Question 4 The term structure of risk-free interest rates is flat at 1% per year. Consider the following risk-free bonds

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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 Bond 1 0%
Bond 2 5%
Face value € 100
€ 100
Maturity 1 year 2 years
Price
€ 99.01 € 107.88
a) What is the yield-to-maturity of Bond 2?
(10 marks) (10 marks)
b) Determine the Macaulay duration of Bond 1 and the Macaulay
duration of Bond 2?
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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)