news news (events)(events)

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Event study analysisEvent study analysis

How quickly does the market How quickly does the market react to new information?react to new information?

0 +t-t

Announcement Date

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Event study analysisEvent study analysis

Measure the speed and magnitude of Measure the speed and magnitude of market reaction to a certain eventmarket reaction to a certain event– High-frequency (usually, daily) dataHigh-frequency (usually, daily) data– Ease of use, flexibilityEase of use, flexibility– Robustness to the Robustness to the joint hypothesis joint hypothesis

problemproblem Experimental designExperimental design

– Pure impact of a given eventPure impact of a given event– Role of info arrival and aggregationRole of info arrival and aggregation

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Reaction to the Reaction to the unexpected eventunexpected event

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MethodologyMethodology: : iidentification of the dentification of the event and its dateevent and its date Type of the event Type of the event

– Share repurchase / dividend / M&AShare repurchase / dividend / M&A Date of the event τ=0Date of the event τ=0

– Announcement, not the actual paymentAnnouncement, not the actual payment– The The event windowevent window: several days around : several days around

the event datethe event date Selection of the sampleSelection of the sample

– Must be representative, no selection Must be representative, no selection biasesbiases

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Methodology: modelling Methodology: modelling the return generating the return generating processprocess Abnormal return: ARAbnormal return: ARi,ti,t = R = Ri,ti,t – E[R – E[Ri,ti,t | X | Xtt]]

– Prediction error: ex post return - normal returnPrediction error: ex post return - normal return Normal return: expected if no event Normal return: expected if no event

happenedhappened– The The mean-adjusted mean-adjusted approach: Xapproach: Xtt is a constant is a constant– The The market modelmarket model: X: Xtt includes the market includes the market

returnreturn– Control portfolioControl portfolio: X: Xtt is the return on portfolio is the return on portfolio

of similar firms (wrt size, BE/ME)of similar firms (wrt size, BE/ME) The The estimation windowestimation window: period prior to : period prior to

the event windowthe event window– Usually: 250 days or 60 monthsUsually: 250 days or 60 months

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Methodology: testing Methodology: testing the hypothesis AR=0the hypothesis AR=0 HH00: the event has no impact on the firm's : the event has no impact on the firm's

value value For individual firm: For individual firm:

– Estimate the benchmark model during the Estimate the benchmark model during the estimation period [τ-testimation period [τ-t11-T: τ-t-T: τ-t11-1]:-1]:

RRi,ti,t = α = αii + β + βiiRRM,tM,t + ε + εi,ti,t, where ε ~ N(0, σ, where ε ~ N(0, σ22(ε))(ε))

– During the event period [τ-tDuring the event period [τ-t11: τ+t: τ+t22], under H], under H00: :

ARARi,ti,t = R = Ri,ti,t - a - aii - b - biiRRM,tM,t~ N(0, V~ N(0, Vi,ti,t), ),

var(ARvar(ARi,ti,t) = s) = s22(ε)[1+1/T+(R(ε)[1+1/T+(RM,tM,t--μμMM))22/var(R/var(RMM)])]

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Methodology: testing Methodology: testing the hypothesis AR=0the hypothesis AR=0 Aggregating the results across firms: Aggregating the results across firms:

– Average aAverage abnormal returnbnormal return: AAR: AARtt = (1/N) = (1/N) ΣΣii AR ARi,ti,t

– Computing var(Computing var(AARAAR):): Using the estimated variances of individual ARs, or…Using the estimated variances of individual ARs, or… Cross-sectionally: var(Cross-sectionally: var(AARAARtt) = (1/N) = (1/N22) ) ΣΣii (AR (ARi,ti,t - AAR - AARi,ti,t))22

Aggregating the results over time: Aggregating the results over time: – Cumulative aCumulative abnormal returnbnormal return: :

CARCAR[τ-t[τ-t11: τ+t: τ+t22]] = = ΣΣt=t=τ-t1: τ+t2τ-t1: τ+t2 AR ARi,ti,t

– Similarly, average CAR: ACAR = (1/N) Similarly, average CAR: ACAR = (1/N) ΣΣii CAR CARii

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Methodology: Methodology: explaining abnormal explaining abnormal returns returns Relation between CARs and Relation between CARs and

company characteristics:company characteristics:– Cross-sectional regressionsCross-sectional regressions

OLS with White errors OLS with White errors WLS with weights proportional to WLS with weights proportional to

var(CAR)var(CAR)

