Financial Econometrics II презентация

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?

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

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) σ2
Assuming that each AR has the same variance σ2, which is measured on the basis of N observed ARs: σ2 = (1/N2) Σi (ARi,t - AARt)2

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

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

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

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?

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

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

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

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

to public equity offerings
Dividends
Negative reaction to dividend cuts
M&A
Positive reaction for the target
Neutral reaction for the acquirer

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

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

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)

management: ΔRi ≈ βiΔRM
Total risk is a sum of the systematic (market) risk and idiosyncratic risk: var(Ri)=βi2σ2M+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

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

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

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

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

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)

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

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)

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,…