1. INDIVIDUAL STOCK
PATTERNS
And the Overall Market
NOVEMBER 11, 2016
DEJA MILLER
STA 4102 Computational Statistics
Draft II
DLM
iller

2. Miller 1
The stock market is one of the greatest opportunities to achieve The American Dream.
However it has also lead to the financial ruin of many. Are the winners more educated or are
they simply lucky? The first step for any stock investment strategy is to examine the overall
market. Timing the entrance to the stock market is a crucial decision that can make or break the
success of a venture. According to Jim Graham at discoveroptions.com “individual stocks have a
strong tendency to move in the direction of the overall market”. Therefore if one can calculate
the direction of the overall market and find stocks that are moving in the direction of the index
one can potentially choose an entry point where both the stock and the market are gaining and
our initial investment will be more likely to compound.
Accumulation and distribution of stock shares drives the market. According to Dr. Brett
Steenbarger of Traderfeed.blogspot.com “when the volume of a stock rises significantly and the
price of a stock also rises significantly large institutions are accumulating the stock”. Moreover a
correlation coefficient for adjusted price and volume close to one indicates strong positive
correlation and strong accumulation of stock by institutions whereby a strong negative
correlation indicates that institutions are selling the stock. Comparing strong positive and
negative correlations between stocks and their sector for time periods corresponding to visual
assessments of the graphs will provide a deeper understanding of the behavior of the overall
market. Both price and volume were available for the Standard and Poor’s 500 index. This data
was evaluated for price-volume correlation along with five randomly chosen stocks BLL, CAT,
GIS, AON, and MKC.
The first assessment was conducted for the year 2007 which corresponds to a down swing
on the graph as shown in Figure 1. The correlation between price and volume for the overall
DLM
iller

3. Miller 2
index during this period is -0.22. It is a weak negative correlation and reveals that the overall
market is not acting correctly. “The theory is that when price and volume move together, the
stock is "acting" correctly. Therefore, the higher the correlation, the better acting the stock is. If
the correlation was strongly negative, we may see a constructive short forming”.
(seekingalpha.com) However since there is no strong correlation between price and volume one
can deduce that large institutions are neither entering nor fleeing the market at this time and
investors may wish to hold their positions as well or sell some shares lest the market should turn
down. Furthermore all of the randomly chosen stocks validate this assessment. All five stock
correlations proved to be neither accumulating nor distributing shares and are in fact following
the weakness of the overall market.
The same data sets were tested for correlation over the time period for the year 2009 which
corresponds to an upswing on the graph in Figure 1. During this time frame the overall market
demonstrated a weak negative correlation for price and volume indicating weak
accumulation/distribution. The five arbitrary stocks tested for this time period also generated
weak to moderate correlations mirroring the weakness in accumulation /distribution in the
overall market even though the graphs appear to be showing an uptrend. Under these conditions
investors may choose to wait for correlation coefficients approaching positive one before they
enter the market.
The object of the stock market is to buy low and sell high. Since the correlation
coefficient tells us when large institutions are buying and selling one might wish to confirm
which stocks are actually moving with the overall market and which stocks are not. One method
used to verify whether a stock is moving in the same direction as the market is through
calculation of beta. A positive beta calculation indicates that the stock is moving with the market
DLM
iller

4. Miller 3
index and a negative beta calculation signifies that it is not. In order to calculate beta the
covariance between the price percent change for the index and the price percent change for the
stock is divided by the variance of the price percent change for the index. The price percent
changes are determined by subtracting the previous month adjusted price from the adjusted price
for the current month, dividing by the current month, then multiplying the result by 100.
(Current month-previous month)/previous month x 100
The following formula for adjusted price found on the “quick reference list” website gives a
close approximation when verified by hand calculations of the formula above and was used to
calculate the percent price changes in “R”.
prices2returns <- function(x) 100*diff (log(x))
The sample covariance between the index and the stock is computed by
Sxy =
𝟏
𝒏−𝟏
∑ (xi – 𝒙̅) (yi – 𝒚̅)
Where x represents values from the S&P 500 and y represents values from the stock being
evaluated.
The formula for sample variance is
S2
=
𝟏
𝒏−𝟏
∑ (xi –𝒙̅)2
And beta is calculated as
β =
𝑺𝒙𝒚
𝐒𝟐
Furthermore beta values was used to assess volatility. The beta value for the benchmark is
always one. A stock with a beta over one is more volatile than the benchmark and a stock with a
beta less than one is less volatile than the benchmark. Therefore a stock with a beta value of .5 is
half as volatile than the index and a stock with a beta of 2 is twice as volatile as the index.
Finally the coefficient of determination was calculated in order to measure the correlation
DLM
iller

