1. Financial Econometrics II Lecture 3

2. 2 Up to now: Event study analysis: effective test of SSFE Measuring the magnitude and speed of market reaction to events Methodology: abnormal return and its variance Do we suffer from the joint hypothesis problem? How to measure average reaction accounting for the differences across firms and across time?

3. 3 Plan for today: Advanced topic: event study analysis How to solve potential issues Examples of event studies New topic: beta and the market model Interpretation of beta (CAPM!) How to measure and predict beta Adjustments for the measurement error and illiquidity

4. 4 How to measure average reaction to the event? Aggregating the results across firms Average abnormal return: AAR t = (1/N) Σ i AR i,t Its variance: var(AAR t ) = (1/N 2 ) Σ i var(AR i,t ) –Using the estimated variances of individual ARs and assuming zero correlation between them Or cross-sectional: var(AAR t ) = (1/N)  2 –Assuming that each AR has the same variance  2, which is measured on the basis of N observed ARs:  2 = (1/N 2 ) Σ i (AR i,t - AAR t ) 2

5. 5 What if the event date is uncertain? Aggregating the results over time: Cumulative abnormal return around the day of the event τ (from τ-t 1 to τ+t 2 ):CAR i [τ-t 1 :τ+t 2 ] = Σ t=τ-t1:τ+t2 AR i,t It variance: var(CAR i ) = Σ t=τ-t1:τ+t2 var(AR i,t ) –Assuming zero autocorrelation Aggregating the results across firms Average CAR: ACAR = (1/N) Σ i CAR i Its variance: –Based on the estimated variances of individual CARs, or… –Cross-sectional, measured on the basis of N observed CARs

6. 6 Example: reaction to earnings announcements CLM, Table 4.1, Fig 4.2: 30 US companies, 1989-93 Positive (negative) reaction to good (bad) news at day 0 No significant reaction for no-news The constant mean return model produces noisier estimates than the market model

7. 7 CARs based on the market model

8. 8 CARs based on the constant mean return model

9. 9 Methodology: explaining abnormal returns Relation between CARs and company characteristics: Cross-sectional regressions: CAR i = a + b*Cap i + c*Transp i +… –OLS with White (heteroscedasticity-consistent) standard errors –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

10. 10 Other potential issues How to measure AR for a stock after IPO? How to construct a control portfolio? Why are tests usually based on CARs rather than ARs? How to control for the event-induced volatility? How to control for the heteroscedasticity in ARs? What are the problems with long-run event studies? What if we have several events for the same company in a short period of time?

11. 11 Goriaev&Sonin (2006): YUKOS case, 2003

12. 12 Data Daily returns on YUKOS Sample period: 1/1/2003-27/11/2003 Before YUKOS received official charges Events: publications mentioning YUKOS and one of the state agencies 10 positive events 37 negative events –16 employee-related events, law enforcement agencies –16 company-related events, law enforcement agencies –12 company-related events, other state agencies

13. 13 Summary statistics

14. 14 How did YUKOS stock react to events? The market model with dummies for different types of events R Y,t = α 0 + α 1 Pos t + α 2 Neg t + βR M,t + ε t Abnormal returns Positive events: 1.4% Negative events: -1.2% –Not driven by arrests –Mostly driven by negative employee-related events involving law enforcement agencies

15. 15 How did YUKOS stock react to events?

16. 16 How did other companies react to YUKOS events? Pooled cross-sectional regression for different subsets of events R i,t = a’*RISK i + (b’*RISK i ) R Yt +ε t where R i,t : company i’s return at the event day R Y,t : YUKOS return at the event day RISK includes –Gvt i : government ownership –TD i : Transparency&Disclosure score by S&P –Oil: oil industry dummy –LS: % shares sold via ‘loans-for-shares’ auctions –Olig: dummy for companies controlled by oligarchs

17. 17 How did other companies react to YUKOS events?

18. 18 Conclusions Russian firms were very sensitive to political risk Especially non-transparent private companies, transparent state- controlled companies, oil companies and those privatized via shady schemes Consistent with the “oil rent,” “tax review,” “privatization review,” and “visible hand” hypotheses The “politics” hypothesis cannot fully explain the market reaction

19. 19 Other examples of event studies Security offerings Neutral reaction to bond offerings Negative reaction to public equity offerings Dividends Negative reaction to dividend cuts M&A Positive reaction for the target Neutral reaction for the acquirer

20. 20 Strengths of the event study analysis 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 In general, strong support for ME Testing whether market reacted significantly to a certain event Useful for asset management and corporate finance

21. 21 Why beta? Main conclusion from tests of return predictability Need a better model than constant expected return… To explain cross-sectional differences in returns due to risks CAPM: E t-1 [R i,t ] - R F = β i (E t-1 [R M,t ] – R F ) This equation is valid if the market portfolio is efficient Higher beta implies higher expected return Can we test/apply this model empirically? Expectations One period Market portfolio

