EMF Part 2 Flashcards
Exam (47 cards)
What type of market efficiency can we test and what information is contained in that type
Semi strong mkt efficiency. Definition: prices reflect all public information
What does efficiency in face of EMH mean
Efficiency refers to the direction and magnitude of price fluctuations
What is strong EMH
prices reflect no only public but all relevant information
What are the three steps of Event study design?
1) Identify event and timing
2) Specify benchmark model for normal returns
3) Calculate abnormal returns : AR = R - NR
Name three types of benchmark models
Mean adjusted model, Market adjusted model (assumes beta of firm is 1), CAPM (NR = rf +betaMRP)
How do we compute AAR, CAR, CAAR in AR matrix where rows are firm, and columns are time?
1) computing average value of each column gives us AAR. Summing a row gives CAR. CAAR = 1/nSum(CAR) and CAAR=sum(AAR)
Event clustering can induce cross-sectional correlation. How is cross sectional correlation defined, and what is the impact on statistical inference? how do we solve it?
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
Solution: Clustered SE or alternative benchmark model that include common determinants such as FF3 or Cahart 4
Non Parametric tests are used when sample is too small and we cannot envoke CLT in the case of NON-NORMALITY. What are they ?
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.
How do we deal with cross-sectional heteroskedasticity?
1) Adjust SE of AAR and CAAR
2) Standardize AR by firm
How do we estimate NR if time horizon is long? What is a benefit of this approach?
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!!!
Describe the Pooled OLS approach in Panel Data
Model pools observations from different time periods ignoring firms. This effectively combines panel data into one cross-section. Mitigates event clustering.
What do fixed firm and time effects do? What are drawbacks of fixed effects?
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.
Drawbacks:
FFE: Cannot identify effects of variables that are constant over time
TFE: Cannot identify effects of var. constant across firms.
How can we mitigate that SE are correlated across time or firms?
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.
if we cluster by firm, then we allow for time series covariation but
cov(uit ; ujt)=0
If we cluster by both then we fix only for cov(uit ; ujs) = 0
Do fixed effects take away the need for clustering of SE?
NO! Fixed effects do not fix the issue. Autocorrelation among error terms still remains.
FMB. Describe the process
1) Run a time series regression on each stock and obtain factor loadings (betas).
2) For each time periods do a cross-sectional regression with factor loading betas as predictors. The resulting parameter estimates - gammas are the risk premia.
What are benefits of FMB?
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
What are the five OLS assumptions, with mathematical notation?
1) Linearity : yt = at + bxt + et
2) Random Sampling:
cov(u_t ; u_t+j) = 0
3) Sample variaiton: 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)
What is the impact if x is not exogenous?
This implies that E[u_t|x]!=0
This means that x and y are jointly determined at the same time. Cant make causal inference.
A potential cause of endogeneity is measurement error in x_t
If we observe non-stationarity, which assumption is violated?
Stationarity means: Unconditional joint probability distribution does change over time. This implies constant unconditional mean and variance. Hence Homoskedasticity is violated.
When we have non-normality in small samples which test can we use to check for non-normality?
Bera-Jarque test. It tests whether skewness (b1) and kurtosis (b2) are jointly zero.
What solutions exist for dealing with non-normality or error term?
1) Log transformation of of IV
2) Winsorize data
Which assumption is violated if we have autocorrelation. How do we test for autocorr, when do we reject h0?
Autocorr. violates A2. Breusch-Godfrey test finds up to rth order autocorr.
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
What does positive autocorr do? How do we fix autocorr. What is impact of autocorr on estimates?
1) SE are too low –> t-test is biased upward –> Reject H0 too much.
2) Newey-West (HAC) –> Adds less weight to to higher autocovariance
3) Estimates are no longer EFFICIENT
We can also add lagged effects to deal with autocovariance. How?
What is a potential issue with lags?
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.