– Account for potential selection biasAccount for potential selection bias The characteristics may be related to the The characteristics may be related to the

extent to which the event is anticipatedextent to which the event is anticipated

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Asquith&Mullins Asquith&Mullins (1983)(1983)""The impact of initiating dividend The impact of initiating dividend

payments on shareholder wealthpayments on shareholder wealth"" Measure stock price reaction to dividend Measure stock price reaction to dividend

announcementsannouncements– Costs vs clientele vs signaling vs other theoriesCosts vs clientele vs signaling vs other theories

Sample of companies Sample of companies initiating initiating dividend paymentsdividend payments– No need to model investors’ expectationsNo need to model investors’ expectations

Explicitly control for other newsExplicitly control for other news Relate ARs to the magnitude of dividendsRelate ARs to the magnitude of dividends

– The first cross-sectional analysis of factors explaining ARsThe first cross-sectional analysis of factors explaining ARs Compare reaction to initial and subsequent Compare reaction to initial and subsequent

dividendsdividends

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DataData

168 firms that initiated dividend 168 firms that initiated dividend payments to common stockholders payments to common stockholders in 1963-1980in 1963-1980– 114 increased dividends within 3 years114 increased dividends within 3 years– 7 decreased dividends7 decreased dividends

The announcement date: The announcement date: – Publication in the Publication in the Wall Street JournalWall Street Journal

Other announcements in +/- 10 day Other announcements in +/- 10 day interval around the event dateinterval around the event date

Daily stock returnsDaily stock returns

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MethodologyMethodology

Normal return: Normal return: – Return on control portfolio with similar betaReturn on control portfolio with similar beta

Each year, stocks traded in NYSE and ASE were Each year, stocks traded in NYSE and ASE were grouped into 10 portfolios ranked by betagrouped into 10 portfolios ranked by beta

Event window: [-1:0]Event window: [-1:0]– To capture cases when the news was To capture cases when the news was

published the next day after the published the next day after the announcementannouncement

Main variable: CAR[-1:0] = ARMain variable: CAR[-1:0] = AR-1-1 + AR + AR00

Cross-sectional approach to compute stdCross-sectional approach to compute std– t(ACARt(ACARtt) = √N ACAR) = √N ACARtt / std(CAR / std(CARi,ti,t))

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ResultsResults

Table 1, all firms in the sampleTable 1, all firms in the sample– ARAR-1-1=2.5%, AR=2.5%, AR00=1.2%, both with t>3=1.2%, both with t>3

– Two-day ACAR=3.7% with t=6.6Two-day ACAR=3.7% with t=6.6– Almost 70% of firms experienced Almost 70% of firms experienced

positive market reactionpositive market reaction– Other ARs are small and insignificantOther ARs are small and insignificant

Consistent with MEConsistent with ME No leakage of info prior to div No leakage of info prior to div

announcementannouncement

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Results (cont.)Results (cont.)

Table 3, subsamples of firmsTable 3, subsamples of firms– 88 firms with no other new info: 88 firms with no other new info:

two-day ACAR = 4.7% with t=5.9two-day ACAR = 4.7% with t=5.9 Dividend and earning announcements Dividend and earning announcements

may be partial substitutes!may be partial substitutes!

– Firms that subsequently raised Firms that subsequently raised dividends: smaller and marginally dividends: smaller and marginally (in)significant ACARs(in)significant ACARs No expectation model for subsequent No expectation model for subsequent

dividends!dividends!

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Results (cont.)Results (cont.)

Table 4, CS regression of CARs on the Table 4, CS regression of CARs on the change in payout yieldchange in payout yield– Slope coefficient: captures the effects of an Slope coefficient: captures the effects of an

unexpected div increaseunexpected div increase Positive relation for both initial and subsequent Positive relation for both initial and subsequent

dividendsdividends The reaction is stronger for subsequent dividendsThe reaction is stronger for subsequent dividends

– The intercept: captures the expected div The intercept: captures the expected div increase (with negative sign)increase (with negative sign)

Negative for subsequent dividends (they are Negative for subsequent dividends (they are partially forecast)partially forecast)

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ConclusionsConclusions

First clean test of the market First clean test of the market reaction to dividendsreaction to dividends

Positive effects of dividends Positive effects of dividends overweigh negative onesoverweigh negative ones– Support for signaling modelSupport for signaling model

Market efficiency is not rejectedMarket efficiency is not rejected

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Strengths of the event Strengths of the event study analysisstudy analysis Direct and powerful test of SSFEDirect and powerful test of SSFE

