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Question 1

What type of market efficiency can we test and what information is contained in that type?

Answer 1

Semi strong mkt efficiency. Definition: prices reflect all public information

Question 2

What does efficiency in face of EMH mean?

Answer 2

Efficiency refers to the direction and magnitude of price fluctuations

Question 3

What is strong EMH?

Answer 3

Prices reflect not only public but all relevant information

Question 4

What are the three steps of Event study design?

Answer 4

1) Identify event and timing
2) Specify benchmark model for normal returns
3) Calculate abnormal returns : AR = R - NR

Question 5

Name three types of benchmark models.

Answer 5

Mean adjusted model, Market adjusted model (assumes beta of firm is 1), CAPM (NR = rf + beta MRP)

Question 6

How do we compute AAR, CAR, CAAR in AR matrix where rows are firm, and columns are time?

Answer 6

1) Computing average value of each column gives us AAR. Summing a row gives CAR. CAAR = 1/n Sum(CAR) and CAAR = sum(AAR)

Question 7

What is cross-sectional correlation and its impact on statistical inference?

Answer 7

cov(ARi,t ; ARj,t) != 0
Impact: T-test becomes invalid. If cov >0 then: Variance is bigger than estimated –> SE are too low –> t-test is too high –> H0 rejected too often

Question 8

How do we solve cross-sectional correlation?

Answer 8

Solution: Crude dependence SE or Average all returns cross-sectionally and treat these –> effectively we reduce matrix to one row only

Question 9

What are Non Parametric tests?

Answer 9

Sign Test: Tests proportion of negative to positive returns. Under H0: Distribution is symmetric and proportion is 50/50.
Rank Test: It is better than Sign test since it takes into consideration magnitude of AR.

Question 10

How do we deal with cross-sectional heteroskedasticity?

Answer 10

1) Adjust SE of AAR and CAAR
2) Standardize AR by firm

Question 11

How do we estimate NR if time horizon is long?

Answer 11

In such a case it is more proper to use FF3-factor model.
NR= Ri-rf=a + b(MRP)+ gSMB + gHML + eit
Benefit: leads to lower cross-sectional corr of AR!!!

Question 12

Describe the Pooled OLS approach in Panel Data.

Answer 12

Model pools observations from different time periods ignoring firms. This effectively combines panel data into one cross-section. Mitigates event clustering.

Question 13

What do fixed firm and time effects do?

Answer 13

FFE: Controls for cross-sectional heterogeneity. Captures effects that vary across firms but not in time.
TFE: Controls for time level heterogeneity. Captures effects of variables that vary across time but are constant cross-sectionally.

Question 14

What are drawbacks of fixed effects?

Answer 14

FFE: Cannot identify effects of variables that are constant over time
TFE: Cannot identify effects of var. constant across firms.

Question 15

How can we mitigate that SE are correlated across time or firms?

Answer 15

We can cluster SE. In that way error terms can covary within clusters but not between. We can cluster by firm, by time, or by both.

Question 16

Do fixed effects take away the need for clustering of SE?

Answer 16

NO! Fixed effects do not fix the issue. Autocorrelation among error terms still remains.

Question 17

Describe the FMB process.

Answer 17

1) Run a time series regression on each stock and obtain factor loadings (betas).
2) For each time period do a cross-sectional regression with factor loading betas as predictors. The resulting parameter estimates - gammas are the risk premia.

Question 18

What are benefits of FMB?

Answer 18

1) Allows for time variation in IV’s
2) Betas are allowed to change over time
3) Does not use forward looking inf.
4) Corrects for cross-sectional correlation of error terms

Question 19

What are the five OLS assumptions, with mathematical notation?

Answer 19

1) Linearity : yt = at + bxt + et
2) Random Sampling: cov(u_t ; u_t+j) = 0
3) Sample variation: Var[x] >0
4) ZCM: E[u_t |x] = 0
5) Homoskedasticity: V[u_t|x] = var < inf
6) Normality: u_t ~ N(0, var)

Question 20

What is the impact if x is not exogenous?

Answer 20

This implies that E[u_t|x]!=0
This means that x and y are jointly determined at the same time. Can’t make causal inference.

Question 21

If we have autocorrelation, which assumption is violated?

Answer 21

Random sample assumption: cov{u_t ; u_t+j) =0 is violated.

Question 22

If we observe non-stationarity, which assumption is violated?

Answer 22

Stationarity means: Unconditional joint probability distribution does change over time. This implies constant unconditional mean and variance. Hence Homoskedasticity is violated.

Question 23

When we have non-normality in small samples which test can we use to check for non-normality?

Answer 23

Bera-Jarque test. It tests whether skewness (b1) and kurtosis (b2) are jointly zero.

Question 24

What solutions exist for dealing with non-normality?

