Page 1

Case Western Reserve University
Weatherhead School of Management

FNCE 435 – Empirical Finance
Fall 2021

Individual Assignment (Section II)

(Only students from Section II – Wednesdays 9-11h45AM—should be working on this version of
the assignment.)



(Important: This assignment is to be implemented on an individual basis. No sharing of material—
including data, results, inferences and write-ups—may take place among members of a group nor
across different groups.)
(About the significance level: For all the tests of significance in this assignment, please assume a
5% significance level.)
Examining Stock Splits
A stock split occurs when the company increases the number of shares that are outstanding
by issuing more shares to current shareholders. For example, say a company has 1,000
shares outstanding. A decision to split the stock 2-for-1 means 2 shares are created out of
each share. Another way to say this is that the split carries a split factor of 1, meaning one
extra share for each existing share. After the split, there will be 2,000 shares outstanding
and each shareholder will hold post-split twice as many shares as held before the split.
Of course, a stock split per se should not change the value of the company. In fact the share
price is adjusted such that the value of the company after the split is the same as before the
split. Say in our example above that each share was priced at $10 before the split. Since
there were 1,000,000 shares outstanding, the market value of equity for the company was
1,000,000*$10=$10,000,000. Since each share is split into two shares, the price is split in
half, from $10 to $5, so that the overall holdings of shareholder remains the same. In
particular, the market value of equity after the split is 2,000,000*$5=$10,000,000.
The dataset “d_split.sas7bdat”, available on Canvas, contains data on everyt first
announcement of stock split per company between 2000 and 2016. (If a company splits its
stock more than once in the period, only the first split appears in the sample.)
Each row of the dataset identifies a different stock split announcement. The first few
variables of this dataset are:
 PERMNO: the CRSP identifier for the company announcing the split;
 COMNAM: the name of the company announcing the split;
 DCLRDT: the date the stock split was announced;
 FACPR: the split factor—defined as the number of extra shares a shareholder gets
for each owned share. For example, FACPR=1 implies a 2-for-1 stock split; and
 PRCAFT: the predicted price of each share after the split takes place, defined as the
share price before the announcement divided by (1+FACPR).
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 2

Figure 1 shows some observations in the sample of announcements of stock splits. The first
row refers to the announcement on January 3rd, 2000 by Asyst Technologies that it would
split its stock with a split factor (FACPR) of 1, implying a 2-for-1 split ratio. Given the
price of each share the day before the announcement, the predicted effect of the split, if the
split were to occur immediately with the announcement, is that the price would be $32.78
per share (that is, the price of each share the day right before the announcement was
2*$32.78=$65.56).

Figure 1: A few data points on the stock split announcement data
There are three questions that you will examine with respect to stock splits:
I. Do stock splits have valuation implications? You will examine how markets react
to the company’s decision to split the stock.
II. What are the determinants of market reactions to stock split announcements? In
part I, one examines if markets react to the announcements, while here you examine
in a regression framework what are the determinants of the market reactions to such
announcements.
III. What characteristics seem to drive the decision to split a stock?
Part I: Valuation Implications
We start our investigation by answering question I above:
Do stock splits have valuation implications? You will examine how markets react
to the company’s decision to split the stock.
At face value, stock splits should carry no meaning, since nothing changes fundamentally
about the company. Having 1,000.000 shares priced at $10 or 2,000,000 shares priced at
$5 does not change the value of the company, nor its capacity to run its business. So, the
null hypothesis is that markets should not react to the announcement that a company will
split its stock.
On the other hand, there are many reasons to believe a stock split may carry real outcomes.
For example, splitting a stock may increase its trading liquidity. In the example above of a
2-for-1 split on a stock initially priced at $10, if there a minimum lot of shares to be traded,
for example, 200 shares, the minimum amount one would need to invest to buy these shares
would be 200*$10=$2,000 before the split but only 200*$5=$1,000 after the split. This
can improve the investors’ ability to trade, and thus the trading liquidity.1 There might be
a signaling effect as well—the idea that the management of a company, by initiating a stock
split, is signaling its confidence in the future of the company. Given that some stock

