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Eco 20041 Asset Pricing;

Assignment 2
Provide full details and explain your answers carefully. This assignment will be marked using a 30-point scale.

Interest rates
Suppose that today’s (date 0) term-structure of spot interest rates for safe zero-coupon bonds is as follows:
Maturity, in years   Interest rate (r)
1   7%
2   9%
3   12%
4   13%
5   14%
Investors trade forward contracts at specified rates f2, f3 f4 and f5 for one-year forward transactions for years 2, 3, 4 and 5 respectively. Investors may freely borrow and lend at any quoted rate.
(a) There is a 5-year Annuity T which pays £50 annually. What is the current price of Annuity T? [8 Marks]
(b) Suppose that all the spot rates in current term structure increase. Show how the price of Annuity T will change? [4 marks]
(c) If you agree today a forward delivery of Annuity T in two years (at date 2), what will be the no-arbitrage forward delivery price under the current term-structure? [8 Marks]
(d) Assume that bank XYZ offers a forward rate f3 of 16% for year 3 (from date 2 to date 3). Given the current term-structure, show how you can have an opportunity to earn arbitrage profits. Please describe your trading strategy (Assume that the amount of your initial borrowing or lending (or both) at date 0 is £100. Please describe your actions and related cash flows at all relevant dates). [10 Marks]

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