2a) The following prices and maturities of zero coupon bonds are given below: ...
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2a) The following prices and maturities of zero coupon bonds are given below:
Maturity (Years)
Price ($)
1
925.38
2
890.00
3
816.30
4
735.03
i) A 10% coupon bond with a maturity of 3 years is currently selling at $1,080.07 in the market. The coupons are paid annually. Strip the bond and determine whether there is an arbitrage opportunity. Clearly explain how you would profit from the arbitrage.
ii) Use the given zero coupon bonds to design a synthetic forward loan that starts 2 years from now (at the end of year 2), and is paid back 2 years later (at the end of year 4). Assume you are the lender in this transaction. How is the interest that you charge over the two years of this loan related to the implied forward rates?
2b) A pension plan will pay me $12,000 per year for a 6-year period, starting next year. My pension fund wants to immunize its position.
i) What is the duration of its obligation to me if the yield curve is flat at 5%?
ii) If the pension fund uses a 4-year zero coupon bonds and a perpetuity with yield to maturity of 5% p.a. to construct the immunized position, calculate the fraction of wealth that needs to be placed in each bond.
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