1 A notable example of this story is Berkshire Hathaway, whose Class A shares have never had a stock split.
The price of each share as of June 2080 was $282,040.00. In this case, as expressed by Warren Buffett, the
absence of splits has the intention to reduce trading volume.
PERMNO COMNAM DLCRDT FACPR PRCAFT
1 79568 ASYST TECHNOLOGIES INC 1/3/2000 1 32.78
2 79879 J D S UNIPHASE CORP 1/3/2000 1 80.66
3 86211 MICROSTRATEGY INC 1/4/2000 1 104.25
… … … … … …
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 3

exchanges require listed stocks to maintain a trading price above some threshold ($1 for
NYSE), reducing the share price brings the risk that further reductions take the price below
that threshold, thus forcing the stock to be delisted. Both stories point to stock splits as
carrying good news about the company.
In this part of the project, you will examine how markets react to announcements of stock
splits. You will address this question through event studies—employing the technique
covered in module 4. For each announcement of stock split, you examine the pattern of
abnormal and cumulative abnormal returns over the 11-day window (relative days –5
through +5) around the announcement day (variable DCLRDT).
For the definition of abnormal return, use the CAPM-adjusted return model—that is, define
abnormal return using the following expression (from section 12.3):
)(Re mtiiitit RRturnAbnormal  
where Rit is the firm’s stock return at time t (the variable RET in the CRSP dataset DSF,
located in “/wrds/crsp/sasdata/a_stock”), Rmt is the market return at time t (the variable
VWRETD in the CRSP dataset DSIX, located in “/wrds/crsp/sasdata/a_indexes”), and αi
and βi are parameters from the CAPM model. The parameters αi and βi are already
computed for you and are available in the dataset “d_split.sas7bdat”. Important: notice that
the abnormal return here is different from the abnormal return used in module 4. In module
4 we employed the market-adjusted return model while here we use the contant-mean
return model.
There are two event studies to be analyzed. In the first event study, you analyze the full
sample of stock split announcements. Prepare a table showing average abnormal returns,
t-stats and p-value for 11-day window around announcements. Also create a graph showing
the pattern of average cumulative abnormal returns over the same 11-day window. Then
discuss how the markets interpret the announcements of stock splits. Anchor your
inferences on formal hypotheses testing. Finally, examine whether markets respond
efficiently to news in such announcements. (For this you can assume that some
announcements happen after the close of the market—that is, market reactions to such
announcements could happen up to one day after the event date.)
One concern of our study is that some announcements of stock splits come with further
news of increase in dividends. Therefore, the pattern of market reactions to stock splits
may be confounded with the effect of dividend news. We will examine this idea. Your
dataset on stock splits shows two other variables that record whether the announcement of
stock split also comes with announcements of dividend increase (variable DIVUP=1) or
with announcements of dividend decrease (variable DIVDOWN=1). For example, Figure
2 shows that Alcoa announced on Jan 10, 2000 that it was splitting its stock and (because
DIVUP=1) also increasing its dividend payments.

Figure 2: More data points on the stock split announcement data
PERMNO COMNAM DLCRDT FACPR PRCAFT DIVUP DIVDOWN
… … … … … … … …
9 82810 GLOBIX CORP 10-Jan-00 1 34.06 0 0
10 24643 ALCOA INC 10-Jan-00 1 42.31 1 0
… … … … … … … …
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 4

The idea is to isolate the reactions to stock splits announcements from any effects of news
of dividend changes. For this, the second event study focus on the announcements of stock
splits that did not come with announcements of dividend increases nor with announcements
of dividend decrease. That is, the sample of your second event study includes the
observations in the splits dataset that satisfy the condition that DIVUP=0 and
DIVDOWN=0. For this new sample, repeat the event study analysis. Use the same methods
and types of outputs prescribed for the first event study. Then conclude by extracting
inferences from this second event study.
Part II: More on Valuation Implications
Next step is to understand the market reactions to announcements of stock splits. This refers
to the question II above:
What are the determinants of market reactions to stock split announcements? In
part I, one examines if markets react to the announcements, while here you examine
in a regression framework what are the determinants of the market reactions to
such announcements.
We want to be able to quantify the effect of the announcement on market reactions: the
stronger the signal in an announcement, the more pronounced should be the market
reaction.
How to define the strength of a split? If splits are considered good news because splitting
the shares results in a lower share price, thus improving liquidity, then bigger reductions
in share price would lead to bigger increase in liquidity. The split factor FACPR could be
such a measure of strength. A FACPR=1 implies a 2-for-1 split with post-split price
equivalent to ½ of the initial price, a FACPR=2 implies A 3-for-1 and a post-split price
equal to 1/3 of the initial price, and so on. Thus the higher the FACPR, the stronger the
signal.
But FACPR is incomplete measure of the strength of the split. What really matters for the
liquidity of a stock is the share price that results from the stock split (call it PRCAFT), and
that variable depends on both the split factor and the share price before the announcement.
For example, take two stocks, A and B, such that FACPR is 1 for stock A and 2 for stock
B. Each share of A was priced at $100 before the announcement of its split, while each
share of B was priced at $200 because its announcement. Then,
PRCAFTA=$100/(1+1)=$50 and PRCAFTB=$200/(2+1)=$66.67. In this example, the split
factor of B was larger than that of A but A’s final share price was smaller than that of B.
Likewise, a lower final share price would be a better indication of manager’s confidence
in the company’s future prospects. In sum, markets would be more responsive to the
announcement of stock split by company A because of a lower share price resulting from
its split.
We thus want to examine the relation between the strength of a stock split announcement,
measured by its PRCAFT, and market reactions around the announcement. The event study
does not address this question because it pools together all announcements, disregarding
the information about the announcements’ characteristics (in particular, information about
the strength of the split).
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 5