– Shows whether new info is fully and Shows whether new info is fully and instantaneously incorporated in stock instantaneously incorporated in stock pricesprices

– The The joint hypothesis problem is joint hypothesis problem is overcomeovercome At short horizon, the choice of the model At short horizon, the choice of the model

usually does not matterusually does not matter– In general, strong support for MEIn general, strong support for ME

Testing corporate finance theoriesTesting corporate finance theories– Average AR measures market reaction Average AR measures market reaction

to a certain type of the eventto a certain type of the event

Event studies: Event studies: advanced leveladvanced level

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QuizQuiz

How to construct a control How to construct a control portfolio?portfolio?

Why are tests usually based on Why are tests usually based on CARs rather than ARs?CARs rather than ARs?

How to deal with infrequently How to deal with infrequently traded stocks?traded stocks?

What are the problems with long-What are the problems with long-run event studies?run event studies?

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Problems and Problems and solutionssolutions Uncertain event dateUncertain event date

– Use cumulative abnormal returnUse cumulative abnormal return Event-induced varianceEvent-induced variance

– Use cross-sectional approach to Use cross-sectional approach to compute var(ACAR)compute var(ACAR)

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Problems and Problems and solutionssolutions HeteroscedasticityHeteroscedasticity

– Use cross-sectional approach for Use cross-sectional approach for standardized abnormal returns: standardized abnormal returns:

SARSARi,ti,t = AR = ARi,ti,t/std(AR/std(ARi,ti,t)) Event clustering => cross-Event clustering => cross-

correlation in ARscorrelation in ARs– Analyze portfolios of correlated Analyze portfolios of correlated

stocksstocks– Regression with event dummiesRegression with event dummies

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Performance of short-Performance of short-run event studiesrun event studiesBrown and Warner (1980, 1985)Brown and Warner (1980, 1985) For large cross-sections of For large cross-sections of

frequently traded stocks:frequently traded stocks:– The t-tests have the correct size and The t-tests have the correct size and

powerpower For smaller cross-sections or For smaller cross-sections or

returns with fat tails:returns with fat tails:– The t-tests show significant size The t-tests show significant size

distortionsdistortions– Solution: nonparametric tests (e.g., the Solution: nonparametric tests (e.g., the

rank test)rank test)

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Performance of short-Performance of short-run event studiesrun event studies Of all potential statistical problems, only Of all potential statistical problems, only

the event-induced variance is seriousthe event-induced variance is serious– The solution is to estimate the variance over The solution is to estimate the variance over

the cross-section of ARsthe cross-section of ARs Other potential problems, such as cross-Other potential problems, such as cross-

dependence, auto-correlation and thin dependence, auto-correlation and thin trading vanish if ARs are based on the trading vanish if ARs are based on the market model (except for very illiquid market model (except for very illiquid stocks)stocks)

The power of tests decreases considerably The power of tests decreases considerably if there is event date uncertaintyif there is event date uncertainty

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Problems Problems of event of event studies studies for illiquid for illiquid stocksstocks Thin trading in the estimation period Thin trading in the estimation period

– Bias in betaBias in beta Thin trading in the event periodThin trading in the event period

– Unreliable ARsUnreliable ARs Higher bid-ask spread => negative Higher bid-ask spread => negative

auto-correlationauto-correlation– The variance of observed returns is The variance of observed returns is

inflatedinflated

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Estimation of betaEstimation of beta

Choice of the return interval and length Choice of the return interval and length of the estimation periodof the estimation period– Usually, monthly returns during a five-year Usually, monthly returns during a five-year

periodperiod The sampling error => betas deviate The sampling error => betas deviate

from the meanfrom the mean– Bayesian adjustment, Vasicek (1973):Bayesian adjustment, Vasicek (1973):

ββadjadj = w*β = w*βOLSOLS + (1-w)*β + (1-w)*βavgavg where w=where w=σσ22((ββOLSOLS)/[)/[σσ22((ββavgavg)+)+σσ22((ββOLSOLS)])] ββOLSOLS and and σσ22((ββOLSOLS): ): the OLS estimate of the individual the OLS estimate of the individual

stock beta and its variancestock beta and its variance ββavgavg and and σσ22((ββavgavg): ): the average OLS beta of all stocks the average OLS beta of all stocks

and its cross-sectional varianceand its cross-sectional variance

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Estimation of betaEstimation of beta