22. 22 CAPM vs. the market model Time series regression: R i,t -R F = β i (R M,t -R F ) + ε i,t, where R M is the (stock) market index, E t-1 (ε i,t )=0, E t-1 (R M,t ε i,t )=0, E t-1 (ε i,t, ε i,t+j )=0 (j≠0) Assuming Rational expectations for R i,t, R M,t : ex ante → ex post –E.g., R i,t = E t-1 [R i,t ] + e i,t, where e is white noise Constant beta The market model: R i,t = α i + β i R M,t + e i,t, where E t-1 (e i,t )=0, E t-1 (R M,t e i,t )=0, (Ideally, also E t-1 (ε i,t, ε i,t+j )=0 for j≠0)

23. 23 Use of the market model R i,t = α i + β i R Mt + ε i,t Risk management: ΔR i ≈ β i ΔR M Total risk is a sum of the systematic (market) risk and idiosyncratic risk: var(R i )=β i 2 σ 2 M +σ 2 (ε) i The market risk is managed by beta The idiosyncratic risk may be reduced by diversification Computing covariance:cov(R i, R j ) = β i β j σ 2 M Assuming no idiosyncratic cross-correlation: E(ε i ε j )=0 for i≠j Simple correlations give bad forecasts Performance evaluation (e.g., of a mutual fund) Beta shows the investment style of a fund

24. 24 Estimating beta β=cov(R i, R M )/var(R M ) In Excel (see ch. 29 of Benninga, Financial Modeling) Beta: Covar(R i, R M ) / Varp(R M ) Beta: Slope(R i, R M ) Regression output (coef., s.e., R 2 ): LINEST(R i,R M,,TRUE) Beta: INDEX(LINEST(D4:D13,C4:C13,,TRUE),1,1) S.e.(beta): INDEX(LINEST(D4:D13,C4:C13,,TRUE),2,1) Choice of the return interval and estimation period US: usually, monthly returns during a five-year period Russia: weekly returns over 1 year Is historical beta a good predictor of future beta? The sampling error => betas deviate from the mean

25. 25 Is historical beta a good predictor of future beta? Blume (1971) Past and future betas are highly correlated for diversified portfolios The correlation is much lower for small portfolios and esp. for individual securities Is it due to changing betas or measurement error? Changes in beta are larger for assets with extreme betas Betas tend to regress towards one! Blime’s technique: Autoregression of betas: β t = 0.4 + 0.6*β t-1

26. 26 How are betas correlated over time?

27. 27 Mean reversion in betas

28. 28 Autoregression of betas

29. 29 Vasicek’s adjustment Bayesian adjustment, Vasicek (1973): The adjusted beta of a stock is a weighted average of the stock’s historical beta and average in the sample β adj = w*β OLS + (1-w)*β avg where 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 beta of all stocks and its cross-sectional variance The weights of betas are inversely related to their variances: w=σ 2 (β OLS )/[σ 2 (β avg )+σ 2 (β OLS )] Klemkovsky and Martin (1975): The adjusted betas give more precise forecasts than raw ones

30. 30 Estimating beta for illiquid stocks Assume that the stock is not traded in dates t 1, t 2,… What would be the prices in the non-traded days? Same as in the last trading day, thus zero return –Large return in the first trading day after the break Predicted by the market model: R t = β*R M,t –In the first trading day after the break, the stock’s return will accumulate all idiosyncratic noise over the non-traded period Betas will be biased! Dimson (1979): regression including lead and lag values of the market index 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

31. 31 Estimating beta for illiquid stocks The “trade-to-trade” approach: Compute stock returns from the last traded day to the next traded day (if necessary - over 2, 3 or n t days) Compute market returns for the same periods Run a regression with matched multi-period returns: R j,nt = α j, n t + β j R M,nt + Σ t=0:nt-1 ε j,t How to control for heteroscedasticity? –WLS: the variances are proportional to n t –OLS regression with data divided by √n t (R j,nt / √n t ) = α j *√n t + β j (R M,nt /√n t ) + (Σ t=0:nt-1 ε j,t /√n t )

32. 32 What if the stock has a large weight in the index? Endogeneity problem In the extreme, when the index is dominated by one stock, this stock will have beta of 1 by construction In Russia, this is a problem for Gazprom, Lukoil, … How to solve it? Usual way: exclude this stock from the index “Theoretical” solution: use IV approach with other blue chips (or industry indices) as instruments

33. 33 Fundamental beta Can we explain betas by company characteristics? Beaver et al. (1970): Dividend payout (dividends to earnings) Asset growth Leverage Liquidity (current assets to current liabilities) Size (total assets) Earning variability (st.dev. of E/P) Accounting beta (based on a regression of the company’s earnings against the average earnings in the economy)

34. 34 Next class Advanced topic: testing CAPM Is beta sufficient to describe systematic risks? Time series and cross-sectional tests Market anomalies New topic: multi-factor models How to construct and interpret risk factors? Most popular models: Fama-French, Carhart,…