Event study analysis

NES EFM 2005/6 2 Plan Up to now: Up to now: –Low-frequency analysis of return predictability –Search for stable relationship between stock returns and publicly available variables Today: Today: –High-frequency analysis of changes in security prices in response to news (events)

NES EFM 2005/6 3 Event study analysis Measure the speed and magnitude of market reaction to a certain event Measure the speed and magnitude of market reaction to a certain event –High-frequency (usually, daily) data –Ease of use, flexibility –Robustness to the joint hypothesis problem Experimental design Experimental design –Pure impact of a given event –Role of info arrival and aggregation

NES EFM 2005/6 4 Reaction to the unexpected event

NES EFM 2005/6 5 Methodology: identification of the event and its date Type of the event Type of the event –Share repurchase / dividend / M&A Date of the event τ=0 Date of the event τ=0 –Announcement, not the actual payment –The event window: several days around the event date Selection of the sample Selection of the sample –Must be representative, no selection biases

NES EFM 2005/6 6 Methodology: modelling the return generating process Abnormal return: AR i,t = R i,t – E[R i,t | X t ] Abnormal return: AR i,t = R i,t – E[R i,t | X t ] –Prediction error: ex post return - normal return Normal return: expected if no event happened Normal return: expected if no event happened –The mean-adjusted approach: X t is a constant –The market model: X t includes the market return –Control portfolio: X t is the return on portfolio of similar firms (wrt size, BE/ME) The estimation window: period prior to the event window The estimation window: period prior to the event window –Usually: 250 days or 60 months

NES EFM 2005/6 7 Methodology: testing the hypothesis AR=0 H 0 : the event has no impact on the firm's value H 0 : the event has no impact on the firm's value For individual firm: For individual firm: –Estimate the benchmark model during the estimation period [τ-t 1 -T: τ-t 1 -1]: R i,t = α i + β i R M,t + ε i,t, where ε ~ N(0, σ 2 (ε)) –During the event period [τ-t 1 : τ+t 2 ], under H 0 : AR i,t = R i,t - a i - b i R M,t ~ N(0, V i,t ), var(AR i,t ) = s 2 (ε)[1+1/T+(R M,t -μ M ) 2 /var(R M )]

NES EFM 2005/6 8 Methodology: testing the hypothesis AR=0 Aggregating the results across firms: Aggregating the results across firms: –Average abnormal return: AAR t = (1/N) Σ i AR i,t –Computing var(AAR): Using the estimated variances of individual ARs, or… Using the estimated variances of individual ARs, or… Cross-sectionally: var(AAR t ) = (1/N 2 ) Σ i (AR i,t - AAR i,t ) 2 Cross-sectionally: var(AAR t ) = (1/N 2 ) Σ i (AR i,t - AAR i,t ) 2 Aggregating the results over time: Aggregating the results over time: –Cumulative abnormal return: CAR[τ-t 1 : τ+t 2 ] = Σ t=τ-t1: τ+t2 AR i,t –Similarly, average CAR: ACAR = (1/N) Σ i CAR i

NES EFM 2005/6 9 Methodology: explaining abnormal returns Relation between CARs and company characteristics: Relation between CARs and company characteristics: –Cross-sectional regressions OLS with White errors OLS with White errors WLS with weights proportional to var(CAR) WLS with weights proportional to var(CAR) –Account for potential selection bias The characteristics may be related to the extent to which the event is anticipated The characteristics may be related to the extent to which the event is anticipated

NES EFM 2005/6 10 Asquith&Mullins (1983) " The impact of initiating dividend payments on shareholder wealth " Measure stock price reaction to dividend announcements Measure stock price reaction to dividend announcements –Costs vs clientele vs signaling vs other theories Sample of companies initiating dividend payments Sample of companies initiating dividend payments –No need to model investors expectations Explicitly control for other news Explicitly control for other news Relate ARs to the magnitude of dividends Relate ARs to the magnitude of dividends –The first cross-sectional analysis of factors explaining ARs Compare reaction to initial and subsequent dividends Compare reaction to initial and subsequent dividends

NES EFM 2005/6 11 Data 168 firms that initiated dividend payments to common stockholders in firms that initiated dividend payments to common stockholders in –114 increased dividends within 3 years –7 decreased dividends The announcement date: The announcement date: –Publication in the Wall Street Journal Other announcements in +/- 10 day interval around the event date Other announcements in +/- 10 day interval around the event date Daily stock returns Daily stock returns

