Task 2: Hypothesis testing of means and variance equality (4 marks)
(i) Perform and report the Jarque-Berra test of normally distributed returns for each of the two stocks, MSFT and APPL. Given your test results, what do you infer about the distribution of returns to each company’s stock?
(ii) Test the hypothesis that the average return on APPL is different from 3 percent at the 5% level of significance. Make sure you present the test step by step leading to the conclusion, explaining which test statistic you use to perform this hypothesis test and why. [Hint: Hypothesis test about a population mean]
(iii) Before investing in one of the two stocks, we would like to compare the risks associated with the two stocks. For this comparison, perform and present an appropriate hypothesis test at the 5% level of significance, and interpret your result. [Hint: Hypothesis test about the equality of population variances]
(iv) We would also like to check whether both stocks have the same return on average. Using the confidence interval approach, perform and present an appropriate hypothesis test at the 5% level of significance, and interpret your result. Which stock would you prefer and why? [Hint: Hypothesis test about two population means. Zero marks if you test using an approach other than the confidence interval approach.]
Task 3: Regression analysis and inference (5 marks)
In this last part of the assignment, your team will focus on the preferred stock chosen in the last question above.
(i) First, compute the excess market return, i.e. X = RM – RF. Then, compute the excess return on your team’s preferred stock, i.e. Y = Rpreferred company stock – RF. [This is assessed in the Excel file only. Do not include in the PDF file.]
(ii) Estimate the Capital Asset Pricing (CAP) model by regressing the excess return on your preferred stock (Y) on the excess market return (X). Then, report your regression results in an equation form.
(iii) Interpret the estimated CAPM beta coefficient (i.e. slope coefficient) in terms of the stock’s riskiness in comparison with the market. [In not more than a few sentences]
(iv) Interpret the 95% confidence interval for the slope coefficient. [In not more than a few sentences]
(v) Interpret the value of the coefficient of determination R2. [In not more than a few sentences]
(vi) Perform and report a hypothesis test to infer whether your preferred stock is an aggressive stock at the 5% level of significance.
(vii) One of the assumptions of the linear regression model is that random errors are normally distributed. Perform and report an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.
THE END OF TASK DESCRIPTIONS
THE PDF FILE
* This is the team’s main report.
* On the very first page of the report, list the names and student ID numbers of all team members.
* Clearly state which student is the team leader on the first page.
* The report must not exceed 8 pages in total.
* The report must contain the team’s presentation on Tasks 2 and 3 only. (Task 1 is assessed purely in the Excel file. See below.)
* Do not copy and paste each task description from the webpage. For example, when you present the results for Task 2(i), simply use the section heading “Task 2(i)”.
* Answer each question directly and succinctly. Avoid discussing irrelevant matters and including unnecessary materials.
* A lack of explanation is a very common problem. You do not need to type up unnecessarily lengthy explanations, but you do need succinct to-the-point explanations. Your teacher must have advised you on this in workshops throughout the semester.
* Double-check the report for English mistakes at the pre-submission stage.
THE EXCEL FILE
* The first data sheet should present the result of Task 1. (Label the sheet “Task 1”.)
* In the second datasheet within the same file, present Task 2-related numerical and graphical results that your team has generated using Excel. (Label the sheet “Task 2”.)
* In the third datasheet within the same file, present Task 3-related numerical and graphical results that your team has generated using Excel. (Label the sheet “Task 3”.)