FINA1007: Statistical Exercise: Analyzing FTSE100 Company Data

This report presents a statistical analysis of financial data from twelve FTSE100 companies across the Energy, Utility, and Technology sectors, utilizing daily data from January 1, 2018, to January 1, 2020. The analysis, conducted using SPSS, includes descriptive statistics (mean, median, standard deviation, variance, skewness, kurtosis) and inferential statistics. The study focuses on the application of the Capital Asset Pricing Model (CAPM) and regression analysis to assess the relationship between company returns and various independent variables (Adj_Close, Volume, Low, High, Open, Close). The report investigates the significance of beta, reports t-statistics, R-squared values, and discusses the merits and demerits of CAPM, including its limitations and sensitivity to sector characteristics. The findings indicate that several CAPM indicators are good predictors of returns, and that the model explains a small percentage of the variance in the data, thus highlighting the model's strengths and weaknesses in the context of financial analysis. The analysis concludes by discussing the limitations of the model and suggests that certain variables are more sensitive to sector characteristics than others.

Research Methods 1
Coursework Header Sheet
243034-60
Course FINA1007: Research Methods (MSc) Course School/Level B/PG
Coursework Statistical exercise Assessment Weight 30.00%
Tutor J Mundy Submission Deadline 24/03/2020
Coursework is receipted on the understanding that it is the student's own work and that it has not,
in whole or part, been presented elsewhere for assessment. Where material has been used from
other sources it has been properly acknowledged in accordance with the University's Regulations
regarding Cheating and Plagiarism.
001089218
Tutor's comments
Grade Awarded___________ For Office Use Only__________ Final Grade_________
Moderation required: yes/no Tutor______________________ Date _______________

Research Methods 2
Table of Contents
Introduction................................................................................................................................3
Results and Interpretations.........................................................................................................3
Tasks:.........................................................................................................................................6
Question 1 and 2.....................................................................................................................6
Question 3..............................................................................................................................8
Question 4..............................................................................................................................9
Conclusion..................................................................................................................................9
References................................................................................................................................10

Research Methods 3
Introduction
The report has utilized a dataset on 12 different companies from FTSE100, from 3 different
sectors Energy, Utility and Technology. Besides, the Historical Prices of the stock selected
was from 1st Jan 2018 to 1st Jan 2020 with the latest 2 years daily data. For to note, the data
was downloaded as a CSV file named “CCH.L.csv” which was then imported into the SPSS
version for analysis. From the downloaded dataset, there is a total of 6072 observations with
7 variables namely, date, open, high, low, close, adj close and volume.
Results and Interpretations
The results and interpretations have been shown in this section. The analysis was conducted
in SPSS software. Also, both the descriptive statistics and inferential statistics have been
presented. The descriptive statistics such as means, median, minimum and maximum values
of the variables have been presented first. After this, inferential statistics such as standard
deviations, variance, and kurtosis have been presented based on the variables. The main level
of measurements for most variables is numerical hence makes it easy to calculate the
descriptive and inferential statistics. Also, the descriptive statistics have been used to
summarize, describe and present the study findings while the inferential statistics have been
mainly used to conclude the study populations, (Salkind, and Frey, 2019).
From the analysis in Table 1 below, all the variables have a total observation of 6072. The
mean and standard deviation of the adj close variable is calculated to be 2131.03 and
2147.219 respectively with a variance of 4610549.995. Something noted in the analysis is that
the variable “Volume” has the largest quantity in terms of the values. For example, it has the
highest values for the summary statistics except for the standard errors for both kurtosis and
skewness values. Another observation from the statistics is that standard errors for both
kurtosis and skewness are the same for all the variables calculated to be 0.031 and 0.063
respectively.

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Descriptive Statistics
N Range Minimu
m
Maximum Mean Std.
Deviation
Variance Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic Statistic Statistic Std.
Error
Statistic Std.
Error
Open 6072 8779 124 8903 2189.01 2184.852 4773577.31
5 1.065 .031 .100 .063
High 6072 8875 125 9000 2213.18 2206.439 4868374.05
8 1.062 .031 .097 .063
Low 6072 14826 2 14828 2165.98 2168.242 4701275.10
1 1.089 .031 .256 .063
Close 6072 8752 123 8875 2188.03 2184.193 4770700.94
4 1.065 .031 .101 .063
Adj_Close 6072 8759 116 8875 2131.03 2147.219 4610549.99
5 1.115 .031 .257 .063
Volume 6072 25097339
9 0 25097339
9
12563576.
33
26291745.4
40
691255878
279510.100 3.759 .031 17.154 .063
Valid N
(listwise) 6072
12 companies were analyzed representing equal proportions of three main sectors as shown
below.
Sector
Frequency Percent Valid Percent Cumulative
Percent
Valid
Energy 2024 33.3 33.3 33.3
Utility 2024 33.3 33.3 66.7
Technological 2024 33.3 33.3 100.0
Total 6072 100.0 100.0

