ACF6004AA Financial Modelling E1
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MODULE CODE: ACF6004AA
ELEMENT: E1 (Coursework in lieu of Exam)
MODULE TITLE: Financial Modelling
SUMMER REFERRAL TASK
Deadline: 9 am on Monday 14 August 2023
Submission procedure: Via the module page on the DLE
REFERRAL TASK:
Instruction to Candidate
Answer All Questions
Question 1
Stock Z is currently traded at £9.00 per share on the market. It is expected to either grow to £11.00 or fall to £6 in a period of 3 months. The risk-free interest rate is 5.00% pa. You are asked to value the following two options written on stock Z and maturing in 3 months:
. A call option with a strike price of £10.00
. A put option with a strike price of £8.00
(a) What should be the price of the call option? 5 marks
(b) What should be the price of the put option? 5 marks
(c) Discuss the risk-neutral valuation principle in option pricing. Explain why this valuation principle can be and is applied while both the stock and the option are risky securities. 5 marks
(Total: 15 marks)
Question 2
Information on two funds is collected as follows:
. Fund Ω has an expected annual return of 11.25% and the standard deviation of its annual is 9.98%
. Fund Σ has an expected annual return of 7.83% and the standard deviation of its annual return is 6.24%
The correlation between the returns on the two funds is 0.71
Required:
(a) Construct an optimal portfolio with these two funds and solve for the weights of the two funds in the portfolio, assuming the risk-free interest rate is 2.50% per annum. 5 marks
(b) What are the expected return and risk of the portfolio you have made in (a)? 5 marks
(c) If the risk-free interest rate is expected to fall, will you increase or reduce the allocation to fund Σ in the risky portfolio? If the risk-free interest rate is expected to fall, will you increase or reduce the allocation to fund Σ in the risky portfolio? Why? 2 marks
(d) Now the risk-free interest rate is expected to fall to 2.00% per annum, solve for the weights of the two funds in the portfolio under this scenario. 5 marks
What are the expected return and risk of the portfolio you have made in (d)? 3 marks
(Total: 20 marks)
Question 3
The following three bonds all mature in four years. They all have a principal or par value of $100 while coupons are paid annually.
|
|
Bond A |
Bond B |
Bond C |
|
Coupon rate |
4% |
6% |
6% |
|
YTM |
6% |
6% |
4% |
Required:
(a) Calculate either Macaulay duration or modified duration for these three bonds. 5 marks
(b) Compare the durations of these bonds and explain why they differ with regard to the differences in their YTM and/or coupon rates. 5 marks
(c) Define bond duration from two perspectives, explain its purpose and use in bond analysis and bond portfolio management. 3 marks
(Total: 15 marks)
Question 4
Assume that stock market returns have a normal distribution with a mean of 6% p.a. and a standard deviation of 18% p.a. Over the last 4 years stock market returns have averaged negative 2% p.a. Your client is very upset and claims that results this bad should never occur:
(a) Construct a 95% confidence interval of stock market returns for a sample of 4 year returns.
(b) What is the probability of negative 2% returns over a 4 year period? (15 marks)
Question 5
We want to test the hypothesis that the mean P.E. ratio of companies that receive a takeover offer is the same as the mean P.E. ratio of companies that do not receive a takeover offer in the same industry. Explain under what conditions we would commit a type 1 and a type 2 error. (20 marks)
2023-08-10