Financial Engineering – IC302
Autumn Term 2020/1
Seminar 2: Simple Interest Rate Derivatives Questions
1. Suppose that an investment will pay you $110.25 in two years in exchange for investing $100 today. Calculate its annual percentage return based on:
(a) annual compounding
(b) semi-annual compounding
(c) quarterly compounding
(d) continuous compounding
2. Consider a market that contains risk-free bonds with the following zero-coupon yields (all expressed with annual compounding):
(a) Does this market contain an arbitrage opportunity? Explain your answer.
[Hint: Begin by calculating the discount factors.]
(b) What practical factors might limit the ability of market participants to eliminate arbitrage opportunities in bond markets?
3. Consider an investor who plans to make an investment with principal amount $10 million for a three-month period beginning on 16 December 2020. The investment will pay interest at a rate equal to 3-month USD LIBOR. She would like to use Eurodollar futures to lock in the interest rate on her investment. The December 2020 Eurodollar futures contract is currently trading at a price of 99.755.
(a) Should she go long or short Eurodollar futures?
(b) How many futures contracts should she trade?
Maturity (years)
1
2
3
Zero-coupon yield
3.09%
2.60%
1.55%
(c) Suppose that the investor implements the hedge you have just described, and the USD LIBOR fixing for the three-month period covered by the investment and the futures contract turns out to be 0.195%. Calculate the total profit or loss on her futures position and the interest rate that she will earn on her investment after taking into account that profit or loss.
(d) Suppose that the investor implements the hedge you have just described, and the USD LIBOR fixing for the three-month period covered by the investment and the futures contract turns out to be 0.295%. Calculate the total profit or loss on her futures position and the interest rate that she will earn on her investment after taking into account that profit or loss.
(e) Has the investor succeeded in locking in the interest rate on her investment?
(f) What factors might lead hedges based on Eurodollar futures to perform less perfectly than in this simple example?
4. Suppose that you are an international bank that can obtain funding and deposit funds at LIBOR. For the purpose of this question, you may also assume that you discount derivative cash flows at LIBOR. Explain how you could use a FRA to lock in the interest rate for a floating-rate loan of $N million in which you receive money at date 𝑡! and repay the loan with interest at rate 𝐿”! at date 𝑡# , where 𝐿”! is the LIBOR rateatdate𝑡! fortheperiod𝛿=𝑡# −𝑡!.
[Hint: Be sure to take into account the fact that the FRA settlement will take place at date 𝑡!.]