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MSFI 435 – Empirical Finance
创建日期：2024-05-14 14:50:59
所属分类：金融Finance
标签： MSFI 435
Empirical Finance

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MSFI 435 – Empirical Finance

Part I - Concepts
1. Let’s reexamine the concepts of type I and type II error in a hypothesis testing
framework.
Recall from our discussion in section 6.5 that a type I error occurs when the null hypothesis
is incorrectly rejected; that is, the null is correct but is rejected in the test.
In the context of a hypothesis testing for a regression coefficient
H0: βk = βk,0
Ha: βk ≠ βk,0
we’ve seen (see section 6.4) that the t-statistic for such test,

follows a standard normal distribution, t~N(0,1). Notice that the t-statistic depends on the
null hypothesis, so we can say if the null is correct, t will follow a standard normal. If we
set a significance level α=0.05, we establish a rejection region as shown in the shaded area
of Figure 1. This means there is a 5% chance of the t-statistic falling in the rejection region,
or a 5% chance of rejecting the null when it is in fact true. Thus, the probability of a type I
error is the significance level that one establishes for the hypothesis testing.

Figure 1. Rejection region, α=0.05

)βˆ(SE
ββˆ
t
k
,kk 0
FNCE 435 Fall 2022 Assignment 8
Page 2

We drew parallels between the justice system and hypothesis test. The system works as a
test of hypothesis in which the null is that the defendant is not guilty, or:
H0: Defendant not guilty
Ha: Defendant is guilty
a) Now, (finally!) a question for you. If one sets a significance level for testing the
defendant hypothesis equal to α=0.1, and the system handles 150 innocent defendants per
year, how many of them will be deemed guilty on average per year?
b) The American judicial system is comprised of two different types of cases: civil and
criminal. Criminal cases are harsher and can take you to jail; civil cases, on the other hand,
usually bring penalties in terms of monetary compensation. According to the Findlaw
website, “criminal offenses and civil offenses are generally different in terms of their
punishment. Criminal cases will have jail time as a potential punishment, whereas civil
cases generally only result in monetary damages or orders to do or not do something. Note
that a criminal case may involve both jail time and monetary punishments in the form of
fines.”
Still according to Findlaw website, “The standard of proof is also very different in a
criminal case versus a civil case. Crimes must generally be proved "beyond a reasonable
doubt", whereas civil cases are proved by lower standards of proof such as "the
preponderance of the evidence" (which essentially means that it was more likely than not
that something occurred in a certain way). The difference in standards exists because civil
liability is considered less blameworthy and because the punishments are less severe.”
What can you say regarding the probability of type I error that the judicial system needs to
impose on criminal vs. civil offenses? Which type of case should have a lower significance
level? Please explain.
c) We now turn to the type II error. A type II error occurs when the null hypothesis is false
but we fail to reject it.

Figure 2. Acceptance region, α=0.05
To compute the probability of a type II error, we need to know the alternative hypothesis
that holds when the null hypothesis is false. Take our previous example that under the null
the t-statistic for a test on the coefficient of a regression follows a standard normal. We will
fail to reject the null if the t-statistic falls in the shaded region in Figure 2.
FNCE 435 Fall 2022 Assignment 8
Page 3

