36. The following market-based FRA rates are provided.
| Period (months) | Forward Rates (%) |
| 0-6 | 3.00 |
| 6-12 | 4.00 |
| 12-18 | 5.00 |
| 18-24 | 6.00 |
Answer the following questions:
(a) Find the price of a two-year maturity security with a coupon of 4.5%.
(b) Find the price of a six-month bond future on this bond.
(c) What is the price of a twelve-month bond future on this bond.
(d) Find the durations of all the three instruments above.
(e) If we invest $100 in the two-year bond, then how many units of the two futures contracts should we buy such that we have equal numbers of units in each contract, and we optimize our duration-based hedge?
(f) After setting up the hedge, the next instant, the entire forward curve shifts up by 1% at all maturities. What is the change in the value of the hedged portfolio? Is it zero? If not, explain the sign of the change.
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