Question 4

The term structure of risk-free interest rates is flat at 1% per year. Consider the following risk-free bonds with annual coupon payments: Coupon rate	Face value	Maturity	Price
Bond 1	0%	100	1 year	99.01
Bond 2	5%	100	2 years	107.88

a) What is the yield-to-maturity of Bond 2?

(10 marks)

b) Determine the Macaulay duration of Bond 1 and the Macaulay duration of Bond 2?

(10 marks)

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c) Consider Portfolio P which is composed of some long positions in Bond 1 and some short positions in Bond 2 such that the value of the portfolio is zero. If the yield curve shifts up, does the value of Portfolio P: (i) increase; (ii) decrease; (iii) does not change; (iv) may either increase or decrease. [Justify your answer in 1 line.]

(10 marks)

d) (10 points) Assume for this question only that a 2-year risk-free zero-coupon bond with face value 100 is trading at 99. Is there an arbitrage opportunity? If yes, find an arbitrage strategy that uses only Bond 1, Bond 2, and the zero-coupon bond. All the bonds are infinitely divisible. [Clearly show the exact composition of your portfolio, but you are not asked to show the arbitrage table with the cash flows.]

(10 marks