Now assume we know the null is false, and that in fact the t-statistic follows a normal
distribution with µ=1 and σ=1, or t~N(1,1). Then we can compute the probability of a type
II error by getting Pr(–1.96
Figure 3. Computing the probability of a type II error
Compute the probability in the shaded area of Figure 3. (Recall you can use the
NORM.DIST function in Excel.)
d) There is a trade-off between the probability of getting a type I error and the probability
of getting a type II error. Reducing the probability of getting a type I error means reducing
the significance level of the test, but that comes at the expense of increasing the probability
of getting a type II error.
Let’s see that in our example in part c). Suppose you reduce your significance level from
α=0.05 to α=0.01, so that the new cutoff values for the rejection region in Figure 2 (and for
the acceptance region in Figure 3) become –2.57 and +2.57. Recompute the probability of
a type II error in part c) and verify that it has increased from the number you got in part c).
2) We will examine a phenomenon that came to be known by academics and investment
advisors as the post–earnings announcement drift (PEAD). The PEAD—as defined in
Wikipedia—is the “tendency for a stock’s cumulative abnormal returns to drift in the
direction of an earnings surprise for several weeks (even several months) following an
earnings announcement.”
We all know and tested how investors strongly react to the news in earnings announcement,
with event reactions (let’s say, cumulative abnormal returns over the announcement day
and the day after the announcement) being positive when the earnings carry good news and
negative when the earnings carry bad news.
The PEAD implies that, despite this strong event reaction, investors do not react enough!
Consequently, abnormal returns still correlate with the type of news in the earnings
announcement long after the earnings announcement date. For example, if earnings carry
good news, then abnormal returns will keep on being positive on average for weeks after
the earnings announcement. Therefore, PEAD exists when the surprise at the earnings
announcement and the post-earnings abnormal returns are positively correlated.
In order to test for the possible manifestation of PEAD, a sample of quarterly earnings
announcements is collected, and the following regression model is run:
FNCE 435 Fall 2022 Assignment 8
Page 4


Here is a brief description of the variables measured for each earnings announcement:
 CAR_2_60: the cumulative daily abnormal return from day +2 to day +60, where
day=0 is the earnings announcement date (that is, from 2 trading days after the
announcement to 60 trading days after the announcement). Daily abnormal return
is defined as the firm’s stock return minus the market return in that day.
 SURPRISE: the gap between the actual earnings and the analyst’s expectation
about the earnings right before the announcement date.
 MOM: the average daily return of the firm announcing earnings, where the average
is computed over the 60 calendar days preceding the earnings announcement (that
is, from calendar day –60 to calendar day –1, where day 0 is the earnings
announcement date).
 LASSETS: the logarithm of total assets, where total assets is measured in the year
prior to the earnings announcement date.
 BEME: the ratio of book value of equity to market value of equity (variable ME),
both measured in the year prior to the earnings announcement date. Both BE and
ME appear in the accounting dataset.
The sample used in this study appears in Figure 4.

Figure 4: Sample used in the study

Take for example, the first observation of the sample. It is for IBM (PERMNO=12490)
and for the earnings released in April 16th, 2003. For this observation, the post-earnings
abnormal returns for IBM was 3.66% (CAR_2_60=3.66); the earnings surprise was 10
cents per share (SURPRISE=0.10); IBM’s performance prior to the earnings
announcement—measured from the 60th day prior to April 16th, 2003 through the day
before April 16th, 2003—was an average daily return of 0.023% (MOM=0.023); IBM’s
total assets, measured in 2002, was $113 billion (LASSETS=log(146,000,000,000)=25.7);
and book-to-market ratio—also measured in 2002—was 0.8 (BEME=0.8).

iiiiii BEMELASSETSMOMSURPRISECAR   4321060_2_
FNCE 435 Fall 2022 Assignment 8
Page 5

The results of the regression testing for PEAD appear in Figure 5. Recall that the dependent
variable is CAR_2_60.



