Analytical Methods

This document provides study material and solved assignments on Analytical Methods. It covers topics such as descriptive statistics, frequency distribution, z score, covariance, correlation coefficient, and regression analysis. The document also includes relevant computations and hypotheses for each topic.

ANALYTICAL METHODS
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Question 1
The descriptive statistics in relation to the monthly prices of the RIO stock along with two
indices namely S&P 500 and ASX 200 for the data provided is shown below.
Question 2
The requisite frequency distribution for monthly returns of the RIO stock along with two
indices namely S&P 500 and ASX 200 for the data provided is shown below.
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Question 3
The relevant characteristics of the returns on S&P index are summarised below.
The z score can be computed using the following formula
z value= x−μ
standard deviation
Here X = 5% or 0.05
Z value = (0.05-0.003704)/0.041576 = 1.113
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P (Z>1.113) = 1-P(Z≤1.113) = 1-0.867 = 0.133
The relevant characteristics of the returns on ASX 200 are summarised below.
The z score can be computed using the following formula
z value= x−μ
standard deviation
Here X1 = -2% or -0.02 while X2 = 2% or 0.02
The requisite computation has been performed using Excel using NORMSDIST function.
Based on this, it can be concluded that the probability associated with average returns on
ASX 200 index to lie between -2% and 2% has come out as 0.415.
Question 4
The covariance between S&P index returns and ASX returns based on the sample data has
come out as 0.0011 as computed from Excel.
The correlation coefficient between S&P index returns and ASX returns is 0.5431 and this
needs to be checked for significance.
The relevant hypotheses in this regards are as follows.
H0 : ρ=0 i.e. correlation coefficient can be assumed as zero and non-significant
Ha : ρ ≠0i.e. correlation coefficient cannot be assumed as zero and hence is significant.
Significance level of the test is given as 1% or 0.01
The relevant test statistics T can be computed using the following formula.
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Degree of freedom or df = n-2 = 215 – 2 = 213
From the above computation it is apparent that p =0 and lower than significance level of 1%.
The given evidence would warrant null hypothesis rejection leading to acceptance of
alternative hypothesis. As a result, it can be concluded that the correlation coefficient is
statistically significant and cannot be assumed to be zero.
Question 5
The requisite regression output for Model A as obtained using Excel is illustrated below.
The requisite regression output for Model B as obtained using Excel is illustrated below.
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The requisite regression output for Model C as obtained using Excel is illustrated below.
5.1 For Model A, the relevant hypotheses are as stated below.
Null Hypothesis: The intercept value is insignificant and can be assumed as zero.
Alternative Hypothesis: The intercept value is significant and cannot be assumed as zero.
The relevant test statistics is T whose value is 1.712 with a corresponding p value of 0.088.
Assuming 5% significance level, it is apparent that p value exceeds the level of significance.
As a result, rejection of null hypothesis is not warranted. Hence, it may be concluded that the
intercept coefficient in Model A is not statistically significant.
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95% confidence interval for slope coefficient has been obtained for regression Model B is
defined as (0.983, 1.502). This is apparent from the regression output from Model B and the
relevant extract is shown below.
5.2 In order to determine the superior model between A and B, the pivotal factor would be
the R2 value which outlines the predictive ability of the regression model thereby indicating
the more significant independent variable with regards to the dependent variable. Comparing
the respective R2 value for the two models, it is apparent that Model B has the higher value
which indicates that variation in ASX 200 tend to have more influence on the Rio Tinto stock
returns in comparison to changes in S&P 500 index. As a result, Model B would be
considered as superior.
5.3 The requisite hypotheses are stated as follows.
Null Hypothesis: βS&P500= βASX200 = 0
Alternative Hypothesis: Atleast one of the slopes is significant
The appropriate significance level for the test is 0.01.
The relevant computations have been performed in the ANOVA table shown below.
From the above, it is evident that the p value is 0 which is lower than the assumed
significance level of 0.01. As a result, rejection of null hypothesis is warranted. Thereby, it
can be concluded that the returns of the two indices are jointly statistically significant with
regards to the RIO stock returns.
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