deck_17555155

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 and when are they used?

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

Question 12

What is a benefit of using the FF3-factor model?

Answer 12

Benefit: leads to lower cross-sectional corr of AR!!!

Question 13

Describe the Pooled OLS approach in Panel Data.

Answer 13

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

Question 14

What do fixed firm and time effects do?

Answer 14

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 15

What are drawbacks of fixed effects?

Answer 15

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

Question 16

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

Answer 16

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 17

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

Answer 17

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

Question 18

Describe the FMB process.

Answer 18

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 19

What are benefits of FMB?

Answer 19

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 20

What are the five OLS assumptions, with mathematical notation?

Answer 20

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 21

What is the impact if x is not exogenous?

Answer 21

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 22

If we have autocorrelation, which assumption is violated?

Answer 22

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

Question 23

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

Answer 23

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

Question 24

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

Answer 24

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

Question 25

What solutions exist for dealing with non-normality?

Answer 25

1) Log transformation of IV 2) Winsorize data

Question 26

Which assumption is violated if we have autocorrelation?

Answer 26

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

Question 27

How do we test for autocorr, when do we reject H0?

Answer 27

H0: no autocorr. 1) Estimate usual OLS and get all ut. 2) Regress u_t on all IV's plus all errors up to lagged u_t - r, and obtain R^2. if (T-r)R^2 > critical --> reject H0

Question 28

What does positive autocorr do?

Answer 28

1) SE are too low --> t-test is biased upward --> Reject H0 too much.

Question 29

How do we fix autocorr?

Answer 29

Newey-West (HAC) --> Adds less weight to higher autocovariance

Question 30

What is the impact of autocorr on estimates?

Answer 30

Estimates are no longer EFFICIENT

Question 31

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

Answer 31

y_t = a + b1x1,t +...+b_k*x_k,t + g1x1,t-1 +....+ g_k * x_k, t-1

Question 32

What is a potential issue with lags?

Answer 32

Lagged effects can introduce multicollinearity.

Question 33

Why add lagged effects?

Answer 33

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

Question 34

Show the impact of measuring IV wrong.

Answer 34

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

Question 35

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

Answer 35

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

Question 36

What is a parameter stability test?

Answer 36

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 37

Can we have autocorrelation and stationarity at the same time?

Answer 37

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 38

What is the condition for stationarity?

Answer 38

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

Question 39

What is autocorrelation in a simple AR model?

Answer 39

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

Question 40

What is an alternative Stationarity condition?

Answer 40

1) 1-phi*z - .... - phi_p * z^p = 0 where -1 > z > 1 --> (|z| >0)

Question 41

Give two information criterions that help decide how many lags to include.

Answer 41

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

Question 42

What are the drawbacks of AIC and SBIC?

Answer 42

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

Question 43

What is impulse response function?

Answer 43

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.