NES EFM 2005/6 12 Methodology Normal return: Normal return: –Return on control portfolio with similar beta Each year, stocks traded in NYSE and ASE were grouped into 10 portfolios ranked by beta Each year, stocks traded in NYSE and ASE were grouped into 10 portfolios ranked by beta Event window: [-1:0] Event window: [-1:0] –To capture cases when the news was published the next day after the announcement Main variable: CAR[-1:0] = AR -1 + AR 0 Main variable: CAR[-1:0] = AR -1 + AR 0 Cross-sectional approach to compute std Cross-sectional approach to compute std –t(ACAR t ) = N ACAR t / std(CAR i,t )

NES EFM 2005/6 13 Results Table 1, all firms in the sample Table 1, all firms in the sample –AR -1 =2.5%, AR 0 =1.2%, both with t>3 –Two-day ACAR=3.7% with t=6.6 –Almost 70% of firms experienced positive market reaction –Other ARs are small and insignificant Consistent with ME Consistent with ME No leakage of info prior to div announcement No leakage of info prior to div announcement

NES EFM 2005/6 14 Results (cont.) Table 3, subsamples of firms Table 3, subsamples of firms –88 firms with no other new info: two-day ACAR = 4.7% with t=5.9 Dividend and earning announcements may be partial substitutes! Dividend and earning announcements may be partial substitutes! –Firms that subsequently raised dividends: smaller and marginally (in)significant ACARs No expectation model for subsequent dividends! No expectation model for subsequent dividends!

NES EFM 2005/6 15 Results (cont.) Table 4, CS regression of CARs on the change in payout yield Table 4, CS regression of CARs on the change in payout yield –Slope coefficient: captures the effects of an unexpected div increase Positive relation for both initial and subsequent dividends Positive relation for both initial and subsequent dividends The reaction is stronger for subsequent dividends The reaction is stronger for subsequent dividends –The intercept: captures the expected div increase (with negative sign) Negative for subsequent dividends (they are partially forecast) Negative for subsequent dividends (they are partially forecast)

NES EFM 2005/6 16 Conclusions First clean test of the market reaction to dividends First clean test of the market reaction to dividends Positive effects of dividends overweigh negative ones Positive effects of dividends overweigh negative ones –Support for signaling model Market efficiency is not rejected Market efficiency is not rejected

NES EFM 2005/6 17 Strengths of the event study analysis Direct and powerful test of SSFE Direct and powerful test of SSFE –Shows whether new info is fully and instantaneously incorporated in stock prices –The joint hypothesis problem is overcome At short horizon, the choice of the model usually does not matter At short horizon, the choice of the model usually does not matter –In general, strong support for ME Testing corporate finance theories Testing corporate finance theories –Average AR measures market reaction to a certain type of the event

Event studies: advanced level

NES EFM 2005/6 19 Quiz How to construct a control portfolio? How to construct a control portfolio? Why are tests usually based on CARs rather than ARs? Why are tests usually based on CARs rather than ARs? How to deal with infrequently traded stocks? How to deal with infrequently traded stocks? What are the problems with long-run event studies? What are the problems with long-run event studies?

NES EFM 2005/6 20 Plan for today Specifics of modelling illiquid stocks Specifics of modelling illiquid stocks Specifics of long-run event studies Specifics of long-run event studies

NES EFM 2005/6 21 Problems and solutions Uncertain event date Uncertain event date –Use cumulative abnormal return Event-induced variance Event-induced variance –Use cross-sectional approach to compute var(ACAR) Heteroscedasticity Heteroscedasticity –Use cross-sectional approach for standardized abnormal returns: SAR i,t = AR i,t /std(AR i,t )

NES EFM 2005/6 22 Problems and solutions Event clustering => cross-correlation in ARs Event clustering => cross-correlation in ARs –Analyze portfolios of correlated stocks –Regression with event dummies Non-normal distribution Non-normal distribution –Nonparametric tests: Sign test (but not for skewed distributions) Sign test (but not for skewed distributions) Rank test, Corrado (1989) Rank test, Corrado (1989)

