Question 1
When answering the question, state any additional assumptions you may need to make. Show all working/calculations.
(a) You have been hired to advise an investment management firm. The firm currently has assets held as cash worth £100 million and liabilities that consist of payments of £15 million in 2 years, £20 million in 3 years, £30 million in 4 years, and £50 million in 5 years. The term structure is flat at 4% per year.
(i) What is the present value of the liabilities? [2 marks]
(ii) What is the Macaulay duration of the liabilities? [3 marks]
(iii) In terms of risk management, explain what your concern is for the investment man- agement firm from holding all their assets in cash. [2 marks]
(iv) The following portfolios all have a present value of £100 million. Which one of the portfolios do you recommend the investment management firm invest its cash in to manage interest rate risk? Explain. [2 marks]
Portfolio A Portfolio B Portfolio C Portfolio D Portfolio E Modified Duration 4.7 3.5 4.2 3.8 2.4
(v) Explain why the strategy you recommend in part (iv) is not a perfect hedge.
[2 marks]
(b) You are a bond trader in the City of London and observe the following information on U.K. default-free government bonds, where all bonds pay annual coupons and have a par value of £100:
Price Maturity Coupon Rate
Bond A £89.760 2 years 4%
Bond B £93.318 2 years 6%
Bond C 2 years 12%
(i) Using Bond A and Bond B, what is the current term structure of interest rates?
[4 marks]
(ii) Explain the current term structure of interest rates from part (i) using term structure theories. [6 marks]
(iii) How many units of Bond A and Bond B do you need to buy/short to replicate the cash flows of Bond C? What is the price of this replicating portfolio? If Bond C is currently trading in the market for £103, is there an arbitrage opportunity? If so, clearly detail the arbitrage strategy and show all resultant cash flows. [4 marks]