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Company
Frequency Percent Valid Percent Cumulative
Percent
Valid
Coca-Cola HBC AG 506 8.3 8.3 8.3
NMC Health Plc 506 8.3 8.3 16.7
BAE Systems plc 506 8.3 8.3 25.0
Just Eat Takeaway.com
N.V. 506 8.3 8.3 33.3
Vodafone Group Plc 506 8.3 8.3 41.7
Tesco PLC 506 8.3 8.3 50.0
Auto Trader Group plc 506 8.3 8.3 58.3
Ashtead Group plc 506 8.3 8.3 66.7
British American Tobacco
p.l.c. 506 8.3 8.3 75.0
Rentokil Initial plc 506 8.3 8.3 83.3
Reckitt Benckiser Group plc 506 8.3 8.3 91.7
Rolls-Royce Holdings plc 506 8.3 8.3 100.0
Total 6072 100.0 100.0
Having created a new variable called “returns”, table 2 results indicate its descriptive
statistics. From the results, the total observations reduce from 6072 to 3093 with a mean and
median value of returns calculated to be -4.8669 and -4.7082 respectively. The standard
deviation and variance of the returns are 1.0989 and 1.208 respectively. The t-statistics of the
returns’ skewness and kurtosis are -0.625 and 1.001 respectively. Similarly, the standard error
of skewness is 0.044 while that of the kurtosis is calculated to be 0.088. The range of the
returns is calculated to be 8.88 as shown in the spss output below.
Table 2: Descriptive Statistics for the return variable
Returns

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N
Valid 3093
Missing 2979
Mean -4.8669
Median -4.7082
Std. Deviation 1.09894
Variance 1.208
Skewness -.625
Std. Error of Skewness .044
Kurtosis 1.001
Std. Error of Kurtosis .088
Range 8.88
Minimum -8.99
Maximum -.11
For to note, the distribution curve in the drawn histogram below on the returns confirms the
existence of asymmetric distribution implying the mean and the median is almost the same
and that the returns over the times are normally distributed, (Koziol, et al, 2016).
Tasks:
Question 1 and 2
According to the findings of the model summary below when he returns are considered as the
dependent variable and other characteristics as the independent variables, the table shows the
multiple linear regression model summary and overall fit statistics. From the results, there is
evidence that the adjusted R² of the model is 0.145 with the R² = .146 which means that the

Research Methods 7
linear regression explains 14.6% of the variance in the data from the 12 companies,
(Karamazova, Jusufi Zenku, and Trifunov, 2017).
Model Summaryb
Model R R Square Adjusted R
Square
Std. Error of
the Estimate
Change Statistics
R Square
Change
F Change df1 df2 Sig. F Change
1 .383a .146 .145 1.01614 .146 105.892 5 3087 .000
a. Predictors: (Constant), Adj_Close, Volume, Low, High, Open
b. Dependent Variable: Returns
Now that it has been observed that the difference from R square and Adjusted R square is
small (0.001) is a clear indication that independent variables were accurate.
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 546.690 5 109.338 105.892 .000b
Residual 3187.449 3087 1.033
Total 3734.140 3092
a. Dependent Variable: Returns
b. Predictors: (Constant), Adj_Close, Volume, Low, High, Open
From the ANOVA table, it shows that all the independent variables which include;
Adj_Close, Volume, Low, High, Open, and Close helps to predict the returns of companies,
(F= 105.892, p.v=.0005<0.05). This implies that the null hypotheses were useless hence
reject the null hypothesis and accept the alternate hypotheses of the independent variables
(Malek, Coburn, and Marelich, 2018).

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Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
T Sig.
B Std. Error Beta
1
(Constant) -4.987 .031 -161.159 .000
Open -.009 .001 -18.268 -12.897 .000
High .010 .001 20.730 20.170 .000
Low -.002 .001 -3.892 -3.149 .002
Volume 1.478E-009 .000 .034 1.906 .057
Adj_Close .001 .000 1.506 3.789 .000
a. Dependent Variable: Returns
Question 3
The results of the regression show that all the CAPM indicators (open, high, low and adj
close) are good predictors of the returns and that they are statistically significant with p-value
< 0.05, (Migliorati, Di Brisco, and Ongaro, 2019) except volume indicator. This finding
implies that CAPM must be done considering the four indicators. For instance, when the
CAPM is open, there are high chances that it attracts several clients than when the volume is
high.
Again, the Unstandardized Coefficients indicate that a decrease in open (-.009) would result
in a decrease in returns holding other independent variables (close) constant. Furthermore, the
increase in close (.001) would increase returns holding other independent variables (open)
constant (Astivia, and Zumbo, 2019). Furthermore, the implication is that CAPM increasing
the openness of the CAPM, in one way or the other affects the portfolio.
In order to show the benefit of the independent variable, the results displayed the beta values
of each independent variable in a standardized term. From the results, all the variables except
the volume variables are significant predictors, secondly, it was established that High has the
highest impact (beta = 20.73) followed by adj close (beta = 1.506) respectively, (Darlington,
and Hayes, 2016).
From the findings, most indicators are good predictors of returns implying that our CAPM is
of advantage and not limited to the fact that it helps in eliminating and even reducing the
risks considered to be unsystematic, (Garg, 2019). For instance, through the CAPM, the

