Question

The risk-free yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives LIBOR at the rate of 9% per annum for a six-month period on a principal of $1,000 starting in two years

Answer 1

c. $8.63

Step-by-step explanation:

Missing word "The forward LIBOR rate is 7%. All rates are compounded semiannually. A. $8.88 , B. $9.12 , C. $8.63 , D. $9.02"

Principal = $1000, FRA Rate = 9 % per annum, LIBOR after 2 years = 7 % per annum, Compounding Frequency: Semi-Annual, Risk-Free Rate = 6 % per annum

The FRA matures 2 years or 24 months from now. Further, the Interest Rate that the FRA hedges will create an interest expense only at the end of the LIBOR loan period which is an additional 6 months after the 24 month period.

Hence, Exchange of Interest Expense at the end of 30 Months = (FRA Rate - LIBOR) x Principal (calculated on a semi-annual basis)

= (0.045 - 0.035) * 1000

= $10

Current Value of FRA = Present Value of Interest Expense at the end of the 30 Months Period

= 10 / [1+(0.06/2)]^(30/6)

= $8.6261

= $8.63