Statistical Analysis of Business and Finance Data - [Semester]

This assignment provides a comprehensive statistical analysis of financial data, focusing on the returns of the S&P price index, Boeing, and General Dynamics. It begins with a Jarque-Bera test to assess the normality of the data. The assignment then proceeds with several hypothesis tests, evaluating claims about mean returns and associated risks for the stocks. The analysis includes t-tests and F-tests to compare returns and risks, leading to a preference for General Dynamics due to its lower risk profile. Furthermore, the assignment delves into the Capital Asset Pricing Model (CAPM), estimating the beta of General Dynamics stock and interpreting the R-squared value. The analysis concludes with a confidence interval approach to hypothesis testing, evaluating the claim that General Dynamics is a neutral stock, and assessing the normality of residuals in the linear regression model. The document provides detailed interpretations of the statistical results, offering insights into the stock's performance and risk characteristics.

STATISTICS OF BUSINESS AND FINANCE
STUDENT NAME/ID
[Pick the date]

(1) Return (%) for S&P Price Index, Boeing Company and General Dynamics is given below.
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Jarque Berra Test to check the normal distribution of the data variables.
JB stat =( N
6 ) ( S2+ ( K−3 ) 2
4 )
Where,
N= Number of observations
K = Kurtosis
S= Skew value
Case 1: Boeing Returns (%)
Null hypothesis H0: Variable follows normal distribution.
Alternative hypothesis H1: Variable does not follow normal distribution.
JB stat = 10.04
The JB stat calculated is lower than critical value and thereby, rejection will not be done for null
hypothesis. Hence, Boeing Retunrs follows normal distribution.
Case 2: General Dynamics Returns (%)
Null hypothesis H0: Variable follows normal distribution.
Alternative hypothesis H1: Variable does not follow normal distribution.
JB stat = 33.0
The JB stat calculated is higher than critical value and thereby, rejection will be done for null
hypothesis as a result of this rejection, alternative hypotehsis is accepted. Hence, General
Dynamics returns do not follow normal distribution.
(2) Hypothesis test
Claim to test: Mean of General Dynamics Returns is not same as 2.8%.
2

Null hypothesis and alternative hypothesis
The population standard deviation = Not given
Relevant test stat = t stat
Degree of freedom (dof) = 60-1 =59
The two tailed p value = 0.02
Significance level = 5% or 0.05
The key observation is that p value is not higher than significance level which means null
hypothesis is rejected and alternative hypothesis is accepted. The claim is right that mean value
of General Dynamics Returns is not same as 2.8%.
(3) Hypothesis test
Claim to test: Associated risk of General Dynamics Returns (GD) and Boeing Company Returns
(BA) is not same.
Null hypothesis and alternative hypothesis
Relevant test stat = F statistic
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The two tailed p value = 2* one tailed p value = 0.0086
Significance level = 5% or 0.05
The key observation is that p value is inferior to significance level which means null hypothesis
is rejected and alternative hypothesis is accepted. The claim is right that associated risk of
General Dynamics Returns (GD) and Boeing Company Returns (BA) is not same.
(4) Hypothesis test
Claim to test: Return of General Dynamics Returns (GD) and Boeing Company Returns (BA) is
not same.
Null hypothesis and alternative hypothesis
Relevant test stat = t statistic
4

The two tailed p value = 0.8827
Significance level = 5% or 0.05
The key observation is that p value is superior to significance level which means null hypothesis
is not rejected and alternative hypothesis is not accepted. The claim is not right that returns of
General Dynamics Returns (GD) and Boeing Company Returns (BA) are not same.
The stock that would be preferred between the given stocks would be General Dynamics which
can be based on the premises that population of the two stock returns tend to have differing risk.
However, the returns of the population of the two stocks are not different. This implies that the
decision for the preferred stock needs to be made on the basis of risk where the stock with lower
risk would be the optimal choice. This is General Dynamics stock.
(5) Once the preferred stock is determined, then the excess returns both for the S7P index and
the GD stock would be determined considering the treasury rates which serve as the risk free
yield. For estimation of the CAPM model the excess returns on the S &P Index serve as the
predictor variable while the excess returns on GD stock tends to service as the dependent
variable. The CAPM related output is as highlighted below.
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The equation representing the CAPM model is indicated as follows.
GD stock excess returns = 0.111 + (0.642 * Market Excess Returns)
(c) R2 value is 0.2237
(d) The confidence interval in relation to GD stock bets with 95% confidence lies within the
range 0.328 and 0.957.
(6) Hypothesis Testing (Confidence Interval Approach)
H0 (Null Hypothesis): βGD = 1
H1 (Alternative Hypothesis): βGD ≠ 1
The hypothesised value for beta is 1 since this value would be indicative of neutral stock. The
confidence interval that has been estimated clearly does not contain the value 1. This is
indicative of the fact that the null hypothesis rejection would not happen considering the fact that
that hypothesised value (i.e.1) is not present in the 95% confidence interval.
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PART B: Interpretation
(1) In relation to the normal distribution, the relevant inferential test indicates that Boeing stock
would have a normal distribution of monthly returns where the GD stock returns would have a
non-normal distribution of monthly returns.
With regards to evaluation of stock, two parameters hold the key which are underlying risks and
return. The risk is captured by the standard deviation of the returns. For the GD stock, the
average monthly returns are higher when compared to Boeing stock. Further, against
expectations the risk associated with GD stock is also lower in comparison to the Boeing stock
which makes GD stock a superior stock based solely on the sample data.
(2) The t student distribution is the appropriate choice to highlight the null hypothesis. Further,
the hypothesis test indicates that the average population monthly returns on the GD stock tend to
deviate significantly from 2.8%.
(3) On the basis of the relevant hypothesis test, it is fair to conclude that deviation does tend to
exist between the population risks associated with the monthly returns on the two stocks.
(4) On the basis of the relevant hypothesis test, it is fair to conclude that no deviation tends to
exist between the population returns associated with the monthly returns on the two stocks. The
stock that would be superior is GD since lower risks is associated with GD in comparison with
Boeing and also the returns not being different in any significant manner.
(5) (b) The stock i.e. GD beta based on CAPM model has come out as 0.642. This implies that
whenever the excess market returns tends to undergo any change by 1%, then parallel change in
the excess returns on GD stock would be 0.642%.
(c) The excess returns on the market has the potential to account for only 22.37% of the total
changes that would be apparent in case of excess stock returns (GD stock). This is indicative of
the CAPM approach not yielding a model with good fit.
(d) The GD stock beta based on the population of monthly returns can be estimated to range
between 0.328 and 0.957 with a 95% chance.
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(6) The confidence interval based hypothesis testing reflects rejection of the claim that GD stock
is a neutral stock.
(7) For ascertaining the residual normality, the requisite hypothesis testing was carried out and
the assumption of the linear regression model in relation to normality of residuals seems
satisfied.
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