Research Methods 9
company investors like Coca Cola easily hold a diversified portfolio, like a market portfolio.
Furthermore, the CAPM takes into consideration all forms of systematic risks especially
those left out of other return models like the dividend discount model, (Fernandez, 2017).
Similarly, the CAPM is one of the most convenient and easy to use the method given that its
calculations can easily be driven from several ranges of outcomes.
However, CAPM in one way or the other has some limitations including too many
assumptions, (Campbell, Giglio, Polk, and Turley, 2018). As a result, most companies view it
as an unrealistic approach thus not able to provide accurate results now that some indicators
have turned to be good predictors of returns unlike others. The fact that CAPM allows the
lender and the borrower to borrow at a free risk also makes it be considered inappropriate
method. For instance, the companies cannot allow lenders to borrow free.
As much as the CAPM stands up well to criticism, until something better presents itself,
though, the CAPM remains a very useful item in the financial management toolkit, (Zhang,
2017) for the twelve companies.
Question 4
Based on the study results, some variables’ findings are not sensitive to sector characteristics.
For instance, the variable “Volume” has the largest quantity in terms of the values. For
example, it has the highest values for the summary statistics except for the standard errors for
both kurtosis and skewness values. Hence, it is normal for the companies to have produced a
minimum and maximum volume of 250973399 and 12563576.33 respectively.
Besides, the distribution curve in the drawn histogram below on the returns confirms the
existence of asymmetric distribution implying the mean and the median is almost the same
and that the returns over the times are normally distributed. This is quite sensitive to the
companies and their sectors meaning that the returns vary with times. In other words, there
times, the returns are high as well as times the returns are low for different sectors implying
that there is no skewness in the returns.
Again, the results indicate that the adjusted R² of the model is 0.145 with the R² = .146 which
means that the linear regression explains 14.6% of the variance in the data from the 12

Research Methods 10
companies. The percentage variance is very low making the accuracy of the prediction to be
compromise thus not very sensitive to the sector characteristics.
From the ANOVA table, it shows that all the independent variables which include;
Adj_Close, Volume, Low, High, Open, and Close helps to predict the returns of 12
companies, (F= 105.892, p.v=.0005<0.05), (Cronk, 2016). This implies that the variables in
one way or the other influence the operations of the company.
Conclusion
In conclusion, a multiple regression was run to predict returns of the twelve companies from
the independent variables (Adj_Close, Volume, Low, High, Open, Close). The results
confirmed that all the company variables; (Adj_Close, Volume, Low, High, Open, Close) are
statistically significantly predicted returns of the companies, p < .05.

Research Methods 11
References
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Analysis: What it is, How to Detect it and How to Solve it with Applications in R and
SPSS. Practical Assessment, Research, and Evaluation, 24(1), p.1.
Campbell, J.Y., Giglio, S., Polk, C. and Turley, R., (2018). An intertemporal CAPM with
stochastic volatility. Journal of Financial Economics, 128(2), pp.207-233.
Cronk, B.C., (2016). How to use IBM SPSS statistics: A step-by-step guide to analysis and
interpretation. Routledge.
Darlington, R.B. and Hayes, A.F., (2016). Regression analysis and linear models: Concepts,
applications, and implementation. Guilford Publications.
Fernandez, P., (2017). Is it ethical to teach that beta and CAPM explain
something?. Available at SSRN 2980847.
Garg, N., (2019). Study of Capital Asset Pricing Model in the Nordic Stock Market.
Karamazova, E., Jusufi Zenku, T. and Trifunov, Z., (2017). Analyzing and Comparing the
Final Grade in Mathematics by Linear Regression Using Excel and SPSS. International
Journal of Mathematics Trends and Technology, 52(5), pp.334-344.
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of the Bell-Shaped Curve. In Large-Scale Brain Systems and Neuropsychological
Testing (pp. 49-61). Springer, Cham.
Malek, M.H., Coburn, J.W. and Marelich, W.D., (2018). Advanced statistics for kinesiology
and exercise science: a practical guide to ANOVA and regression analyses. Routledge.
Migliorati, S., Di Brisco, A.M. and Ongaro, A., (2019). The Flexible Beta Regression
Model. Data Analysis and Applications 1: Clustering and Regression, Modeling‐estimating,
Forecasting and Data Mining, 2, pp.39-52.
Salkind, N.J. and Frey, B.B., (2019). Statistics for people who (think they) hate statistics.
Sage Publications, Incorporated.
Zhang, L., (2017). The investment CAPM. European Financial Management, 23(4), pp.545-
603.