CAPM Beta Regression Analysis, Interpretation, and Hypothesis

This assignment analyzes the Capital Asset Pricing Model (CAPM) beta through regression analysis. The solution presents the regression equation, interprets the slope coefficient (beta), and explains the 95% confidence interval and the coefficient of determination. It also includes a hypothesis test, formulating null and alternative hypotheses, calculating the t-value, and interpreting the results to determine whether the stock is aggressive based on its beta. The analysis further examines the normality of random errors using statistical tests, with the results presented in an appendix. This comprehensive analysis provides insights into the risk and return characteristics of a stock relative to the market.

TASK 3 REGRESSION
ANALYSIS AND
INFERENCE

ii. Reporting the regression results in equation form
Y = a + bx
a = intercept = -0.011
b = Slope = 0.99
x = excess market return
y = excess return of preferred stock that is, BHP
Therefore, the regression equation would be as follows:
Y excess return on BHP = -0.011 + 0.99Xexcess market return
iii. Interpretation of estimated CAPM beta coefficient or slope coefficient
Through the regression equation, the slope coefficient identified as 0.99 which entails that with
the 1US dollar changes in market would led to 0.99 UD dollar changes in the price or returns of
BHP stock. A beta lower than 1 means the stock would be having less variation as compared to
the market and accordingly it is considered as less risky than the market.
iv. Interpretation of 95% confidence interval for the slope coefficient
Identified 95% confidence interval = [0.968, 1.017]
Therefore, it can be interpreted that with the one-point increase in the prices or return of market
that is, NSDQ, the increase in the prices or returns of the stock of BHP would fall between 0.968
and 1.017 points.
v. Interpretation of coefficient of determination
The identified value of coefficient of determination is 0.991 which entails that a 99.1% change in
dependent variable (excess returns on BHP stock) can be explained through the change in
independent variable (excess market return).
vi.
Null hypothesis: The value of Beta would be less than or equal to 1.
Alternative hypothesis: The value of Beta would be greater than 1.

Degrees of freedom = n – 1 = 59 – 1 = 58
Significance level = 0.05.
It is a right sides one tailed test, therefore, the critical t value = 1.67
x̄1 = -0.8799 (average of excess market returns)
x̄2 = -0.8843 (average of excess returns on stock)
Standard error = 0.073
n1 and n2 are 59.
t = -0.8799 – (-0.8843) /√0.073 (1 / 59 + 1 / 59)
t = 0.0044 / √0.073 * 2 / 59
t = 0.0044 / √ 0.073 * 0.034
t = 0.0044 / √0.0025
t = 0.0044 / 0.05
t = 0.088
Therefore, calculated t value is less than critical t value and accordingly, null hypothesis would
be accepted. This means the BHP stock is not aggressive due to its beta being lower than or
equal to 1.
vii.
Null hypothesis: The random errors are normally distributed
Alternate hypothesis: The random errors are not normally distributed.
As the significance value comes greater than 0.05 that is, 0.463, the null hypothesis would be
accepted and alternative hypothesis would be rejected. Accordingly, the random errors in the
given data set are found to be normally distributed.

APPENDIX
Tests of Normalitya,c,d,f,g
R_M Kolmogorov-Smirnovb Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
R_BHP
1 .292 3 . .923 3 .463
1 .260 2 .
1 .260 2 .
1 .304 3 . .907 3 .407
1 .260 2 .
1 .119 6 .200* .997 6 1.000
1 .105 8 .200* .988 8 .992
1 .156 7 .200* .968 7 .887
1 .385 3 . .750 3 .000
1 .300 5 .161 .822 5 .122
1 .274 4 . .831 4 .171
1 .198 3 . .995 3 .868
1 .215 5 .200* .970 5 .876
1 .260 2 .
*. This is a lower bound of the true significance.
a. R_BHP is constant when R_M = 1. It has been omitted.
b. Lilliefors Significance Correction
c. R_BHP is constant when R_M = 1. It has been omitted.
d. R_BHP is constant when R_M = 1. It has been omitted.
f. R_BHP is constant when R_M = 1. It has been omitted.
g. R_BHP is constant when R_M = 1. It has been omitted.