Non-synchronous trading => bias in betaNon-synchronous trading => bias in beta– The “trade-to-trade” approach: use matched The “trade-to-trade” approach: use matched

multi-period returns multi-period returns

RRj,ntj,nt = α = αj,j,nntt + β + βjjRRM,ntM,nt + Σ + Σt=0:nt-1t=0:nt-1εεj,tj,t Returns on the index are matched to the same Returns on the index are matched to the same

consecutive trading days as the stockconsecutive trading days as the stock Heteroscedasticity =>WLS or OLS with data Heteroscedasticity =>WLS or OLS with data

divided by √ndivided by √ntt

– The Cohen estimators:The Cohen estimators:

RRj,tj,t = = ααjj + + ΣΣl=-l1:l2l=-l1:l2ββj,lj,lRRM,t+lM,t+l + + εεj,tj,t True beta is a sum of all lead-lag betas: ΣTrue beta is a sum of all lead-lag betas: Σl=-l1:l2l=-l1:l2ββj,lj,l

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Solving the problem of Solving the problem of thin trading in the event thin trading in the event periodperiod Exclude the non-traded stocksExclude the non-traded stocks

– Reduces # observations and power of the testsReduces # observations and power of the tests Use daily returns estimated by a certain Use daily returns estimated by a certain

procedure:procedure:– The ‘lumped’ return procedure: The ‘lumped’ return procedure:

Allocate all multi-period return to the first trading dayAllocate all multi-period return to the first trading day Zero returns for non-traded daysZero returns for non-traded days

– The ‘uniform’ return procedure: The ‘uniform’ return procedure: Spread the multi-period return equally during the periodSpread the multi-period return equally during the period

– Heinkel and Kraus (1988):Heinkel and Kraus (1988): Substitute systematic component for non-traded daysSubstitute systematic component for non-traded days Add idiosyncratic component for the first trading dayAdd idiosyncratic component for the first trading day

The ‘trade-to-trade’ approach: use multi-period The ‘trade-to-trade’ approach: use multi-period ARsARs

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DeBondt&Thaler DeBondt&Thaler (1985)(1985)

""Does the stock market Does the stock market overreact?overreact?""

Test the overreaction hypothesis:Test the overreaction hypothesis:– Investors pay too much attention to current Investors pay too much attention to current

earnings and punish companies with low P/E ratioearnings and punish companies with low P/E ratio– Later earnings and prices return to fundamental Later earnings and prices return to fundamental

levelslevels Examine long-run performance of Examine long-run performance of winnerwinner and and

loser loser portfolios formed on the basis of past portfolios formed on the basis of past returnsreturns– Different formation and testing periodsDifferent formation and testing periods

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Data and methodologyData and methodology

Monthly returns of NYSE common Monthly returns of NYSE common stocks in 1926-1982 (CRSP)stocks in 1926-1982 (CRSP)– Stocks with at least 85 months of data (to Stocks with at least 85 months of data (to

exclude small and young firms)exclude small and young firms) Market index: Market index:

– Equal-wtd avg return on all CRSP stocksEqual-wtd avg return on all CRSP stocks Market-adjusted approach for AR: Market-adjusted approach for AR:

ARARii = R = Rii – R – RMM – Similar results for CAPM and market Similar results for CAPM and market

model approaches (unreported)model approaches (unreported)

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Test procedureTest procedure

Consider 16 non-overlapping 3y periods: Consider 16 non-overlapping 3y periods: – 1/1930-12/1932, …, 1/1978-12/19801/1930-12/1932, …, 1/1978-12/1980

In the beginning of each period, t=0: In the beginning of each period, t=0: – Rank all stocks on cumulative excess returns during Rank all stocks on cumulative excess returns during

the formation period (past 36 months)the formation period (past 36 months) Top 35 / top 50 / top decile stocks = winner ptf Top 35 / top 50 / top decile stocks = winner ptf

– Similarly, for loser ptfSimilarly, for loser ptf Compute ARs and CARs for the next 36 months: Compute ARs and CARs for the next 36 months:

t=1:36t=1:36 Tested hypotheses: ARTested hypotheses: ARLL=0, AR=0, ARWW=0, =0,

ACARACARLL=ACAR=ACARWW

– Cross-sectional stdCross-sectional std

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ResultsResults

Figure 1, 3y formation periodFigure 1, 3y formation period– Losers outperform winners by 24.6% Losers outperform winners by 24.6%

during 36m testing period, t=2.2during 36m testing period, t=2.2– Mostly driven by Mostly driven by

Losers that outperform the market by Losers that outperform the market by 19.6%19.6%

January returnsJanuary returns Years 2 and 3Years 2 and 3

– The results may be understated, since The results may be understated, since losers have lower betalosers have lower beta

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Results (cont.)Results (cont.)

