Question

A financial manager needs to hedge against a possible decrease in interest rates. He decides to hedge his risk exposure by going short on a 3x12 FRA at a rate of 6.50%. The current term structure for LIBOR is as follows:

Term Interest rate

30 days 5.83%

90 days 6.00%

180 days 6.14%

360 days 6.45%

It is now 60 days since the manager took a short position in the FRA. Interest rates have shifted down, and the new term structure for LIBOR is as follows:

Term Interest rate

30 days 5.50%

300 days 5.62%

The market value of this FRA based on a notional principal of $20 000,000 is:

Answer 1

3x12 FRA means that the contract will expire after 3 months and that the loan is to be taken for 12-3 =9 months

After 60 days, Theoretical interest rates for 9 months at the expiry

= (1+ 300 days interest rate * 300/360) / (1+30 days interest rate* 30/360) - 1

= (1+0.0562*300/360) / (1+ 0.055*30/360) - 1

=0.042057 which is the interest rate for 9 months or 270 days

This is equivalent to an annual interest rate of 0.042057*360/270 =0.056076 = 5.6076%

As the FRA was shorted at 6.5% and the interest rate now is expected to be 5.6076% for the 9 month loan, the position is in profit

The value of FRA at the end of loan period

= principal * (contracted rate - theoretical rate) * 270/360

=$20000000*(0.065-0.056076)*270/360

=$133860

Value of FRA today = Present value of $133860 discounted for 300 days

= 133860/ (1+0.0562*300/360)

=$127871.36 which is the required market value of FRA