Individual Assessment - Exam Instructions and Questions

Warning against plagiarism and collusion

This is an individual assessment, and you must ensure that the work you submit is your own. It is not acceptable to copy from another source without acknowledging that it is someone else’s writing or thinking. This includes using paraphrasing as well as direct quotations.

Copying another student’s work, using previous work of your own or copying large sections from a book or the internet are all examples of plagiarism and carry serious consequences. If you have any questions about plagiarism and collusion, please raise these with the module leader before the exam takes place.

This is an online examination. You are permitted to use any appropriate resources in order to complete the assessment (e.g., books, articles, cases, etc). The assessment is designed to replicate an examination – there is no requirement for full footnote/intext references. However, please note the plagiarism and collusion warning above. Instructions regarding how to complete the examination (including the number of questions you should attempt) are contained within the exam paper. Word-counts for each question are indicated in the paper and should be adhered to.

To accommodate students in different time-zones and those with individual examarrangements, the exam paper will be released to you at 09:00hrs (UK Time) and the submission deadline is 1300hrs (UK Time) on the day of the exam, however it is anticipated that you will need no more than 2 hours to complete the assessment. You will only be permitted to submit your work once, and a similarity report will not be visible. Late submissions will not be marked. Due to the anticipated demands on our IT networks, early submission is STRONGLY encouraged.

Please type your answers in a separate file using Microsoft Word and upload a Word or PDF version to the submission link available on the module Moodle page. Please note that photos of handwritten formulas, calculations, models, diagrams can be included in the document. However, photos of text based answers are not allowed.

Build a portfolio using the data on the monthly rate of return for shares x and y and S&P 500 market index for the past year.

a) Calculate the expected returns of S&P 500 and the expected return on a portfolio consisting of equal proportion (50%) of shares x and y. [20 marks]

b) Calculate the standard deviation for both shares and S&P 500. Taking standard deviation as a measure of risk, compare the riskiness of market index S&P500 with both shares. [20 marks]

c) Calculate the correlation coefficient between share x and y; share x and S&P 500, and share y and S&P 500. Using correlation coefficient as a guide to eliminate riskiness through diversification, which combination of shares and market index would you recommend and why? [25 marks]

d) Taking standard deviation as a measure of risk

1. Calculate the average risk of the share x and the market index, S&P 500 [5 marks]
2. Calculate risk of a portfolio consisting of 50% of share x and 50% of market index S&P 500 [15 marks]
3. Explain why the portfolio risk calculated in ii) above is lower than the average risk calculated in i)? [15 marks]

Suppose students in a finance module had an average mark of 54 with a standard deviation of 18 marks.

Assuming the marks were normally distributed calculate the probability that:

1. a student has first class mark, i.e. has obtained a mark of 70 or above. [15 marks]
2. a student has passed the module but did not achieve 1st class mark, i.e. their marks is above 40 but less than 70. [15 marks]
3. If there were 200 students on the course, how many were expected to have passed the course? (Minimum pass mark is 40) [10 marks]

Suppose the average mark was 50 on the MSc course as whole. Using this average mark and the data from part I above, answer the following questions:

1. Formulate the null and the alternative hypotheses to test if the average mark in finance module is indeed higher than the average mark on the MSc course. [10 marks]
2. Calculate the appropriate test statistics for the null hypotheses in a). Using a 5% significance level and the critical value approach what is your conclusion? [20 marks]
3. Conduct the same test using the p-value approach and compare your conclusion with part b). [15 marks]
4. When is poisson distribution appropriate explain using examples and what are the properties of this distribution?

a) Interpret the impact of each independent variables on the log of wages (lw) in and explain whether the estimates are as expected giving your reasons. You must pay attention to the units of measurement.

b) Test for the statistical significance of each independent variable on the log of wages (lw) in Model 3.1 using 1% significance level. You must clearly explain each step of the procedure you use. [25 marks]

c) Evaluate Model 3.1 using the F-test and the coefficient of determination, R2 . Use 5% significance level where required. Comment which measure provides better evaluation of the model and why [30 marks]

d) Based on the above answers, how can Model 3.1 be improved? (Word count: max 100 words