Consider a $1 million 90-day forward rate agreement based on 60-day London Interbank Offered Rate (LIBOR) with a contract rate of 5%. If, at contract expiration, 60-day LIBOR is 6%, the short must pay:
A) $1,652.89. B) $1,666.67. C) $1,650.17.
The correct answer is: $1,650.17.
[(0.06 − 0.05)(60 / 360)(1,000,000)] / [1 + 0.06(60 / 360)] = 1,650.17. Can anybody explain why you have to discount $1,666.67 by [1+0.06*(60/360)] to me? Thanks!
First, I think that this is a 60-day FRA, not a 90-day FRA.
I wrote an article on this which may help: http://financialexamhelp123.com/fras/.
The short answer is that an FRA is very similar to entering into two loans:one long, one short; one fixed, one floating. The difference between an FRA and actually entering into the loans is that the loans would be settled at the end of the 60-day period, whereas the FRA is settled at the beginning of the 60-day period (at the expiration of the FRA. Thus, you take the difference in the rates times the notional amount – what you’d pay or receive 60 days from today – and discount it back to today to settle it.
Note that you discount it at the current LIBOR rate.
Thanks again, Magician!
My pleasure.