30 days ago, J. Klein took a short position in a $10 million 90-day forward rate agreement (FRA) based on the 90-day London Interbank Offered Rate (LIBOR) and priced at 5%. The current LIBOR curve is: 30-day = 4.8% 60-day = 5.0% 90-day = 5.1% 120-day = 5.2% 150-day = 5.4% The current value of the FRA, to the short, is closest to: A) −$15,495. B) −$15,154. C) −$15,280.
B
R(150) = 1.0225 R(60) = 1.00833 1.0225/1.00833 - 1 = 0.01405294 0.01405294*360/90=0.05621176 (0.05-0.05621176)*90/360 = -0.00155294 -0.00155294/1.0225 = -0.0015187677 -0.0015187677*10000000= -15187.677 = closest to B?
I get B
I just got 15,158.92… B. similar to SWG, tiny rounding diff i’m sure.
1+0.05*(90/360) = 1.008333333 1/1.00833333333 = .9917355 1+0.05*(90/360) = 1.0125 1+(0.054*(150/360)) = 1.0225 1.0125/1.0225 = .99022 (.9917355-.99022)* 10,000,000 = 15,154.88 B
Thanks for the help. I’ve never fully grasped this FRA Business. What is the formula I need to jam in my head?
Trick is not in the formulas. I’d recommend you go through a few more examples, and in each one, draw out the timeline of what is done. Drawing the timeline helps in determining which rates need to be used to calculate the swap rate, and also which rate you would need to discount.
I use this… (1/1+ rx new) - (1+ Fraprice/1+rynew) where rx is the periodic rate on 60 day libor in this case ry is the periodic rate on 150 day libor in this case and the fra price is periodic based on 90 day in this case. so basically this was a 3*6 FRA - after 30 days i think of it as a 2*5 so rx is 2 months (60days) ry is 5 months (150 days) and the fra price is periodic based on the gap between 2 and 5, 3 months (90 days) thats just how i think about it, works for me.
R(150) = 1.0225 R(60) = 1.00833 1.0225/1.00833 - 1 = 0.01405294 0.01405294*360/90=0.05621176 .0125-.01405294 * 10,000,000 = 15,530 15,530/1.0225 = 15,187 B? this question sucks because depending on how many decimals you go out you can get an answer close to any of the above
mp2438 Wrote: ------------------------------------------------------- > Trick is not in the formulas. I’d recommend you go > through a few more examples, and in each one, draw > out the timeline of what is done. Drawing the > timeline helps in determining which rates need to > be used to calculate the swap rate, and also which > rate you would need to discount. I’m starting to scramble. I’m hitting the tough parts of the curriculum. Rest assured it might by an FRA Friday for me!
No need to cram anything here… You just find the implied forward rate on the said date after FRA initiation. The difference between FRA Price (rate initially determined) and the rate on the date is applied to notional principle and discount it back to the date at which you are valuing the FRA. I draw a timeline and never go wrong on this. Also take care to deannualize the rates as and when required… I’m not sure if that helped…
i really hope we don’t have to wory about rounding like this on the test
DanLieb Wrote: ------------------------------------------------------- > i really hope we don’t have to wory about rounding > like this on the test The answers won’t be that close together. They will be so far apart the answer will be obvious. That’s one thing I noticed about the Level 1 exam.
got 15,154.882903271434056052860231567. 
Any recommendation to use calculator? So many strokes, could get it wrong on the exam day.
Warning: Stupid question —> Why is it that you raise 1+r to a power in one present value calculation but in another you multiply r? Does that make sense to you? PVC = $30 / (1.05)^183/365 = $29.28. The present value of the FRA at settlement is: 38,000 / {1 + [0.042 × (180 / 360)]} = 38,000 / 1.021 = $37,218
^ libor convention - they use simple multiplication based on 360 day year - no other reason.
I get everything but the time line use to select the appropriate R. When I “draw the timeline” I am getting a 1 x 4 (90 day loan 30 days ago). So I want to look at R120 and R30. How did you know to use 2 x 5 R150 and R60?
bunky, HTH ! At the Initiation : t=0| -------------------------------------- t=90|------------------------------------ t=180| After 30 days : t=30| -------------------------------------- t=60|------------------------------------ t=150| We just move 30 days ahead in time.