Figure 5: OLS regression results

For each coefficient, we show the coefficient’s estimate, its standard error, the t-statistic,
and the p-value. (Some of these data can be redundant; for example, remember that the p-
value is obtained from the value of the t-stat.)
Based on these results please answer the following questions.
a) Is PEAD happening in the sample examined in the study? Formulate your hypothesis
clearly. Then, assess the effect of earnings surprise on the firm performance in the post-
earnings period.
b) Interpret the coefficient on LASSETS. Does total assets matter for the post-earnings
returns? How so?
c) Your colleague argues that it is irrelevant to control for LASSETS in the regression
model—that is, that you should remove this variable from the model—since you are
interested mostly on the effect of SURPRISE. Please explain some conditions under
which removing LASSETS from the model makes the inferences on SURPRISE
problematic.
d) Suppose you observe a specific earnings announcement, with the following values of
the explanatory variables: SURPRISE is 4 cents per share, MOM is 0.011%, total assets
measured the year before earnings is $46 billion, and book-to-market measure is 0.50.
What is the model’s predicted value for the post-earnings abnormal returns?
e) Construct a 95% confidence interval for the coefficient on MOM. Then use the
confidence interval to conclude whether past performance (MOM) is related to post-
earnings abnormal returns.
f) Suppose you want to test the hypothesis that the PEAD phenomenon is exacerbated for
the sample of firm in the tech industry. Explain how you would proceed (for example,
somehow expanding the regression model).
You can assume you have data that allows you to create a dummy variable, TECH, that
is equal to one if the firm announcing earnings belongs to the tech industry.
g) After running the regression model whose results appear in Figure 5, you were shown
the following pattern the errors in the regression.
FNCE 435 Fall 2022 Assignment 8
Page 6


Figure 6: Errors from regression model explaining firm performance

What does that illustrate as a problem with respect to the assumptions required to run a
regression model? If this is indeed a problem, what procedure can you use to remedy the
problem?
Part II – Exploring Executive Compensation (Continued)
We will continue the exploration of the topic of executive compensation carried out in
module 9.
Your starting point is a modified version of the regression explaining cashpay (which
equals salary plus bonus). The model is

which resembles a mix of the regressions shown in columns 3 and 4 of Figure 9-4, but with
the caveat that we are not controlling for the LMB here. This is the starting point for many
of the models used in this assignment.
Also, we are using the same time period as in module 9. So, you should download the code
used in module 9, work on the necessary adjustments of library locations, etc, and then run
a regression as shown above. (To make sure your code is running properly, you may
compare the results of the regressions in that code with the ones shown in Figure 9-4. You
do not need to show this comparison, though, in your write-up. Also be aware of very tiny
differences between your new results and the ones printed in the lecture notes. The results
in the lecture notes were generated a few years ago, and there might have been updates in
the WRDS database since then.)
Please run the regression model above: generate and show the results of the regression in
a formatted output similar to the ones we have used in past assignments (that is, an output
showing the estimated coefficients, their t-statistics, then then number of observations in
the regression, and the adjusted-R2).
Note: This is one of those rare assignments when you do not need to show summary
statistics. This is because the assignment is deemed a continuation of module 9.
-15
-10
-5
0
5
10
15
20
25
30
-6 -4 -2 0 2 4 6
Residual
Predicted
CAR_2_60
iiiiiii CEOAGELATLSALEROAAVGRETCASHPAY   543210
FNCE 435 Fall 2022 Assignment 8
Page 7

Let’s first examine the residuals:.
For the model shown above, generate the residuals. Then test whether the residuals are
different from zero. That is, treat the residual as a random variable and test whether the
expected value of the residuals is equal to zero (your null). For this you can run a PROC
MEANS or PROC TTEST on the residual variable.
Let’s now examine the robustness of our results to the concerns regarding
heteroscedasticity.
For the model shown above, generate a plot of residuals vs. predicted value of CASHPAY.
Does heteroscedasticity stand out visually from the graph?
Then, run the regression with the White test for heteroscedasticity. Does the test reject the
null of homoscedasticity?
If so, rerun the regression asking for t-statistics (and standard errors) that are robust to
heteroscedasticity. Create and show a new output for the regression results, and comment
on whether the inferences are robust to this change. That is, for each hypothesis testing on
a regression coefficient, does the inference you had before change after the correction for
heteroscedasticity?)
We then examine the robustness of our results to the concerns regarding correlation of
residuals.
First, make sure the data is sorted by the company identifier, that is, first run the code
proc sort data=d;
by permno;
run;
then run the regression asking for the Durbin-Watson test for serial correlation and
comment whether serial correlation seems to be a problem for this regression specification.
Now test for the Durbin-Watson again, but, before running the regression, sort the data by
BONUS, that is, run the statement:
proc sort data=d;
by bonus;
run;
Finally, test for the Durbin-Watson again after sorting the data by the STOCKOPTION
variable, or:
proc sort data=d;
by stockoption;
run;
Comment on the results you get for the Durbin-Watson test. (Hint: this is a test about
correlation of consecutive residuals, so it depends on sorting the data…)
Let’s now explore collinearity.
You will add to your dataset another measure of firm size, defined as the log of market
value of equity as of December of two years ago. (Since past performance is measured over
FNCE 435 Fall 2022 Assignment 8
Page 8