NES EFM 2005/6 23 Performance of short-run event studies Brown and Warner (1980, 1985) For large cross-sections of frequently traded stocks: For large cross-sections of frequently traded stocks: –The t-tests and the non-parametric rank test have the correct size and power –The power of the sign test is always lower For smaller cross-sections / returns with fat tails: For smaller cross-sections / returns with fat tails: –The t-tests show significant size distortions –The rank test retains correct size, has higher power

NES EFM 2005/6 24 Performance of short-run event studies (cont.) Of all potential statistical problems, only event- induced variance is serious Of all potential statistical problems, only event- induced variance is serious –The solution is to estimate the variance over the cross- section of ARs Other potential problems, such as cross- dependence, auto-correlation and thin trading vanish if ARs are based on the market model Other potential problems, such as cross- dependence, auto-correlation and thin trading vanish if ARs are based on the market model –Except for very illiquid stocks The power of tests decreases considerably if there is event date uncertainty The power of tests decreases considerably if there is event date uncertainty

NES EFM 2005/6 25 Problems of event studies for illiquid stocks Thin trading in the estimation period Thin trading in the estimation period –Bias in beta Thin trading in the event period Thin trading in the event period –Unreliable ARs Higher bid-ask spread => negative auto- correlation Higher bid-ask spread => negative auto- correlation –The variance of observed returns is inflated

NES EFM 2005/6 26 Estimation of beta Choice of the return interval and length of the estimation period Choice of the return interval and length of the estimation period –Usually, monthly returns during a five-year period The sampling error => betas deviate from the mean The sampling error => betas deviate from the mean –Bayesian adjustment, Vasicek (1973): β adj = wβ OLS + (1-w)β avg where w=σ 2 (β OLS )/[σ 2 (β avg )+σ 2 (β OLS )] where w=σ 2 (β OLS )/[σ 2 (β avg )+σ 2 (β OLS )] β OLS and σ 2 (β OLS ): the OLS estimate of the individual stock beta and its variance β OLS and σ 2 (β OLS ): the OLS estimate of the individual stock beta and its variance β avg and σ 2 (β avg ): the average OLS beta of all stocks and its cross-sectional variance β avg and σ 2 (β avg ): the average OLS beta of all stocks and its cross-sectional variance

NES EFM 2005/6 27 Estimation of beta (cont.) Non-synchronous trading => bias in beta Non-synchronous trading => bias in beta –The trade-to-trade approach: use matched multi- period returns R j,nt = α j, n t + β j R M,nt + Σ t=0:nt-1 ε j,t Returns on the index are matched to the same consecutive trading days as the stock Returns on the index are matched to the same consecutive trading days as the stock Heteroscedasticity =>WLS or OLS with data divided by n t Heteroscedasticity =>WLS or OLS with data divided by n t –The Cohen estimators: R j,t = α j + Σ l=-l1:l2 β j,l R M,t+l + ε j,t True beta is a sum of all lead-lag betas: Σ l=-l1:l2 β j,l True beta is a sum of all lead-lag betas: Σ l=-l1:l2 β j,l

NES EFM 2005/6 28 Solving the problem of thin trading in the event period Exclude the non-traded stocks Exclude the non-traded stocks –Reduces # observations and power of the tests Use daily returns estimated by a certain procedure: Use daily returns estimated by a certain procedure: –The lumped return procedure: Allocate all multi-period return to the first trading day Allocate all multi-period return to the first trading day Zero returns for non-traded days Zero returns for non-traded days –The uniform return procedure: Spread the multi-period return equally during the period Spread the multi-period return equally during the period –Heinkel and Kraus (1988): Substitute systematic component for non-traded days Substitute systematic component for non-traded days Add idiosyncratic component for the first trading day Add idiosyncratic component for the first trading day The trade-to-trade approach: use multi-period ARs The trade-to-trade approach: use multi-period ARs

NES EFM 2005/6 29 Performance of event studies for illiquid stocks Maynes and Rumsey (1993) The traditional tests are misspecified The traditional tests are misspecified Only the rank test together with trade-to- trade approach performs well Only the rank test together with trade-to- trade approach performs well

NES EFM 2005/6 30 DeBondt&Thaler (1985) " Does the stock market overreact? " Test the overreaction hypothesis: Test the overreaction hypothesis: –Investors pay too much attention to current earnings and punish companies with low P/E ratio –Later earnings and prices return to fundamental levels Examine long-run performance of winner and loser portfolios formed on the basis of past returns Examine long-run performance of winner and loser portfolios formed on the basis of past returns –Different formation and testing periods

