1. The duration of a bond that makes an equal payment each year in perpetuity is (1 _ yield)/ yield. Prove it.
2. What is the duration of a common stock whose dividends are expected to grow at a constant rate in perpetuity?
3. a. What spot and forward rates are embedded in the following Treasury bonds? The price of one-year strips is 93.46%. Assume for simplicity that bonds make only annual payments. ( Hint: Can you devise a mixture of long and short positions in these bonds that gives a cash payoff only in year 2? In year 3?)
Maturity (year) | Coupon (%) | Price (%) |
4 | 2 | 94.92 |
8 | 3 | 103.64 |
b. A three-year bond with a 4% coupon is selling at 95.00%. Is there a profit opportunity here? If so, how would you take advantage of it?
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