Financial Econometrics II

Lecture 3

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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?

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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

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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

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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

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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

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CARs based on the market model

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CARs based on the constant mean return model

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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

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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?

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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

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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?

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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

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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

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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

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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

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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)

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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

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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

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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

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How are betas correlated over time?

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Mean reversion in betas

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Autoregression of betas

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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

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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

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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)

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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

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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)

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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,…