Financial Econometrics II Lecture 3. 2 Up to now: Event study analysis: effective test of SSFE...
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Transcript of Financial Econometrics II Lecture 3. 2 Up to now: Event study analysis: effective test of SSFE...
Financial Econometrics II
Lecture 3
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
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
How to measure average reaction to the event?
Aggregating the results across firms
Average abnormal return: AARt = (1/N) Σi ARi,t
Its variance: var(AARt) = (1/N2) Σi var(ARi,t)
– Using the estimated variances of individual ARs and assuming zero
correlation between them
Or cross-sectional: var(AARt) = (1/N) 2
– Assuming that each AR has the same variance 2, which is measured on
the basis of N observed ARs: 2 = (1/N2) Σi (ARi,t - AARt)2
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-t1 to τ+t2): CARi[τ-t1:τ+t2] = Σt=τ-t1:τ+t2 ARi,t
It variance: var(CARi) = Σt=τ-t1:τ+t2 var(ARi,t)
– Assuming zero autocorrelation
Aggregating the results across firms
Average CAR: ACAR = (1/N) Σi CARi
Its variance:
– Based on the estimated variances of individual CARs, or…
– Cross-sectional, measured on the basis of N observed CARs
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
CARs based on the market model
8
CARs based on the constant mean return model
9
Methodology: explaining abnormal returns
Relation between CARs and company characteristics:
Cross-sectional regressions: CARi = a + b*Capi + c*Transpi +…
– 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
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
Goriaev&Sonin (2006): YUKOS case, 2003
90
100
110
120
130
140
150
160
170
180
190
200
04/0
1/03
18/0
1/03
01/0
2/03
15/0
2/03
01/0
3/03
15/0
3/03
29/0
3/03
12/0
4/03
26/0
4/03
10/0
5/03
24/0
5/03
07/0
6/03
21/0
6/03
05/0
7/03
19/0
7/03
02/0
8/03
16/0
8/03
30/0
8/03
13/0
9/03
27/0
9/03
11/1
0/03
25/1
0/03
08/1
1/03
22/1
1/03
Days
Pri
ce
YUKOS S&P/RUX PosD NegD
Arrest of M. Khodorkovsky
Arrest of P. Lebedev
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
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Summary statistics
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How did YUKOS stock react to events?
The market model with dummies for different types of
events
RY,t = α0 + α1Post + α2Negt + βRM,t+ εt
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
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How did YUKOS stock react to events?
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How did other companies react to YUKOS events?
Pooled cross-sectional regression for different subsets of events
Ri,t = a’*RISKi + (b’*RISKi) RYt+εt
where Ri,t: company i’s return at the event day
RY,t: YUKOS return at the event day RISK includes
– Gvti: government ownership
– TDi: 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
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How did other companies react to YUKOS events?
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
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
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
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: Et-1[Ri,t] - RF = βi (Et-1[RM,t] – RF)
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
CAPM vs. the market model
Time series regression: Ri,t-RF = βi(RM,t-RF) + εi,t,
where RM is the (stock) market index,
Et-1(εi,t)=0, Et-1(RM,tεi,t)=0, Et-1(εi,t, εi,t+j)=0 (j≠0)
Assuming
Rational expectations for Ri,t, RM,t: ex ante → ex post
– E.g., Ri,t = Et-1[Ri,t] + ei,t, where e is white noise
Constant beta
The market model: Ri,t = αi + βiRM,t + ei,t,
where Et-1(ei,t)=0, Et-1(RM,tei,t)=0,
(Ideally, also Et-1(εi,t, εi,t+j)=0 for j≠0)
23
Use of the market model
Ri,t = αi + βiRMt + εi,t
Risk management: ΔRi ≈ βiΔRM
Total risk is a sum of the systematic (market) risk and idiosyncratic
risk: var(Ri)=βi2σ2
M+σ2(ε)i
The market risk is managed by beta
The idiosyncratic risk may be reduced by diversification
Computing covariance: cov(Ri, Rj) = βiβjσ2M
Assuming no idiosyncratic cross-correlation: E(εiεj)=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
Estimating beta
β=cov(Ri, RM)/var(RM)
In Excel (see ch. 29 of Benninga, Financial Modeling) Beta: Covar(Ri, RM) / Varp(RM) Beta: Slope(Ri, RM) Regression output (coef., s.e., R2): LINEST(Ri,RM,,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
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: βt = 0.4 + 0.6*βt-1
26
How are betas correlated over time?
27
Mean reversion in betas
28
Autoregression of betas
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
βadj = w*βOLS + (1-w)*βavg
where βOLS and σ2(βOLS): the OLS estimate of the individual stock beta and
its variance βavg and σ2(βavg): the average beta of all stocks and its cross-sectional
variance The weights of betas are inversely related to their variances:
w=σ2(βOLS)/[σ2(βavg)+σ2(βOLS)]
Klemkovsky and Martin (1975): The adjusted betas give more precise forecasts than raw ones
30
Estimating beta for illiquid stocks
Assume that the stock is not traded in dates t1, t2,…
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: Rt = β*RM,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
Rj,t = αj + Σl=-l1:l2βj,lRM,t+l + εj,t
True beta is a sum of all lead-lag betas: Σl=-l1:l2βj,l
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 nt days) Compute market returns for the same periods Run a regression with matched multi-period returns:
Rj,nt = αj,nt + βjRM,nt + Σt=0:nt-1εj,t
How to control for heteroscedasticity?
– WLS: the variances are proportional to nt
– OLS regression with data divided by √nt
(Rj,nt / √nt) = αj*√nt + βj(RM,nt /√nt) + (Σt=0:nt-1εj,t /√nt)
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
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
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,…