General Instructions
This assignment is designed to help you practice the concepts we have learned on the Research Methods Module.
You can use RStudio or Excel to perform the calculations required for this assessment.
Grading Scheme
The grades for each question can be interpreted as:
Grade Meaning
0 Not attempted.
1% to 39.49% No understanding of the relevant concepts.
39.5% to 49.49% Poor understanding of the relevant topics.
49.5% to 59.49% Fair understanding of the relevant topics.
59.5% to 69.49% Good understanding of the relevant topics.
69.5% and above Great understanding of the relevant topics.
Questions
1) Suppose that you calculate the sample correlation between long-term money supply growth and long-term inflation in ten (n = 10) industrialized countries to be 0.78 (?? = .78). Test the null hypotheses ??0, that the true correlation in the population is 0 (?? = 0) against the alternative hypothesis, ????, that the correlation in the population is different from 0 (?? ? 0) at a 5% level of significance.
Marks (10)
2) A portfolio manager advertises that its portfolio monthly returns have a standard deviation equal to 3%. You want to verify whether this claim is valid or not. You collect monthly returns for the last three years and measures the standard deviation of 3.7%.
a) State the Null and alternative Hypotheses.
Marks (5)
b) Assuming that the portfolio’s returns are normally distributed, determine if the calculated standard deviation is different than the advertised one at a 5% level of significance.
Marks (10)
c) Make a decision based on the results of the test.
3) A new trader has joined your firm and has been trading his own strategy, which he believes to be more predictable than the standard strategy employed by your firm. You suspect that his strategy is more unpredictable (measured as the standard deviation of the returns) than the standard strategy. You calculate the sample standard deviation of the standard strategy returns to be $3.5 in the last 50 days and the sample standard deviation of the new strategy to be $3.8 in the last 40 days.
a) State the null and alternative Hypotheses.
Marks (5)
b) Test the hypothesis that the new strategy is more unpredictable than the standard strategy at a 5% level of significance assuming that the strategies are independent and normally distributed.
Marks (10)
c) Make a decision based on the results of the test.
Marks (10)
4) You are an investor in JP Morgan stock and want to estimate its beta. You hypothesize that JPM has an average beta of one i.e. same risk as the market. You build a linear regression using the Capital Asset Pricing Model and obtain the following results.
Model: Risk.Premium.JPM = Alpha + Beta(Risk.Premium.Market)
Coefficients:
Estimate Std. Error t value
Alpha 0.0036 0.0127 0.2840
Beta 1.1958 0.2354 5.0795
Observations 60
Residual standard error: 0.0985 on 58 degrees of freedom Multiple R-squared: 0.5549 Adjusted R-squared: 0.3079
a) Create a 95% confidence interval for the value of the Beta coefficient.
Marks (10)
b) What fraction of the total variation in JPM risk premium is explained by the variation of the market risk premium?
Marks (10)
c) Make a prediction for JPM risk premium when the market risk premium is 2%.
d) Create a 95% confidence interval around this prediction using the formula below for the variance of the prediction. The sample mean of Market risk premium is 1.5% (??¯ = 0.015) and the sample variance is 0.25% (??2 = 0.0025).
Marks (10)
??2 = ??2 [1 + 1
??
(?? - ??¯)2
+ (?? - 1)??2]
Where:
??2 = squared standard error of estimate
n = number of observations
X = value of the independent variable
??¯ = estimated mean of X
??2 = variance of the independent variable