NES EFM 2005/6 31 Data and methodology Monthly returns of NYSE common stocks in (CRSP) Monthly returns of NYSE common stocks in (CRSP) –Stocks with at least 85 months of data (to exclude small and young firms) Market index: Market index: –Equal-wtd avg return on all CRSP stocks Market-adjusted approach for AR: Market-adjusted approach for AR: AR i = R i – R M –Similar results for CAPM and market model approaches (unreported)

NES EFM 2005/6 32 Test procedure Consider 16 non-overlapping 3y periods: Consider 16 non-overlapping 3y periods: –1/ /1932, …, 1/ /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 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 ptf Compute ARs and CARs for the next 36 months: t=1:36 Compute ARs and CARs for the next 36 months: t=1:36 Tested hypotheses: AR L =0, AR W =0, ACAR L =ACAR W Tested hypotheses: AR L =0, AR W =0, ACAR L =ACAR W –Cross-sectional std

NES EFM 2005/6 33 Results Figure 1, 3y formation period Figure 1, 3y formation period –Losers outperform winners by 24.6% during 36m testing period, t=2.2 –Mostly driven by Losers that outperform the market by 19.6% Losers that outperform the market by 19.6% January returns January returns Years 2 and 3 Years 2 and 3 –The results may be understated, since losers have lower beta

NES EFM 2005/6 34 Results (cont.) Table 1, 1y to 5y formation periods Table 1, 1y to 5y formation periods –Price reversal is the strongest for 3y and 5y intervals –Momentum effect for 1y formation and 1y testing periods Figure 3, annual rebalancing Figure 3, annual rebalancing –Even large return differential –Jumps in January during each of the next 5 years! –No statistical tests (due to autocorrelation)

NES EFM 2005/6 35 Conclusions Rejection of WFE Rejection of WFE Support for the overreaction hypothesis: Support for the overreaction hypothesis: –Low P/E companies are temporarily undervalued –Contrarian strategy yields high AR Robustness: similar results for Robustness: similar results for –Different formation periods –Different models for ARs –Annual rebalancing

NES EFM 2005/6 36 Critique Results are sensitive to the inclusion of illiquid small-caps Results are sensitive to the inclusion of illiquid small-caps –Profits disappear if account for transaction costs Results are sensitive to ptf formation period: Results are sensitive to ptf formation period: –No profit if form portfolios in June Results driven by Great Depression and WWII period Results driven by Great Depression and WWII period –Cant reject RW if use GLS

NES EFM 2005/6 37 Critique (cont.) Leverage effect: Leverage effect: –Positive returns => lower leverage => lower risk and required return Higher return on loser ptf may be due to higher risks Higher return on loser ptf may be due to higher risks –DBT (1987): market model, β L-W =0.22, α L-W =5.9% significantly positive But: α L-W 0 if different betas in bull and bear markets But: α L-W 0 if different betas in bull and bear markets –Return differential is fully explained by the Fama- French model

NES EFM 2005/6 38 Specifics of long-run event studies Lyon, Barber, and Tsai (1999) Biases of traditional tests Biases of traditional tests –New listing or survivor bias: + The index (or reference ptf) includes newly added stocks, excludes dead ones The index (or reference ptf) includes newly added stocks, excludes dead ones –Rebalancing bias: - The index is periodically rebalanced The index is periodically rebalanced –(Positive) skewness bias: -

NES EFM 2005/6 39 Specifics of long-run event studies (cont.) Approach 1: traditional event study and BHARs Approach 1: traditional event study and BHARs –Carefully constructed reference portfolios –BHARs: buy-and-hold abnormal returns –Skewness-adjusted t-stat.: bootstrap or simulations of long-run ARs of pseudoportfolios –But: still unable to control for cross-sectional dependence in sample observations

NES EFM 2005/6 40 Specifics of long-run event studies (cont.) Approach 2: calendar-time portfolios Approach 2: calendar-time portfolios –Construct time series of mean ARs in the sample in a given month –Inference is based on t-statistics of the time-series of monthly ARs –But: does not precisely measure investor experience All long-run tests are sensitive to the poorly specified asset pricing model! All long-run tests are sensitive to the poorly specified asset pricing model! –Controlling for size and B/M is not sufficient