the previous years, if we collected firm size as of the end of the previous year we would by
construction create a correlation between firm size and past performance.) Since we have
compensation data for year 2000, you need to collect market value of equity as of
December 1998. Market value of equity is defined as the price of each stock (variable PRC
in the MSF dataset on CRSP) times the number of shares outstanding (variable SHROUT
in the dataset MSF on CRSP). Also, due to the fact that sometimes CRSP records stock
price as a negative number, you need to use the absolute value of the stock price measure.
Thus, if PRC and SHROUT are collected, you define LMVE as
log(abs(prc)*shrout)
where ABS(a) is a SAS function that returns the absolute value of a.
Then run the 4 regressions shown in Figure 7 below. That is, run regressions separately
with LSALE, then LAT, then LMVE; then add them all in the same specification.

Figure 7. Regression results

Generate and show Figure 7 with the regression results. Interpret the effect of LMVE on
cashpay.
Do you see any issues with the inferences, regarding the proxies for firm size (LSALE,
LAT, and LMVE)? Can you get a hint of what is going on? You can use a PROC CORR
to help you in your analysis.
Our last task is to examine predictions.
Using the model for cashpay as

first compute the predicted cashpay for AT&T (PERMNO=10401) in year 2000. That is,
write down the 95% confidence interval for the cashpay of a CEO of a specific firm exactly
like AT&T.
Second, compute the 95% confidence interval for the mean cashpay across all firms that
look like AT&T.
Discuss the two confidence intervals, and why they are different.
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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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FN1024 MATH0094 MANG 6554 ECOS3003 ELEC6252 C2511C PHY328 EC1060 ECON32202 COMP4002-E1 MATH3063 EFIMM0124 QBUS2310 ECON4411 FUNDAMENTALS ACCT20001 18YX RPM COMP 2711 QBUS6600 BUSS5221 ST3189 FIT1047 MAT344 EGB375 MATH60013 MATH96011 COMP3557 MAST20029 ECM159 EAE1011 ENSCEN 105 SECTION A STA 141C SOSE 2022 PAM006 COMP0048 M40007 ISOM2500 CMPE 142 A06472 MCC150 ACST 8083 GEOG6087 ECON920 FINM7008 ENVENG 4110 COMPSCI 361 ENGRCEE 21 PHYS 1112 ACF2100 ECMM108 COMPS267F MAT00050M MAST30025 CSIT970 MSCI 224 INT202 PUBL0054 MSDM5004 BMAN 21020 BMAN21020 MGMT1002 MATH11150 LAWS7023 ACTL30002 CIVL3340 MATH1002 ECON 8069 COMPSCI 351 IBUS7302 STAT4528 CHEM1101 STAT3925 BUSN 7008 Comp 3120 ECOS2040 SWEN90010 ENGN6528 ECM158 ECON20022 COMP6452 Calculation CITS1401 S1889112 BUS 351 ACTL30008 FIT2091 ECON6002 IBUS6020 PHI 001 ECON30290 MATH7501 ECON10004 MFIN7017 ISYS90043 LAWS7012 ECON30025 COMP30023 COMM1190 ECOM20001 GSBS6009 STAT 337 EMET8002 ECOM90001 ECOM30001 FINC 2012 BUSINESS ENGCV512 ECO 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