Table 1, 1y to 5y formation periodsTable 1, 1y to 5y formation periods– Price reversal is the strongest for 3y and 5y Price reversal is the strongest for 3y and 5y

intervalsintervals– Momentum effect for 1y formation and 1y Momentum effect for 1y formation and 1y

testing periodstesting periods Figure 3, annual rebalancingFigure 3, annual rebalancing

– Even large return differentialEven large return differential– Jumps in January during Jumps in January during each each of the next 5 of the next 5

years!years!– No statistical tests (due to autocorrelation)No statistical tests (due to autocorrelation)

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ConclusionsConclusions

Rejection of WFERejection of WFE Support for the overreaction hypothesis:Support for the overreaction hypothesis:

– Low P/E companies are temporarily Low P/E companies are temporarily undervaluedundervalued

– Contrarian strategy yields high ARContrarian strategy yields high AR Robustness: similar results for Robustness: similar results for

– Different formation periods Different formation periods – Different models for ARsDifferent models for ARs– Annual rebalancingAnnual rebalancing

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CritiqueCritique

Results are sensitive to the inclusion of Results are sensitive to the inclusion of illiquid small-capsilliquid small-caps– Profits disappear if account for transaction Profits disappear if account for transaction

costscosts Results are sensitive to ptf formation Results are sensitive to ptf formation

period:period:– No profit if form portfolios in JuneNo profit if form portfolios in June

Results driven by Great Depression and Results driven by Great Depression and WWII periodWWII period– Can’t reject RW if use GLSCan’t reject RW if use GLS

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CritiqueCritique (cont.)(cont.)

Leverage effect:Leverage effect:– Positive returns => lower leverage => Positive returns => lower leverage =>

lower risk and required returnlower risk and required return Higher return on loser ptf may be due Higher return on loser ptf may be due

to higher risksto higher risks– DBT (1987): market model, DBT (1987): market model, ββL-WL-W=0.22, =0.22, ααL-L-

WW=5.9% significantly positive=5.9% significantly positive But: But: ααL-WL-W≈0 if different betas in bull and bear ≈0 if different betas in bull and bear

marketsmarkets

– Return differential is fully explained by Return differential is fully explained by the Fama-French modelthe Fama-French model

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Specifics of long-run Specifics of long-run event studiesevent studies

Lyon, Barber, and Tsai (1999)Lyon, Barber, and Tsai (1999) Biases of traditional testsBiases of traditional tests

– New listing or survivor bias: +New listing or survivor bias: + The index (or reference ptf) includes The index (or reference ptf) includes

newly added stocks, excludes dead onesnewly added stocks, excludes dead ones

– Rebalancing bias: -Rebalancing bias: - The index is periodically rebalancedThe index is periodically rebalanced

– (Positive) skewness bias: -(Positive) skewness bias: -

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Specifics of long-run Specifics of long-run event studies (cont.)event studies (cont.) Approach 1: Approach 1: traditional event study traditional event study

and BHARsand BHARs– Carefully constructed reference Carefully constructed reference

portfolios portfolios – BHARs: buy-and-hold abnormal returnsBHARs: buy-and-hold abnormal returns– Skewness-adjusted t-stat.: bootstrap or Skewness-adjusted t-stat.: bootstrap or

simulations of long-run ARs of simulations of long-run ARs of pseudoportfoliospseudoportfolios

– But: still unable to control for cBut: still unable to control for cross-ross-sectional dependence in sample sectional dependence in sample observationsobservations

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Specifics of long-run Specifics of long-run event studies (cont.)event studies (cont.) Approach 2: calendar-time portfoliosApproach 2: calendar-time portfolios

– Construct time series of mean ARs in the Construct time series of mean ARs in the sample in a given monthsample in a given month

– Inference is based on t-statistics of the time-Inference is based on t-statistics of the time-series of monthly ARsseries of monthly ARs

– But: does not precisely measure investor But: does not precisely measure investor experienceexperience

All long-run tests are sensitive to the All long-run tests are sensitive to the poorly specified asset pricing model!poorly specified asset pricing model!– Controlling for size and B/M is not sufficientControlling for size and B/M is not sufficient