Answer ALL 4 questions.

Total marks: 100

*Show all steps in your calculations clearly.  For each question, write a brief report explaining your choice of method, analysing your findings and discussing any limitations of your results. (Refer to the final page for report writing guidelines.)

Question 1. (Total marks: 30)

This question consists of parts a, b and c. Answer all parts of the question.

The table below gives the annual total returns on the MSCI World Index from 2012 to 2021. The returns are in the local currency.

Year

Return

2012	16 .54%
2013	27 .37%
2014	5 .50%
2015	−0 .32%
2016	8 . 15%
2017	23 .07%
2018	−8 .20%
2019	28 .40%
2020	16 .50%
2021	22 .35%

a. Describe the central tendency of the distribution.                      (10 marks)

i) Calculate the mean return.

ii) Calculate the median return.

iii) Identify the mode(s) of the returns.

b. Describe the performance of the above index.                           (10 marks)

i) Calculate the arithmetic mean return and geometric mean return.

ii) Comment on the difference between the above results and suggest why one of them is more commonly used in investment calculations.

c. Describe the dispersion of the distribution.                                 (10 marks)

i) Calculate the range.

ii) Calculate the variance.

ii) Calculate the standard deviation.

iv) Suggest whether range or standard deviation is more appropriate in describing dispersion of a distribution. Explain briefly.

Question 2 (Total marks: 20)

This question consists of parts a, b, c and d. Answer all parts of the question.

The expected sales of a product in a city are assumed to be affected by the per capita discretionary income (PCDI) and the population of the city.  Thus, the following model is hypothesized as:

E(Y) = B0 + B1 X1 where,

Y = Sales (in thousands of dollars)

X1 = Per Capita Discretionary Income (in dollars)

A sample of 15 cities, along with their sales, and per capita discretionary income, is given below:

PCDI (X1)          SALES (Y)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

2450

3254

3802

2838

2347

3782

3008

2450

2137

2560

4020

4427

2660

2088

2605

162

120

223

131

67

169

81

192

116

55

252

232

144

103

212

a. Graph the data with appropriate labelling.                                                                         (5 marks)

b. Calculate the linear correlation coefficient, and comment.                                               (5 marks)

c. Find the regression equation.                                                                                             (5 marks)

d. Interpret the regression equation, and comment on the significance of the relationship.  (5 marks)

Question 3 (Total marks:30)

This question consists of parts a to f. Answer all parts of the question.

An analyst is conducting a hypothesis test to determine if the mean time spent on investment research is different from three hours per day. The test is performed at the 5% level of significance and uses a random sample of 64 portfolio managers, where the mean time spent on research is found to be 2.5 hours. The population standard deviation is 1.5 hours.

a. Determine the null and alternative hypotheses.                                                      (4 marks)

b. Determine whether this is a one-tailed or two-tailed test.                                       (2 marks)

c. Calculate the z statistic.                                                                                           (6 marks)

d. Calculate the critical z-value(s) of the test statistic.                                                (6 marks)

e. Determine the population mean under an appropriate confidence interval.           (8 marks)

f. Determine whether the null hypothesis should most appropriately be rejected.     (4 marks)

Question 4 (Total marks: 20)

This question consists of parts a, b and c. Answer all parts of the question.

a. Choose between the two options below. Explain your answers with detailed calculations.   (Assume that the time deposit rate is 3% per annum.)                                          (10 marks)

•    Option 1: you deposit £10,000 today and receive £9,900 a year later .

•    Option 2: you receive £9,900 today and pay £10,000 a year later .

 

b. Your client, Magdalene, invests £1,000 in an exchange traded fund today, expecting that it will generate 12% per year. How much will she have in the account in two years?        (5 marks)

c. Joshua expects to receive a cheque of £25,000 in three years and the discount rate is 9%. Calculate the present value.                                                                                                        (5 marks)