Answer 24

1) Log transformation of IV
2) Winsorize data

Question 25

Which assumption is violated if we have autocorrelation?

Answer 25

Autocorr. violates A2. Breusch-Godfrey test finds up to rth order autocorr.

Question 26

What does positive autocorr do?

Answer 26

1) SE are too low --> t-test is biased upward --> Reject H0 too much. 2) Newey-West (HAC) --> Adds less weight to higher autocovariance 3) Estimates are no longer EFFICIENT

Question 27

We can also add lagged effects to deal with autocovariance. How?

Answer 27

y_t = a + b1x1,t +...+b_k*x_k,t + g1x1,t-1 +....+ g_k * x_k, t-1 OLS can become biased but still consistent.

Question 28

Why add lagged effects?

Answer 28

1) Delayed Response 2) Over/Underreaction 3) Reduction of serial autocorrelation

Question 29

Show the impact of measuring IV wrong. What is the bias if b2>0?

Answer 29

New error term: (u_t - b2v_t) We have negative bias if b2>0 Estimated parameters will be biased towards zero

Question 30

What does it mean for estimated to be consistent and unbiased?

Answer 30

unbiased : E[b_hat] = b consistent: lim P[|b_hat - b|0

Question 31

What is a parameter stability test?

Answer 31

We want to test whether parameters are constant over time. Introduce dummies for sub periods. Then we deploy a chow test (H0: b1=b2) hence no structural break.

Question 32

Can we have autocorrelation and stationarity at the same time?

Answer 32

Yes, stationarity requires the underlying structure to be the same, so no mean and variance change. Thus if within that probability distribution there is autocorrelation, it is possible.

Question 33

What is the condition for stationarity?

Answer 33

-1 < phi < 1 || The weight of past shocks decreases the further away in time they are.

Question 34

What is autocorrelation in a simple AR model?

Answer 34

It is the autoregressive coefficient to the power of the lag number.

Question 35

What are two information criterions that help decide how many lags to include?

Answer 35

1) AIC: ln(var) + 2k/T 2) SBIC: ln(var) + (K/T) * ln(T)

Question 36

What are the drawbacks of AIC and SBIC?

Answer 36

AIC is more stable but non-consistent --> tends to choose bigger models. SBIC is more consistent but inefficient.

Question 37

What is impulse response function?

Answer 37

It gives the long term impact of the shock to the variable in the AR model. When calculating it, we do it in ceteris paribus way -- assumption that all other shocks are zero.

Question 38

What do AAR and CAR tell us?

Answer 38

AAR: Measure of the short-term impact of the event. CAR: Measure of total impact of event on specific i

Question 39

What is crude dependence SE?

Answer 39

If we have cross-sectional correlation of error terms, for example due to multiple events occurring at the same time, SE become biased.

Question 40

What does CAR assume compared to BHAR?

Answer 40

CAR assumes investors rebalance holdings at each time step. To the contrary, BHAR is the returns until end of holding period without rebalancing.

Question 41

How are crude dependence SE computed?

Answer 41

We estimate var(AAR) directly from time series observations of AAR IN ESTIMATION PERIOD.

Question 42

Which dimension (T or N) must be large enough in order for there not to be an error in firm fixed effects?

Answer 42

T. Since if T is small we will not have enough variation within each firm.

Question 43

If we have a regression with firm fixed effects, how else can we estimate the regression such that we get the coefficients?

Answer 43

1) Include N dummies 2) Demean by entity: yit - y_bar = beta(xit - x_hat) + uit - u_hat

Question 44

In small sample if error term is not normally distributed, what is the problem and what can we do?

Answer 44

We cannot do valid hypothesis testing. What to do? Winsorize data or log transform IV.

Question 45

Why is a measurement error in y not a problem?

Answer 45

Measurement error will not be dependent on x. However, a measurement error in x causes violation of A4 --> ZCM assumption!!

Question 46

How do we detect non-normality?

Answer 46

We detect non-normality by Sign Test or Rank test.

Question 47

Define strong stationarity and weak stationarity.

Answer 47

Strong: Unconditional joint probability distribution does not change over time. Weak: constant mean and variance over time + covariance of lags depends on the lag --> cov(y_t; y_t - k) = (phi^k)*var(yt)

Question 48

What are the two tests to determine if series has unit root?

Answer 48

DF test and KPSS test. DF: H0: Series has a unit root KPSS: H0: Series has no unit root

Question 49

What are two types of non-stationarity?

Answer 49

1) Random walk process with drift 2) Deterministic Trend Process

Question 50

What does a high lambda in EMWA method of volatility estimation imply?

Answer 50

Higher lambda places more weight on past volatility. The lower the lambda the more the shocks can affect our estimate.

Question 51

If we regress two non-stationary variables, what is the impact?

Answer 51

Spurious relationship. We cannot extract any meaningful conclusion.