# Empirical Methods in Finance

**Instructions**

This assignment will require you to go through the exercises below using Stata. You can use Wordto type the answers to the questions, and Excel to produce the tables. Follow the format of thetables that is described at the end of each question.

**Becoming part of an index****
**When a firm enters into an index, such as the S&P500, more attention is paid to the firm financialsas more investors are interested in holding its shares. In this exercise, you will analyse the effect ofbecoming part of an index on the price of the firms’ shares. To do that, you must use the datasetnamed EnteringIndex.dtawhich consist of the following 4 variables:

• return: the daily return of a firm (in percentage points).

• marketreturn: the daily return of the market portfolio (in percentage points).

• eventtime: indicates the number of days from the inclusion of the firm in the index. Hence

the event day is t=0.

• new: takes value one if it is the first time the firm belongs to the index (new), and 0 if the

firm belonged to the index before (not new).

• eventnr: identities all the observations from the same event.

1. Test if the inclusion into the index has an effect on prices. For that you will have to:

(a) Compute the normal returns using the market model and an estimation window from

t = -50 to t = -1.

(b) Obtain the abnormal returns using an event window between t = 0 and t = 5.

(c) Provide the test to check if the abnormal returns are different from 0 at t = 0; 1; 2; 3; 4; 5.

Report the average abnormal return on column (1) of the first table for each time t with

their respective t-test below between brackets. Report 3 stars for statistical significance at

the 1% level, 2 stars for 5%, and 1 star for 10%.

2. Explain if your results are compatible (or not) with each of the different definitions of market

efficiency (strong, semi-strong, weak).

3. Prices of firms that were part of the index before might react differently than those of new

firms. Repeat the tests in 1.c for new and not new firms separately.

Report the average abnormal return on column (2) of the first table for new firms and on column (3) for not new firms for each time t with their respective t-test below between brackets.

Report 3 stars for statistical significance at the 1% level, 2 stars for 5%, and 1 star for 10%.

4. There is a concern that firms differ in their volatility and outliers are driving the results.

Propose a way to solve for this issue and execute it.

Report the average standardized abnormal return on column (4) of the first table for new firms

and on column (5) for not new firms for each time t with their respective t-test below between

brackets. Report 3 stars for statistical significance at the 1% level, 2 stars for 5%, and 1 star

for 10%.

5. Finally, we might also be concerned that abnormal returns are not normally distributed.

(a) Explain why this concern is more relevant for the case of not new firms.

(b) For the case of not new firms, compute two different tests that do not assume normality.

Report and interpret the average rank minus a half and the proportion of positive AR for

each time t with their respective t-test below between brackets in the last two columns of

the first table. Report 3 stars for statistical significance at the 1% level, 2 stars for 5%,

and 1 star for 10%.

Instead of using event study methods, you might want to use panel data. For the following

questions assume that in the dataset there is only one event for each rm. Moreover, for the

rest of the assignment use the whole sample (t = -50;:::;0;:::;50).

On top of the previously defined variables, you need to create a new variable called eventwindowthat takes value 1 if t ≥ 0 and 0 otherwise.

6. Your first approach is to consider the following model:

returni;t= αi + βmarketreturni;t+ γeventwindowt+ γnewnewi× eventwindowt+ “i;t

*(a) Estimate the model using the xedeect estimator. To make inference, rely on the*

standard errors that are robust to heteroscedasticity.

Report the estimates with their corresponding t-test (to test the null hypothesis that the

coefficients are 0) in the first column of table 2. Report 3 stars for statistical significance

at the 1% level, 2 stars for 5%, and 1 star for 10%.

(b) Interpret the estimates of β;γ; and γnew.

(c) Explain two differences between this model and using the event study methodology (question 1 of this assignment) in terms of the assumptions that we are making.

7. Next you decide to estimate the following model:

returni;t= αi + βmarketreturni;t+ βpostmarketreturni;t× eventwindowt

*+ γeventwindowt+ γnewnewi× eventwindowt+ “i;t*

*(a) Estimate the model using the fixed effect estimator. To make inference, rely on the standard errors that are robust to heteroscedasticity.*

Report the estimates with their corresponding t-test (to test the null hypothesis that the coefficients are 0) in the second column of table 2. Report 3 stars for statistical significance

at the 1% level, 2 stars for 5%, and 1 star for 10%.