For that, one needs a regression framework that relates the market reaction with the
information in the stock split announcement. The left-hand side variable (named CAR) is
defined as the cumulative abnormal return from relative day 0 (the announcement day) to
relative day +1 (the day after the announcement). This variable can be obtained from the
data used to analyze the event study in part I.
The main explanatory variable in the regression is LPRCAFT, defined as the natural
logarithm of PRCAFT. The variable PRCAFT is already collected for you and is available
in the stock split dataset; all that you need to do is to define LPRCAFT=log(PRCAFT).
Notice, thus, that our objective is to examine how rates of change in PRCAFT affect the
response to the announcement of a stock split. The idea is thus to run a regression as
iii LPRCAFTAR   10C
Please collect the results of the regression, then analyze whether LPRCAFT and CAR are
related, and, if so, what is the magnitude of the effect of LPRCAFT on the market reaction
to the company’s stock price.
(You can start part II even without concluding part I. The dataset “d_split_car.sas7bdat”,
available on Canvas, contains a measure of the CAR variable generated by the instructor.
Each row of this dataset has the variables PERMNO, DCLRDT and CAR, so that you can
combine this dataset with the stock splits dataset in order to obtain the CAR measure for
each stock split announcement.
The CAR measure in “d_split_car.sas7bdat” is not exactly the measure you may obtain
from your event study, and thus should not be used to evaluate whether you event study is
correct. However, the CAR measure in this dataset is close enough to the true measure and
can be employed as a starting point for your analysis in part II.
If you do not conclude part I, you can still rely on the supplied measure of CAR to finish
part II; otherwise, you should in your final version of part II employ the CAR measure
extracted from your own event study.)
However, the problem with inferences from the simple regression model above is that we
may need to control for other potential determinants of market reactions. Since the model
aims at explaining returns, we may need to control for other determinants of returns, such
as the CAPM’s beta and company size. One can quickly build up stories that leaving these
out of the model may bring the wrath of the omitted variable bias. For example, perhaps
LPRCAFT is also related to company size—say, because smaller companies can “restart”
trading from a lower value of share price. If smaller companies have lower returns, then
this size effect might be biasing the results of a regression model that omits size from the
set of explanatory variables.
To avoid the perils of the omitted variable bias, the idea is to run a multiple regression
model, as in
iiiiiii DIVUPPASTPERFBETASIZELPRCAFTAR   543210C
where the other control variables in the model are described here:
 SIZE: the natural logarithm of total assets of the company splitting its stock,
measured in the year before the year of the announcement—that is, as of
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 6

YEAR(DCLRDT) – 1. Total assets is the variable AT in Compustat dataset
FUNDA, located at “/wrds/comp/sasdata/nam”). We use the log formulation so
that our analysis refers to rates of change in total assets being associated with
market reactions
 BETA: the beta of the company’s stock. The information is available on the stock
splits dataset.
 PASTPERF: Firm’s recent performance may also drive reactions (remember the
momentum effect)? The firm’s past performance is defined as the average daily
stock return during the period DCLRDT – 180 and DCLRDT – 10. Stock return is
the variable RET, available in the CRSP dataset “dsf.sas7bdat” (located in
“/wrds/crsp/sasdata/a_stock”).
 DIVUP: perhaps the market reaction is not due to the stock split but rather to
announcement of dividend increase that may occur simultaneously. Therefore,
please add the dummy for whether there is an announcement of dividend increase.
This variable is available on the stock splits dataset.
Given that many of these variables are new, it is a good idea to create a summary statistics
of the variables involved in this study. You can also create a correlation table involving
them. Having the summary statistics and the correlation table, discuss whether the concerns
about the omitted variable bias are warranted.
One can learn a lot from the regression results. In particular, you should address the
following items:
 For each of the control variables in the regression, discuss whether it is related to
market reactions to the announcement. If so, please discuss the magnitude of the
effect.
 Discuss the R2 of the model. What does the R2 represent here? (You should present
the adjusted-R2.)
 Discuss whether the residuals in the model are homoscedastic or not. That is,
implement the White test and conclude whether you should worry about
heteroscedasticity. If you end up worrying about heteroscedasticity, use the
heteroscedasticity-consistent standard errors in your inferences.
In your last step, examine a possible nonlinearity in the multiple regression model above,
in that the effect of PRCAFT on market reactions depends on past performance. That is,
add the variable LPRCAFT_PASTPERF=LPRCAFT*PASTPERF in the model, rerun the
regression, and discuss the inferences you learn from the interaction effect (i.e., reexamine
the effect of PRCAFT on market reactions).

FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 7

Part III: Determinants of the Decision to Split a Stock
This part of the project will examine the determinants of a company’s decision to split a
stock. The idea is to look at a company that announced a stock split and compare it with a
company that did not announce a split. The comparison takes places the year before the
announcement occurs. Thus, each company announcing a split in the stock splits dataset is
randomly matched to another company and another date such that this other company had
not decided to split its stock around that other date. Examples appear in Figure 3.
Take the first record. We know already know that Asyst Technologies (PERMNO=79568)
announced on January 3rd, 2000 that it would split its stock. The variable
MATCHED_PERMNO contains the identifier of a second company that did not split its
stock in the same year as of MATCHED_DCLRDT. Thus, the company with permanent
number 10019 did not announce a stock split on January 15, 2008 (nor in the year
surrounding that date). Similarly, the company with permanent number 79879 announced
a stock split in January 3, 2000, but the company with permanent number 79080 did not
announced a split in January 24, 2000.

Figure 3: More variables in the stock split announcement data
The dataset allows us to analyze stock splits, since we have data on companies that decided
to split their stocks and companies that decided not to. No surprise here, since the decision
to split the stock is a binary variable, you should use the PROC LOGISTIC to implement
your regression model, as

Notice that in order to run this regression, you need to have a dataset with a different row
for each company—such that each row of the stock splits dataset yields two rows of your
regression dataset. Take the first row in Figure 3, for example. From that row, you need to
create one row with PERMNO=79569, DCLRDT=1/3/2000 and SPLIT=1 and one row
with PERMNO=10019, DCLRDT=1/15/2008 and SPLIT=0, as in Figure 4 here:

Figure 4: Reorganizing the stock split data for a logistic regression
The explanatory variables of the logistic regression come from the understanding of what
may motivate a company to split its stock. Recall that one basic outcome of a stock split is
PERMNO COMNAM DLCRDT … MATCHED_PERMNO MATCHED_DCLRDT …
1 79568 ASYST TECHNOLOGIES INC 1/3/2000 … 10019 1/15/2008 …
2 79879 J D S UNIPHASE CORP 1/3/2000 … 79080 1/24/2000 …
3 86211 MICROSTRATEGY INC 1/4/2000 … 89245 2/21/2002 …
… … … … … … … …
SPLIT PERMNO DCLRDT …
1 1 79568 1/3/2000 …
2 0 10019 1/15/2008 …
3 1 79879 1/3/2000 …
4 0 79080 1/24/2000 …
5 1 86211 1/4/2000 …
6 0 89245 2/21/2002 …
… … … … …
)...()1(Prob 110 ikikii XXfSplit  
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 8

