For my IB Pre-Calculus class, I have been working on an extensive math exploration essay. The subject was left very open so I naturally chose to do mine on the stock market! If you're a "mathy" person then I think you will enjoy it! Here it is:
Using Probability in the Stock Market
Jeffrey Searle
Warren Buffett,
the most successful investor this world has ever known, once said: “Price is
what you pay. Value is what you get.” The stock market has always amazed me.
The whole premise is kind of mind-boggling, and it’s one of the few things I
don’t think I’ll ever completely understand. For this reason, and also because
I love money, I chose to pursue this topic.
A month ago, I
joined an investing simulation game on MarketWatch and began testing investment
strategies. I settled on one technique that seemed effective. After a lot of
consistent success (I made a 30% return in one month), I started to wonder if
there was any real correlation
between the numbers I was basing my decisions on and the success I was having.
I asked myself the age-old question of “can I really predict what stocks will
do?”
Ever since the New
York Stock Exchange opened on May 7, 1792, people have been wrestling with that
question. If someone could actually predict what the stock market would do then
they would never have to graduate high school, and could easily become the
richest person in the world, assuming they have access to a little bit of
money. Now I know that no one can actually predict the future with absolute
certainty. It is possible, however, to use probability to find correlations
between past figures and future ones. That is simply what I am setting out to
do. I want to find a way to link past stock figures to future ones with a
reasonable success rate.
Two weeks ago, I
invested $1000 into the stock market through a USAA brokerage account with the
hope of making a nice profit. I’m currently investing on what I would call
“educated whims,” but by the end of this exploration I hope to be investing
solely using the strategies I discover to be effective.
By
this point you may be wondering what exactly I’m talking about. As you probably
know, the market is all about buying shares in a business and selling those
shares for a higher price later. It’s like a flea market for intangible goods
that’s run so efficiently and effectively that you seldom need to worry about
anything other than investing in the right stock.
So
how do you go about picking the right
stock? I base my investment decisions around when companies release earnings
reports. By law, corporations must release financial statements every quarter
that detail the previous quarter’s earnings and cash flows. I have found that
every time a business releases earnings, their stock either soars or tanks. The
trick now becomes finding which stocks are going to jump. I have found a few
figures within earnings reports that seem to always be paired with the “winner
stocks.” I am going to focus my efforts on trying to find correlations between
selected figures and stock increases.
In
simple terms, I will be checking if what I think affects stock price actually
does. I am primarily going to use the Chi-squared Test for Independence for
this investigation.
First though, let
me explain my struggle with finding a way to make this whole probability
application work. I first wanted to use percentage changes in stocks within the
Chi-squared test. This became a problem because you need frequencies to do the
test. I just hated this because it meant that I had to “water down” the whole
test. I know what you’re thinking, you can change percentages to
frequencies, but I am not working with percentages in the sense of probability
where the percentages add up to one, I’m working with percentages that
represent how much a stock went up or down and price. This type of percentage
cannot be converted to frequencies. Instead, I had to assign ranges of what I
decided were small, reasonable, and large percentage increases or decreases. I
had to decide which figures would fall into which of those categories as well
in order for the test to work. I explain in the index what exactly these ranges
are. At first I thought by doing this it would not give me the accurate results
that I wanted, but after thinking about it I realized that the premise is still
the same and if there is a correlation I should still be able to see it.
In the index you
will find all the data I collected. All of my tests will be testing between the
percent change and various figures that I’ve been collecting. I will first test
between forecast change of EPS over the last quarter (last quarter’s EPS minus
the EPS forecast for this quarter). Here is my Chi-Squared test made by using
the data from the index:
Test of Independence for EPS Change in
Forecast and Percent Change
Hypothesis: Ho-
variables are independent; Ha- variables are dependent
Because I want to see a fairly
definite correlation between the two variables, I will be using an α value
of 5%
fo
fe
I performed the above equation on my TI-83 Plus by using the STAT
and LIST functions. By doing so, I received a x^2 score of 9.918577075! Then I just
plugged it into the calculator using 5 degrees of freedom (6 rows and 2
columns). This gave me a P-value of .0776.
Conclusion (of test): My
P-value was greater than my α value, but not by a whole lot. That means that
the test was inconclusiveL.
However, it was fairly close to my α value!
In
review, percent changes in price for a stock is not shown to be dependent upon
EPS forecast changes between two quarters.
So what does this
mean for me? These figures are what I’ve been basing my decisions on for the
past month, and I’m a little disappointed that they weren’t conclusive. Since I
began this paper, I can see why my initial success doesn’t seem to line up with
what I’m coming up with after doing this test. I can see this because since
that point I have begun to lose money. Not a whole lot, but a substantial
amount. It makes sense that this would happen because if there really was a
correlation between EPS forecasting and stock price changes then I would have
continued success. I really thought my results would turn out conclusive, but
I’m glad that I understand they’re not.
It
actually makes a lot of sense that there isn’t a correlation. I mean, if
someone like me could just look at a number available to the public and control
the stock market then everyone would be doing it. The stock market is complex
and unpredictable. There are “experts” out there who will tell you conflicting
thoughts about what you should invest in and why every day. They’re only right
half the time though. That’s the thing about the market- it always seems like
one day you’re right and the next day you’re not. In order to be considered a
successful investor, you have to use your strategy for a long period of time
and see if the overall trend of your investments has been positive. That’s why
so many people screw up with short-term investing. Short-term investors will
see one failure and never invest the same way again. I have been looking at
data from one day. It’s no wonder that my results were inconclusive when
I’m looking at a short period of time in a market that has countless things
influencing it at the same time.
Before
I started investing, I did some research on “day traders.” Everything I read
was telling me that it’s a bad idea because for the most part, those that do it
eventually become failures. The results from my test support this claim. What
this whole exploration has taught me is this- I need to invest with a broader
scope and for longer periods of time. I think this is a better and safer way to
be successful.
My
findings will help me in future investments. Even though the market completely
boggles my mind, I will not stop in my efforts to understand and conquer it. My
goal by the end of the school year is to have implemented what I discovered
during this exploration and make $200 in profit through investing. While the
stock market may be unpredictable, some things are for sure, I will have
failure and I will have success.
Index
Explanation of Ranges:
EPS-
The range of figures between 0 and
±.049, I considered as “small” increases/decreases.
The range of figures between ±.05
and ±.099, I considered as “medium” Increases/decreases.
The range of figures between ±.1
and ±∞, I considered
as “large” Increases/decreases.
Percent Changes-
Percentage changes between 0% and 4.9%, I considered
as “small.”
Percentage changes between 5% and 9.9%, I considered
as “medium.”
Percentage changes between 10% and ∞%, I considered
“large.”
Bibliography
"DIGSTATS:
Chi-Squared." DIGSTATS: Chi-Squared. N.p., n.d. Web. 3 May 2014.
<http://www.sv.vt.edu/classes/digstats/main/inferant/d_chi.html>.
"Pearson's chi-squared
test." <i>Wikipedia</i>. Wikimedia Foundation, 5 Mar. 2014.
Web. 3 May 2014.
<http://en.wikipedia.org/wiki/Pearson's_chi-squared_test>.
"Earnings
Calendar for April 13, 2014." NASDAQ.com. N.p., n.d. Web. 3 May
2014. <http://www.nasdaq.com/earnings/earnings-calendar.aspx>.
"Market Watch
Stock Quotes."
Market Watch. N.p., n.d. Web. 1 May 2014.
<http://www.marketwatch.com/>.
