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P1.T3.207. Hull's interest rate futures (II)

Suzanne Evans

Well-Known Member

207.1. Assume the following zero (spot) rate curve with continuous compounding: 1.0% (1 year), 1.6% (2 years), 2.0% (3 years), and 2.4% (4 years). What is the value of a forward rate agreement (FRA) that will pay a fixed rate of 3.0%, measured in annual compounding, on a notional of $10.0 million between the end of the second and third year?

a. -15,109
b. -5,446
c. +3,777
d. +16,043

207.2. A company will receive $100.0 million in one year, an amount which will then (i.e., in one year) need to be invested for the subsequent six-month period. In order to hedge this future interest rate risk, the company sells (take a short position in) a 12 x 18 forward rate agreement (FRA) to Counterparty C. Each of the following is true EXCEPT:

a. In the short FRA position, the company will be receiving a fixed rate and paying a future spot rate
b. The FRA is economically similar to borrowing the present value of $100.0 million for one year and investing the proceeds for 1.5 years
c. The duration of the FRA is approximately 1.5 years (or ~ 18 months)
d. Counterparty C has a long FRM position and consequently will benefit from an increase in rates

207.3. Assume the 360-day LIBOR zero rate has been calculated as 2.40% with continuous compounding and an actual/360 day count convention. Also, the Eurodollar futures quote for a contract maturing in 360 days is 97.00. Which is nearest to the implied 450 day (15-month) LIBOR zero rate with quarterly compounding?

a. 1.99%
b. 2.53%
c. 3.10%
d. 4.27%