# FRAs

Can someone please explain which rate we use to calculate this and why? I can’t seem to figure this one out (sorry if its easy, I’m severely challenged when it comes to derivatives…) 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:

90 day forward rate, 90 day LIBOR so 3 x 6 FRA, when it started. Fixed price was 5%. 0…90…180 (at start) now we are 30 days in. so 60, 150 days (1+.054*150/360)/(1+0.05*60/360) = 1.014049587 so long to short will be (.014049587 - 0.0125) [which is 0.05/4] = 0.001549587 since this is paid at the end - discount at the 150 day rate: 0.001549587 / (1+0.054*150/360) = 0.001515488 for 10 Mill 15154.88\$ this is long to short. so for short it is -15154.88\$.

CPK to the rescue as always!

newRate = R150/R60 - 1 InterestSaving = (newRate - contractRate) This saving comes after 105 days, so discount by R150 to get today’s amount Ans for Long = InterestSaving* Z150 Ans for Short = - Long

That’s a more intuitive way to think about it… thanks!

Cool ! CPK

Take a look at this thread from JScott that Banni mentioned from from last year … great explanation. http://www.analystforum.com/phorums/read.php?12,754042,754696#msg-754696

Clama, The post starts saying that Jscott explained even swaps too. Do you know that post too?

cpk123 - any insight into why CFAI does the calculation differently, which equates to a slight difference of the amount owed to short. I come up with the same as you when doing the Schweser way but last night I noticed CFA does it slightly different. when calculating the value they use: 1/(1+60day rate(90/360) = 1.00833) - (1+ intitial price (5%)(90/360)=1.0125 / (1+150 rate (5.4%)(150/360)=1.0225 =.99173-.99022 = .00151 .00151 * 10,000,000 = 15,100 15,100/1.0228 = 14,763

in the cfai book for this session - they do a lot of rounding related stuff, I have seen. so you might find differences in the answers

i dont think its a difference of rounding. they just do the calc a little different. Same thing happened last night on CFAI questions. I came up with an amount of \$8,500 and CFAI answer was \$8,100. Just wondering if I am doing something wrong. If they had both answers on the test we would be screwed.

MrGrey Wrote: ------------------------------------------------------- > cpk123 - any insight into why CFAI does the > calculation differently, which equates to a slight > difference of the amount owed to short. I come up > with the same as you when doing the Schweser way > but last night I noticed CFA does it slightly > different. when calculating the value they use: > > 1/(1+60day rate(90/360) = 1.00833) - (1+ intitial > price (5%)(90/360)=1.0125 > > / > > (1+150 rate (5.4%)(150/360)=1.0225 > > =.99173-.99022 = .00151 > > .00151 * 10,000,000 = 15,100 > > 15,100/1.0228 = 14,763 I think your formula may be a little off…the CFAI says it should be: (1 / (1 + 60 Day rate (60/360))) - ((1 + FRA Rate (90/360))/(1 +150 Day Rate (150/360))) (1 / (1 + 5%(60/360))) - ((1 + .05(90/360))/(1 + 5.4%(150/360))) Which gives the same exact answer as cpk. I am still trying to figure out how to do it the schweser way… Best, TheChad

my forumla was most likely off. I was going off memory and last night was the first time I noticed CFA does it a little different. It was late and I was tired so maybe I was delirious. all I know is I was coming up with slightly different answers.

MrGrey Wrote: ------------------------------------------------------- > my forumla was most likely off. I was going off > memory and last night was the first time I noticed > CFA does it a little different. It was late and I > was tired so maybe I was delirious. > > all I know is I was coming up with slightly > different answers. I hear ya…Derivatives are killing me…I am getting frustrated because the formula that CFAI provides does not come to the same answers as schweser in some instances… 5 weeks seems like such a short time… Best, TheChad

just keep plowing through. these little nuances now will help down the line.

Aimee Wrote: ------------------------------------------------------- > Can someone please explain which rate we use to > calculate this and why? I can’t seem to figure > this one out (sorry if its easy, I’m severely > challenged when it comes to derivatives…) > > 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: 90 day contract that starts in 90 days so 180 days or a 3X6 contract. 30 days have passed so we use 60 day rate and 150 day rate. Unannualize the rates for everything. .05*60/360 & .054*150/360 --> (1+.054*150/360)/(1+.05*60/360) .01404 - .05/4 = .00154/(1+.054*150/360)*10000000 = 15,061.1 Now short is paying fixed and long is paying floating. Floating > fixed so long pays short this amount. (I believe)