Stock Market Analysis and Risk Assessment

This assignment analyzes the performance of Boeing and IBM stocks from 2011 to 2019, examining trends, risk-return profiles, and using CAPM to evaluate systematic risk. It involves calculating descriptive statistics, conducting hypothesis tests, interpreting beta values, and assessing the validity of linear regression assumptions.

STATISTICS FOR BUSINESS & FINANCE
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PART A: Computation
1. The respective graphs for the two stocks and market index in relation to the relevant
period are as shown below.
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2. a) For the stocks highlighted above along with the index, the returns on monthly basis
have been calculated in accordance with the formula stated and the resultant returns are
summarised in the tabular form as indicated below.
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2. b) Summary Statistics (Monthly Returns)
In order to check for normality the Jarques Bera Statistic (JB statistic) needs to be computed
in line with the following formula.
The respective JB statistic values obtained are summarised below.
The value of statistic that has been calculated for each of the above cases is more than the
critical value applicable. Hence, H0 or null hypothesis tends to be rejected while the
alternative hypothesis (H1) ought to be accepted. Therefore, the implication is that the
probability distribution of the respective returns cannot be considered as normal.
3. Hypothesis Testing
H0: μBoeing ≤ 3% , H1: μBoeing > 3%
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A right tail t test would be applied here as the population standard deviation for returns
remains unknown.
Sample size (n) = 65
Sample Returns (Boeing) = 1.52% per month
Sample standard deviation = 5.72%
Calculated t statistic = (1.52-3)/(5.72/√65) = -2.086
Considering that the test is right tail, hence the rejection area would lie on the positive side
and not on the negative. Thus, clearly evidence seems lacking for H0 rejection. Thus, it is
apparent that the monthly returns on the Boeing stock tend to be lower than 3%.
4) Hypothesis Testing
Applicable Test: F test for comparison of variances
Relevant Excel Output
Relevant p value from the above output = 0.218
Applicable significance level = 5% or 0.05
As p value > α, hence failure to reject Ho and accept H1
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Conclusion can be drawn that the underlying risk associated with the two highlighted stocks
indicates no statistically significant difference.
5) Hypothesis Testing
Appropriate test: T Test for two independent samples. Also, the requisite choice made has
been equal variance since the variance of the two stocks do not show significant difference as
has been already established.
Relevant Excel Output
.
Relevant p value from the above output = 0.087
Applicable significance level = 5% or 0.05
As p value >α, hence failure to reject Ho and accept H1
Conclusion can be drawn that the underlying returns associated with the two highlighted
stocks does not indicate statistically significant difference.
6) Superior stock is Boeing in the given case.
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.
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7)a) Regression Output
From the above regression output, the obtained regression equation is mentioned below.
Excess returns (Boeing stock) = 0.650 + 1.092* Market Excess Returns
c) Value of R2 =0.3127
d) Lower level (Beta 95% confidence interval) = 0.685
Upper level (Beta 95% confidence interval) = 1.500
The hypothesis testing needs to be facilitated using the confidence interval approach. The
underlying decision rule is based on the considering if the hypothesised value is found in the
confidence interval obtained. The 95% confidence interval outlined above tends to contain
the value 1 which implies that evidence available does not facilitate null hypothesis rejection.
Thus, the stock can be assumed as a neutral stock.
9) The applicable normal probability plot for ascertaining the linearity assumption is
indicated as follows.
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.
0 20 40 60 80 100 120
-25
-20
-15
-10
-5
0
5
10
15
Normal Probability Plot
Sample Percentile
Boeing Excess Returns
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Part B: Interpretation
1) S&P 500 – During the given period, the index has been quite bullish and delivered stellar
returns especially between October 2011 and October 2014. However, after this there is
come consolidation observed for a year or so before the uptrend has again continued.
Hence, the index movement clearly indicates the bull-run for the given period.
Boeing Stock – From August 2012 to October 2013, the stock has indicated significant
upmove as the price has more than doubled during this period. However, for the next
three years the stock has been in the consolidation phase where the movements have been
sideways that too in a limited range. But a breakout in the stock has been observed from
October 2016 onwards, when the stock actually surges in a brief amount of time.
IBM Stock – From October 2011 to June 2013, the stock has been primarily range bound
and does not show a particular trend. However, after that there is breakout of the stock on
the lower side and the stock has shown a steady declining trend till February 2016. The
stock during this period has come down more than 40%. However, post this there has
been a recovery is the stock for the remaining period but the losses have not been fully
recovered.
2) b) The risk return characteristics for a stock are imperative which are reflected by the
underlying descriptive statistics. Based on the derived statistics, it becomes apparent that
Boeing emerges as a superior stock. This is because the returns per unit risk tend to be
higher for the Boeing stock in comparison with the iBM stock. Hence, from an investor
perspective, it makes sense to invest in Boeing as compared to IBM based on the given
sample data.
5) The definition of a superior stock is one which would lead in better returns without
assuming a higher risk. The hypothesis tests have been conducted to compare the risk and
returns for the two stocks but have not indicated any significant difference in either case.
Hence, the decision making is to be based on the sample data and hence Boeing stock would
be preferred choice.
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7) b) The beta of the Boeing stock has been computed as 1.09. As this value exceeds 1, hence
it is apparent that the underlying risk associated with the Boeing stock would be greater in
comparison with the market index. However, the higher risk prevalent in the stock would be
compensated by proportionately higher returns and possible also excess returns. In
accordance with the CAPM model, it is expected that a change in the market by 1% would
lead to respective yield of 1.09% in the stock. The actual returns observed during the given
period are much higher than the index and hence the stock seems to deliver excess returns for
the investors.
c) The R2 value for the given regression model capturing the CAPM is 0.3127. As a result,
the index represented by S&P 500 can only account 31.27% changes in the Boeing stock
price that have been witnessed in the given period. This also implies that the remaining
68.73% of the changes are not accounted by the market index and hence incremental
variables need to be introduced. As a result, it would be correct to conclude that the beta does
not capture the systematic risk related to Boeing stock and hence is not able to explain the
changes observed adequately.
d) The 95% confidence interval computed implies that the beta of the Boeing stock would lie
in the range of 0.685 and 1.5 with an underlying probability of 0.95.
9) The checking of the linearity assumption in regression model has been done through the
normal plot of the error term. The relevant output has been already attached in the previous
section. It can be concluded from the same that there is an approximate linear trend visible in
the normal probability plot which implies that the assumption is indeed fulfilled.
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