Fra Rates & Bond Hedging

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Finance 562 - Implied Forward Rate & Bond Duration Hedging Homework 0. Assume that the LIBOR curve is flat with the yield for all maturities from overnight to one-year equal to 1.25%. Given this information, what would the FRA rates be for the following maturities: 1) 3-month X 6-month 2) 6-month X 9-month 3) 9-month X 12-month 4) 6-month X 12-month Answer the four questions below: 1. You estimate that the Cheapest-to-deliver bond on the T-bond futures contract has a Macauley duration of 10.2 years. You want to hedge a medium-term Treasury portfolio that has a Macauley duration of 4.0 years. A T-bond futures contract has a notional value = $100,000. The yield to maturity on the CTD bond and on the portfolio are both 9.50 percent (9.50%). Your portfolio has a market value equal to $120 million and the decimal equivalent T-bond futures price is equal to 68.91. For simplicity’s sake assume the conversion factor of the CTD Bond = 1.0000 and the that the relative yield change = 1.00. How many T-bond futures contracts would you use to hedge the $120 million portfolio? [pic] 2. James Brown has just returned from a seminar on using Treasury futures for hedging purposes. Based on what he has learned, he reexamines his decision to hedge a $500 million face value portfolio of longer-term debt that his firm plans to issue. He is currently hedging with a short position of 5,000 T-bond futures contracts ($100,000 notional value per contract). If the debt could be issued today, it would be priced at 124-16/32 to yield 4.5 percent (4.5%). With its 6% coupon and 30 years to maturity, the Macauley duration of the debt would be 15.80 years. On the futures side, the futures prices are based on the cheapest-to-deliver (CTD) bonds, which are trading at 134-24/32 to yield 4.0 percent (4.0%). These bonds have a Macauley duration

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