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  • 1. Event Studies Motivation Outline 1 Linear Factor Models Motivation Time-series approach Cross-sectional approach Comparing approaches Odds and ends 2 Event Studies Motivation Basic methodology Bells and whistles Michael W. Brandt Methods Lectures: Financial Econometrics
  • 2. Event Studies Motivation What is an event study? An event study measures the immediate and short-horizon delayed impact of a specific event on the value of a security. Event studies traditionally answer the question Does this event matter? (e.g., index additions) but are increasingly used to also answer the question Is the relevant information impounded into prices immediately or with delay? (e.g., post earnings announcement drift) Event studies are popular not only in accounting and finance, but also in economics and law to examine the role of policy and regulation or determine damages in legal liability cases. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 3. Event Studies Motivation Short- versus long-horizon event studies Short-horizon event studies examine a short time window, ranging from hours to weeks, surrounding the event in question. Since even weekly expected returns are small in magnitude, this allows us to focus on the information being released and (largely) abstract from modeling discount rates and changes therein. There is relatively little controversy about the methodology and statistical properties of short-horizon event studies. However event study methodology is increasingly being applied to longer-horizon questions. (e.g., do IPOs under-perform?) Long-horizon event studies are problematic because the results are sensitive to the modeling assumption for expected returns. The following discussion focuses on short-horizon event studies. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 4. Event Studies Basic methodology Outline 1 Linear Factor Models Motivation Time-series approach Cross-sectional approach Comparing approaches Odds and ends 2 Event Studies Motivation Basic methodology Bells and whistles Michael W. Brandt Methods Lectures: Financial Econometrics
  • 5. Event Studies Basic methodology Setup Basic event study methodology is essentially unchanged since Ball and Brown (1968) and Fama et al. (1969). Anatomy of an event study 1. Event Definition and security selection. 2. Specification and estimation of the reference model characterizing "normal" returns (e.g., market model). 3. Computation and aggregation of "abnormal" returns. 4. Hypothesis testing and interpretation. #1 and the interpretation of the results in #4 are the real economic meat of an event study – the rest is fairly mechanical. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 6. Event Studies Basic methodology Reference models Common choices of models to characterize "normal" returns Constant expected returns ri,t+1 = µi + i,t+1 Market model ri,t+1 = αi + βi rm,t+1 + i,t+1 Linear factor models ri,t+1 = αi + βi ft+1 + i,t+1 (Notice the intercepts.) Short-horizon event study results tend to be relatively insensitive to the choice of reference models, so keeping it simple is fine. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 7. Event Studies Basic methodology Time-line and estimation A typical event study time-line is Source: MacKinlay (1997) The parameters of the reference model are usually estimated over the estimation window and held fixed over the event window. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 8. Event Studies Basic methodology Abnormal returns Using the market model as reference model, define ˆ ˆ AR i,τ = ri,τ − αi − βi rm,τ τ = T1 + 1, ..., T 2. ˆ Assuming iid returns 2 ˆ 1 (rm,τ − µm ) ˆ Var AR i,τ = σ 2i + 1+ . T1 − T0 σm ˆ due to estimation error Estimation error also introduces persistence and cross-correlation in the measured abnormal returns, even when true returns are iid, which is an issue particularly for short estimation windows. Assume for what follows that estimation error can be ignored. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 9. Event Studies Basic methodology Aggregating abnormal returns Since the abnormal return on a single stock is extremely noisy, returns are typically aggregated in two dimensions. 1. Average abnormal returns across all firms undergoing the same event lined up in event time ¯ 1 N ˆ AR τ = AR i,τ . N i=1 2. Cumulate abnormal returns over the event window ˆ T2 ˆ CAR i (T1 , T2 ) = τ =T1 +1 AR i,τ or ¯ T2 ¯ CAR(T1 , T2 ) = τ =T1 +1 AR τ . Michael W. Brandt Methods Lectures: Financial Econometrics
  • 10. Event Studies Basic methodology Hypothesis testing Basic hypothesis testing requires expressions for the variance of ¯ ˆ ¯ AR τ , CAR i (T1 , T2 ), and CAR(T1 , T2 ). If stock level residuals i,τ are iid through time ˆ Var CAR i (T1 , T2 ) = (T2 − T1 )σ 2i . The other two expressions are more problematic because they depend on the cross-sectional correlation of event returns. If, in addition, event windows are non-overlapping across stocks ¯ 1 N 2 Var AR τ = 2 i=1 σ i N ¯ T2 ¯ Var CAR(T1 , T2 ) = τ =T1 +1 Var AR τ . Michael W. Brandt Methods Lectures: Financial Econometrics
  • 11. Event Studies Basic methodology Example Earnings announcements Source: MacKinlay (1997) Michael W. Brandt Methods Lectures: Financial Econometrics
  • 12. Event Studies Bells and whistles Outline 1 Linear Factor Models Motivation Time-series approach Cross-sectional approach Comparing approaches Odds and ends 2 Event Studies Motivation Basic methodology Bells and whistles Michael W. Brandt Methods Lectures: Financial Econometrics
  • 13. Event Studies Bells and whistles Dependence If event windows overlap across stocks, the abnormal returns are correlated contemporaneously or at lags. One solution is Brown and Warner’s (1980) "crude adjustment" Form a portfolio of firms experiencing an event in a given month or quarter (still lined up in event time, of course). Compute the average abnormal return of this portfolio. Normalize this abnormal return by the standard deviation of the portfolio’s abnormal returns over the estimation period. Michael W. Brandt Methods Lectures: Financial Econometrics
  • 14. Event Studies Bells and whistles Heteroskedasticity Two forms of heteroskedasticity to deal with in event studies 1. Cross-sectional differences in σ i . ¯ • Standardize ARi,τ by σ i before aggregating to AR τ . • Jaffe (1974). 2. Event driven changes in σ i ,t . • Cross-sectional estimate of Var [ARi,τ ] over the event window. • Boehmer et al. (1991). Michael W. Brandt Methods Lectures: Financial Econometrics
  • 15. Event Studies Bells and whistles Regression based approach An event study can alternatively be run as multivariate regression L r1,t+1 = α1 + β1 rm,t+1 + γ1,τ D1,t+1,τ + u1,t+1 τ =0 L r2,t+1 = α2 + β2 rm,t+1 + γ2,τ D2,t+1,τ + u2,t+1 τ =0 ... L rn,t+1 = αn + βn rm,t+1 + γn,τ Dn,t+1,τ + un,t+1 τ =0 where Di,t,τ = 1 if firm i had an event at date t − τ (= 0 otherwise). In this case, γi,τ takes the place of the abnormal return ARi,τ . Michael W. Brandt Methods Lectures: Financial Econometrics