# FRA question

2x5 FRA \$25,000,000 Notional Principal Beginning Libor rates 30 Day 2.6% 60 Day 2.8% 90 Day 3.0% 120 Day 3.2% 150 Day 3.3% 180 Day 3.4% LIBOR Rates After 30 Days: 30 Day 2.2% 60 Day 2.4% 90 Day 3.6% 120 Day 3.8% 150 Day 3.8% 180 Day 3.8% What is the value of the FRA after 30 Days? Best, TheChad

I’ll take a stab. but I’ve yet to master FRA’s. okay, first you have to get the original price, I get that as 3.615% annualized. then the value after 30 days is 43,948 to the float side?

66902?

43763.90703?

FRA rates at t=0 (at initiation) r=(1+.033*150/360 / 1+.028*60/360) -1 r= .904% = 3.62% annulaized at t=30 r* = (1 + .038*120/360 / 1+ .022*30/360) - 1 r* = 4.33% annualized value of FRA at expiration = (4.33%-3.62%) * 25 mil * 90/360 = 44,375 value of FRA at t=30 = 44375 / (1 + .038\*120/360) = 43,820 am i anywhere close??

Initial Price A = ((1+0.033*150/360)/(1+ 0.028*60/360) )-1 =0.009041141 After 30 days B = ((1+0.038*120/360)/(1+ 0.022*30/360) )-1 = 0.010813509 Value of FRA : ((B-A)*25000000)/(1+0.038*120/360) = 43754.9513

I got \$43,351.6. Same numbers as orange but with some rounding.

i get 43,448

Always draw a timeline with FRAs, god they are tricky. I agree that the fixed price originally is 3.616% 1.01375=1.0047x(1+r/4) now 30days later: calc the new fixed price using method above (I get 4.325%). and then I think work out the difference. This is the rate the long will have made, deannualise it and x the notional (I get 44,309?). Since this amount is paid at the end you need to discount it back to today. ooh I get 43,755. I must have done something wrong, perhaps used the wrong discount rate? i used 120 days 3.8%. Unless its down to rounding. Wish I had my notes with me!

swaptiongamma Wrote: ------------------------------------------------------- > 43763.90703? I got the same thing, however, the correct answer in schweser is \$43,943 which is the same as what jut111 had. Jut, how did you arrive at that answer? Best, TheChad

its just rounding, we were all very close.

my fra value forumla courtesy of stalla is: (1/1+ rxnew) - (1 + original Fra price/1 + rynew) were rx is the shorter period rate, ry longer period rate Fra price is in terms of the periodic rate the fra is based on, so in this case .03615 (90/360)

I also got \$43,754.95. Forgive me for repeating the work, but it will help me if I write it all out. Find r at beginning from 60-day rate and 150-day rate. Deannualized 60-day rate = 0.028*(60/360) = 0.00466667 Deannualized 150-day rate = 0.033*(150/360) = 0.01375 Find r as ((1+.01375)/(1+.00466667) - 1) = 0.00904114 0.00904114 is a 90-day rate. 0.00904114*(360/90) = 3.616% Now at Day 30, use 30-Day rate and 120-Day rate. Deannualized 30-day rate = 0.022*(30/360) = 0.0018333 Deannualized 120-day rate = 0.038*(120/360) = 0.0126667 Find r as ((1+0.012667)/(1+0.0018333)) - 1 = .01081351 0.01081351 is a 90-day rate. 0.01081351*(360/90) = 4.325% Find V at expiration for long position as… 25,000,000*(0.01081351 - 0.00904114) = 44,309.21 Discount back to day 30 using the 120-day LIBOR rate 44,309.21/(1+0.038*(120/360)) = 43,754.95

^^^I got the same things Tom…I guess everyone is just off due to rounding as MrGrey pointed out. Best, TheChad

43953

TheChad Wrote: ------------------------------------------------------- > 2x5 FRA > \$25,000,000 Notional Principal > > Beginning Libor rates > 30 Day 2.6% > 60 Day 2.8% > 90 Day 3.0% > 120 Day 3.2% > 150 Day 3.3% > 180 Day 3.4% > > LIBOR Rates After 30 Days: > 30 Day 2.2% > 60 Day 2.4% > 90 Day 3.6% > 120 Day 3.8% > 150 Day 3.8% > 180 Day 3.8% > > What is the value of the FRA after 30 Days? > > Best, > TheChad 43,945.74 (1+(.051*90/360))/(1+(.048*90/360)) = 1.009038 (1+(.038*120/360))/(1+(.022*30/360)) = 1.01082 (.01082-.009038)/(1+.033*150/360)*250000000 = 43945.74