FRA - Example CFAI p. 15

CFA Level II Derivatives
#1

On page 15 CFAI Vol. 6 2014 is an example referring to the FRA payoff formula.

Short summary of the data given:

  • FRA expiring in 90d

  • underlying 180d LIBOR

  • 180d LIBOR at expiration (in 90d) is 6.0%

  • dealer quotes 5.5%

  • notional principal 10 million

I understand the formula and so on; however, why we discount the payoff with 1+0.06(180/360) and not with 1+0.06(90/360) since 90 days have been already elapsed? I know that the notes say that this is correct. But, do we discount 90 days “too much” using 180 days?

#2

The FRA in question is essentially an agreement to enter into two 90-day loans starting 90 days from today: a fixed-rate loan and a floating-rate loan. Because the loans would be paid at the end of the loan period, the payoff of the FRA is based on paying 180 days from today; that’s why you discount for 180 days, not for 90 days.

I wrote a couple of articles on FRAs that may be helpful:

#3

man, I just love you (do not get me wrong smiley)

#4

I get the same thing from my horse, but with him it’s for carrots, apples, or peppermints.

#5

Now I get it: 90 + 90 = 180. smiley Sometimes it is much more easier than I think. Thanks @ S2000magician

#6

My pleasure.