5. Miller 4
between the stocks returns and the returns of the benchmark thereby establishing the reliability of
the beta values. An R-squared value of 0.8 or above indicates that the price of a stock is highly
correlated to the price of the benchmark index.
The beta value for four out of the five stocks tested from the S&P 500 over the time period
spanning two years from January 2009 to December 2010 were positive and therefore moving in
the same direction as the S&P 500 index. The graph in Figure 1 shows an upswing for the
corresponding time frame therefore BLL, CAT, GIS and MKC were moving in an upward
direction during the same time frame that the index was moving up. Beta for BLL is 0.09 moving
in the direction of the market with almost 9% of the volatility of the index. CAT has a beta of
0.68 in the direction of the market and 68% of the volatility of the index. Beta for GIS was
calculated at 0.19 and MKC came in at 0.09. They are both moving in the direction of the market
and are respectively 19% and 9% as volatile as the overall market. The exception was AON
which produced a beta value of -0.10 which indicates that it was moving in the opposite direction
from the benchmark index and it is 10% as volatile. The coefficient of determination for these
stocks for this two year period were calculated at 0.02, 0.16, 0.09, 0.01 and 0.05 for BLL, CAT,
GIS, AON and MKC respectively. These low estimates expose the minimal significance of these
beta calculations. These stocks are moving in the direction of the market however only a tiny
fraction of this movement can be explained by the movement of the index.
The calculations were repeated for a second two year period from January 2013 to December
2014. BLL, CAT, GIS and MKC returned beta values of 0.47, 0.11, 0.41 and 0.30 respectively
which reveals that these four stocks continued to follow the direction of the index although the
volatility fluctuated considerably. AON returned a -0.31 beta value and continued to move away
from the benchmark while increasing in volatility. The coefficient of determination calculation
DLM
iller

6. Miller 5
for BLL, CAT, GIS, AON, and MKC during this time frame are 0.02, 0.16, 0.04, 0.01, and 0.05
respectively. The coefficient of correlation for all five stocks is very low. Again these results
denote that even though these stocks are indeed moving in the same direction as the market only
a tiny percent of that movement can be explained by the movement of the index therefore the
beta calculations for this particular group of randomly chosen stocks over this duration of time is
unreliable. When stocks that are highly correlated to their corresponding index are more
desirable these calculations should be applied to all companies under consideration until R-
squared values closer to 0.80 are obtained.
There are many factors that influence investors when choosing stocks including breaking
news about potential companies, management history of these companies and local and world
economic indicators to name a few. The point and click method used to choose these random and
little-known stocks is not a true representation of a stock market portfolio since there was no
research what so ever into these companies before their choosing. Consequently these
preliminary studies are merely designed to test the inferential statistics inferred herein. Moreover
the sample size for this test is extremely small and subsequent tests would be needed in order to
determine the accuracy of these experiments and to further explore whether largely known stocks
have a greater tendency to follow the overall market compared to relatively obscure shares.
Another factor that should be taken into consideration is that the data available was for a time
period known to be in extreme recession. Data chronicled over a more prolific era may show
stronger correlation results. With that disclosed, this small sample of data reveals that some
individual stocks do have a tendency to follow the general action of the overall market.
Consequently it is possible to make a more educated guess regarding the timing of a particular
investment. The correlation coefficient between price and volume can potentially be used to
DLM
iller

7. Miller 6
distinguish a strong overall market in which price and volume are positive and highly correlated.
During established healthy market conditions the same correlation between price and volume can
be utilized to pinpoint stocks that are under accumulation. Once identified these stocks can be
further categorized by calculating beta values. Those stocks with positive beta values close to
one are moving in the direction of the market with low variation (volatility) in price change
compared with the price change of the index. Evaluating the coefficient of determination for
stocks of this designation will determine the significance of the aforementioned beta values and
indicate those with price movements that can be explained by the movements of the market.
Subsequently a positive healthy market can be identified. Moreover stocks that are under
accumulation and moving in the direction of the index as a direct result of market influences can
be identified. Therefore it is possible to increase the odds of making a successful trade by
pinpointing stocks that are behaving in a “correct” manner and calculating an entry point where
the overall market is healthy and in an up-trend which may facilitate the realization of profit.
DLM
iller

8. Miller 7
Works Cited
 "Appendix B: Time Series Data." Financial Risk Modelling and Portfolio Optimization
with R Pfaff/Financial Risk Modelling and Portfolio Optimization with R (2012): 324-37.
Web.
 "Creating a Time Series" Quick R/ Robert I. Kabacoff, Ph.D. (2014): Web.
 "The Stock Market and Individual Market Sectors." The Stock Market and Individual
Market Sectors. N.p., n.d. Web. 21 Nov. 2016.
 Steenbarger, Ph.D. Brett. "Price-Volume Correlations: Assessing Stock Market Trends."
Price-Volume Correlations: Assessing Stock Market Trends. N.p., 01 Jan. 1970. Web. 22
Nov. 2016.
 Http://seekingalpha.com/growth-stock-investor/articles. "Price and Volume Correlation."
Seeking Alpha. N.p., 05 Jan. 2011. Web. 22 Nov. 2016.
 "Definition of "Stationary Time Series" - NASDAQ Financial Glossary." NASDAQ.com.
N.p., n.d. Web. 23 Nov. 2016.
 Mitchell, Cory. "How to Calculate a Stock's Beta." Budgeting Money. N.p., n.d. Web. 25
Nov. 2016.
 "Quick Reference List." Intellectual Property Rights (1986): 88-113. Web.
 "R-squared." R-squared. N.p., n.d. Web. 27 Nov. 2016.
DLM
iller

9. Miller 8
Fig. 1.
Fig. 2.
DLM
iller