Question

A person SHORT a 60-day FRA on the 45-day LIBOR with a rate of 8% and $2 million notional amount will have the payoff of ____ on day ____, if the spot rate at the FRA's expiration is 9%.

Please provide detailed solution answer is -2472.19; 60

Answer 1

SUGGESTED ANSWER

Forward Rate Agreement ("FRA") is a forward contract on LIBOR (London Inter-bank rate). It implies it is designed to bet on LIBOR. It is an over the counter derivative in which the bank act as a market maker and provide the bid and ask quotes.

In the present case, the FRA is a bet on 15 days LIBOR after 45 days. Selling this FRA is theoretically a contract to invest $ 2 million after 15 days for 45 days at the rate of 8%. However, no actual investment takes place. Instead FRA is cash settled at the present value of the difference between the actual LIBOR and the FRA rate.

In the above problem, the FRA rate is 9 % and actual LIBOR is 8 %. For the customer to be profitable the LIBOR betting should be below 9 percent. Since the actual LIBOR is 8 %., the customer gains and the bank will pay the customer present value of the difference

= [(9% - 8%) of $2 million] * (45/365)

1 + (8% * 45/365)

= 0.00246575342 / 1.00986301369

= $ 0.00244167118 million or $ 2441.67118

Therefore the customer will have the payoff of $ 2441.67 on day 60.