(b) Interpret the estimate of βpost and γ. Compare this estimate of γ with the one in question

6. In this case, you can include more than 2 number after the decimal point to interpret

the estimate. Do not include these extra digits in the table.

8. Create a new variable intensity that takes a value of 0 if t <0 and a value of e-t if t ≥ 0.

Then, consider the following model:

returni;t= αi + βmarketreturni;t+ βpostmarketreturni;t× eventwindowt

*+ γintensityt+ γnewnewi× intensityt+ “i;t*

*(a) Estimate the model using the xedeect estimator. To make inference, rely on the*

standard errors that are robust to heteroscedasticity.

Report the estimates with their corresponding t-test (to test the null hypothesis that the

coefficients are 0) in the third column of table 2. Report 3 stars for statistical significance

at the 1% level, 2 stars for 5%, and 1 star for 10%.

(b) Interpret the estimate of γ. How does it compare with the one obtained in 7.? Why is it

different? or why is it equal?

Examples Tables 1 and 2:

(1) (2) (3) (4) (5) (6) (7)

Sample all new not new new not new not new not new

t = 0 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

t = 1 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

t = 2 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

t = 3 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

t = 4 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

t = 5 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87) (2.87) (2.87) (2.87) (2.87)

Table 1: Results questions 1 to 5

Variables (1) (2) (3)

marketreturn0.15*** 0.15*** 0.15***

(2.87) (2.87) (2.87)

eventwindow0.15*** 0.15***

(2.87) (2.87)

new ×eventwindow0.15*** 0.15***

(2.87) (2.87)

marketreturn× eventwindow0.15*** 0.15***

(2.87) (2.87)

intensity 0.15***

(2.87)

new × intensity 0.15***

(2.87)

Table 2: Results questions 5 to 7.** **

**Solution**** **

use “C:\Users\alok.singh\Desktop\EnteringIndex_v12.dta”, clear

mean return if eventtime<=-1, over( eventtime, nolabel)

mean return if eventtime<=5 &eventtime>=1, over( eventtime, nolabel)

byeventtime, sort : ttest return == 0 if eventtime<=5 &eventtime>=1

byeventtime, sort : ttest return == 0 if eventtime<=5 &eventtime>=1, level(99)

byeventtime, sort : ttest return == 0 if eventtime<=5 &eventtime>=1, level(98)

byeventtime, sort : ttest return if eventtime<=5 &eventtime>=1, by(new)

byeventtime, sort : ttest return if eventtime<=5 &eventtime>=1, by(new) level(99)

byeventtime, sort : ttest return if eventtime<=5 &eventtime>=1, by(new) level(90)

swilk return if new ==0, lnnormalnoties

swilk return if new ==1, lnnormalnoties

swilk return if new ==1

swilk return if new ==0

gen byte eventwindow = eventtime>= 0

kwallis return if new == 0, by(eventwindow)

generatenewxeventwindow = new * eventwindow

generatenewxeventwindow = new * eventwindow

xtseteventtime

xtreg return marketreturneventwindownewxeventwindow, fe

xtreg return marketreturneventwindownewxeventwindow, fe level(99)

xtreg return marketreturneventwindownewxeventwindow, fe level(90)

xtreg return marketreturnmarketreturnxeventwindoweventwindownewxeventwindow, fe level(99)

xtreg return marketreturnmarketreturnxeventwindoweventwindownewxeventwindow, fe

xtreg return marketreturnmarketreturnxeventwindoweventwindownewxeventwindow, fe level(90)

generate intensity = exp( eventtime)

generatenewxintensity = new * intensity

xtreg return marketreturnmarketreturnxeventwindow intensity newxintensity, fe level(99)

xtreg return marketreturnmarketreturnxeventwindow intensity newxintensity, fe level(90)

xtreg return marketreturnmarketreturnxeventwindow intensity newxintensity, fe