a smaller share price, and also that smaller share prices can be seen as dangerous (in that it
can become even smaller leading to a company being delisted). With these in mind let us
propose some characteristics that may drive the company’s decision to split the stock.
 Share price (LPRC): higher share price should be the main motivator for a stock
split. Assume also you want to examine the effect of a rate of change in share price,
so use as your explanatory the natural logarithm of share price. Share price is the
variable PRC in the MSF dataset, measured 12 months before DCLRDT. That is,
if the announcement date (DCLRDT) happens at month m in year y, collect PRC as
of month m of year y – 1.
 Company size (CSIZE): companies might need to achieve some level of size before
they decide to split a stock. Company size resembles a bit the definition used in part
II. Company size is the natural logarithm of total assets of the company splitting
its stock, measured two years before the year of the announcement—that is, as of
YEAR(DCLRDT) – 2. This is slightly different from the definition in part II, where
total assets was collected as of YEAR(DCLRDT) – 1.2
 Recent performance (PERF): Poor-performing companies should not split the
stock, as splitting the stock and reaching a lower price increases the risk of a stock
falling below a threshold for listing purposes. We define recent performance as the
average daily stock return during the period DCLRDT – 365 – 180 and DCLRDT
– 365. Again, this is a slightly different definition from the measure of past
performance used in part II.
 Company AGE: older companies may be more likely to split. Company age is
defined as year of DCLRDT minus first year of trading (variable FIRST_YEAR in
the dataset “d_first_year.sas7bdat”, available on Canvas)+1.
Prepare and show a summary statistics table of the explanatory variables for the sample
with SPLIT=1 vs. the sample with SPLIT=0. Interpret the numbers.
Then run the logistic regression explaining the likelihood of the company announcing a
stock split,
)f(1)Pr{Split 43210 iiii AGEPERFCSIZELPRC  
Report the regression results. Discuss the significance of each coefficient, and interpret the
effect of each variable on the likelihood that a split is announced. The effect should be
based on the change in the odds that the split is announced. You can play with some specific
changes; for example, when examining the effect of changes in PRC, you may examine the
effect of having the PRC increase by 1%—say from 100 to 101.
Finally, compute the predicted probability of a stock split for a company with the following
values: PRC=40, AT=20,000, PERF=0.001, and AGE=20 (you can an Excel worksheet to
compute this probability).

2 Why the difference in the definition of company size? We want to lag total assets by two years to make
sure this measure is observable one year prior to DCLRDT. For example, if DCLRDT is June 2000, the
measure of total assets the previous year (1999) will not be available before January 2000. If we collect total
assets as of 1998, then we make sure it is available by June 1999.
FNCE 435 Fall 2021 Individual Assignment (Section II)
Page 9

Appendix: Some comments and suggestions:

1. Most if not all of the data analyses here are replications of data analyses implemented in other
assignments throughout the course. For example, a very good starting point for the event studies
in part I come from the event studies we implemented either in module 4 or in assignment 4.
Also, any single control variable described here is some variation of control variables that we
used throughout the course.
2. The same rules on how to generate write-ups for all assignments in the course apply here. In
particular, the write-up should not mention SAS or codes, and an appendix should be included
with all the codes used in the generation of your outputs. An assignment without a code, or any
result that is not supported by a code will not be graded.
3. The assignment does not demand any output specifically, but it is expected that you produce
and show many outputs. For example, if you are going to discuss the results of a regression
model, you should generate the output for that regression model. If any result is required for
your discussion, you should include it in your write-up. SAS output should be avoided; instead
your outputs should be formatted to include only information relevant to the discussion.
4. Be as precise as you can in your discussion. For example, when examining a relationship
between Y and X in a regression framework, make sure you state the hypothesis being tested in
an unambiguous way (e.g., are you testing the regression coefficient based on an one-tailed or
two-tailed alternative hypothesis?); then if you need a number to anchor your conclusion (the
t statistic), refer to the specific number of your analysis. Then, if needed, examine the
magnitude of the effect of X on Y, making sure that you properly describe the units of
measurement of the variables involved in the analysis.
5. The individual assignment deliberately avoids having numbered questions. This way, your
write-up is not an attempt to answer questions 1, 2, 3, etc, but to discuss the theme of stock
splits in a thorough way. Assume that the reader does not have access to this document, so that
your write-up should be self-contained in explaining the motivation for the analyses, the
methodologies adopted, the results, and the inferences. An example of such a self-contained
write-up appears on Canvas, under “Modules”/”Supplementary Material”/”How to Prepare the
Write-Up for the Individual Assignment”.
6. You do not need to be constrained by the control variables (and models) suggested in the
assignment. These control variables are a minimum set of variables necessary for the project.
If you deem another variable X relevant to, say, explain market reactions to announcements of
stock splits (part II), you are free to expand the model and include your new variable.
7. Partial grade is available. If you have problems generating a control variable for your model,
ignore it and go ahead with the model without that control variable. Partial grading is not
available, though, for a code that does not run. Hence, a strong suggestion is for you to build
your model incrementally. For example, in part II, run the simple regression model. If it works,
save your code (under a name, say, p1), then try to include one more control variable. If the
inclusion is successful, then save the new code (call it p2). Repeat the process with each extra
control variable. If you get to a point where the inclusion of an extra variable is unsuccessful,
then return the previous version of the code. It is much better to have a partial model that runs