Question

Pacific Airline wants to borrow $100,000 6 months later for 3 months with a Forward Rate Agreement. The following table shows bond market information.

Maturity (month)	Zero Coupon Bond Price
3	0.988
6	0.971
9	0.953
12	0.933

(a) What is the forward rate of the FRA (effectively for 3 months)?

(b) Suppose 6 months later, the 3-month annualized spot rate is 5%. What is the settlement amount of the FRA if settle in arrears?

(c) Instead of using an FRA directly, what positions in zero coupon bonds could Pacific Airline use to synthetically create the FRA borrower position?

a. Long 6 months ZCB, Short 9 months ZCB

b. Long 6 months ZCB, Long 9 months ZCB

c. Short 6 months ZCB, Long 9 months ZCB

d. Short 6 months ZCB, Short 9 months ZCB

Answer 1

Part (a)

Forward rate (effectively for three months) = P6/P9 - 1 = 0.971/ 0.953 -1 = 1.8888%

Annualized FRA = 4 x 1.8888% = 7.5551%

Part (b)

Settlement amount = PV of differential interest = [Principal x (Spot - FRA) x 90 / 360] / (1 + spot / 4)^(90/360) = 100,000 x (7.5551% - 5%) x 90 / 360 / (1 + 5%/4)1/4 = 636.79

Part (c)

The correct answer is the first option i.e. option a) Long the 6 months zero coupon bonds and short the 9 months zero coupon bonds

By doing so, the three months forward rate is locked and that's exactly what FRA does.