L3 Flashcards
Abnormal Return =
Realized Return - Expected Return
3 ways of calculating expected returns
1 - Mean adjusted returns
2 - Market adjusted returns
3 - Expected returns according to market models
Good practice in event studies windows
Leave space to avoid contamination between estimation window and event window
Longer estimation windows lead to
higher precision
but also
higher risk of structural break
To build event studies we need:
- unexpected shocks
- sudden release of information
- high frequency data
To understand stat significance of CAR we need:
Avg CAR(t1,t2) and Var ( Avg CAR(t1,t2) )
Estimate Var ( Avg CAR(t1,t2) )
1 - Sample variance for each stock in estimation window
2 - Take the average
3 - Compute the CAR variance = (t2 - t1+ 1) * Step 2
CAR follows a normal distribution when
Large samples
t-stat for H0: Avg CAR(t1, t2) = 0
Avg CAR (t1, t2) / SQRT ( Var (avg CAR (t1,t2)))
What do Shapiro-Wilk and Breusch-Pagan have in common
We are looking for large p-values
We want to not reject the H0
To trust t-tests and f-tests we need
MLR 1-6
In large sample, OLS estimators are
asymptotically normal
Even if OLS estimators are asymptotically normal, we still need:
erros to be iid(0, sigma-square), independent and identically distributed
in iid, what is i
independent, means that values are uncorrelated
in iid what is id
identically distributed -> values have same variance
Problems with u independence in iid dist
time series data -> serial correlation
cross-sectional data -> group structures
Heteroskedacity in large samples
Does not disappear
Solution to heteroskedacity
RSE
RSE are
usually > se(^B), so t-stats are usually lower than in reality (estimate that we are closer to the true parameter value than we actually are)
Problem with RSE
Not very accurate for small samples
What is panel data
datasets with time series and cross-sectional data
panel data standard model
yit = B0 + B1 xit + u it
Panel data and estimation with fixed effects allows to:
control for time invariant unnobserved heterogeneity
What does demeaning do?
Consider FE model:
yit = B0 + B1 xit + ai + eit
removes fixed effect ai
yit = B0 + B1 xit + ai + eit
what is ai?
variables constant over time that affect y but are different accross i’s
yit = B0 + B1 xit + ai + eit
what is eit?
unnobserved factors that vary accross i and t
Upside and downside of fixed effects estimator
Upside -> controls for all time invariant differences within each i
Downside -> cant be used to investigate time-invariant causes of y
Dummy variable regression in FE model
yit = B0 + B1 xit + Sum ( ai fi ) + eit
Intuitive interpretation allowing for unit specific intercepts
We can also include time fixed effect in FE model
yit = B0 + B1 xit + ht + eit
ht absorbs all shock in valuation common to all i’s at a given time
DiD assumption
Parallel trends
t-stat > 3.2 corresponds to:
F-stat > 10
