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) −$15,154. B) −$15,495. C) −$15,280. Their first step is to find the forward 90-day LIBOR 60-days from now. If that’s the first step, then 60 days from today–the 30 day mark–is at the 90 day mark. They imply in the answer that it expires at the 60 day mark and settles at the 150 day mark? wtf?
Drawing a timeline always helps : 30days (1) (2) Point -1 represents today ; 2 FRA expiration ; 3 Loan expiration Initially FRA was priced at 5%. You have to deannualize the rates before calculation begins. Based on 60 day current rate and 150 day current rate. first step is to find 90 day implied forward rate. If that is less than 5%, short position has pay off from lending at above market rate. This pay off later has to be discounted at 150 day current rate. [since this happens at end of the loan period] I’m just tired to make the calculations …sorry man…! but HTH
Rcontract = 0.05 Rnew = [R150/R60 - 1]*360/90 InterestSaving = (Rcontract*90/360 - Rnew*90/360)*notional Loss = InterestSaving*Z150 Ans A? 15154.88290
swaptiongamma Wrote: ------------------------------------------------------- > Rcontract = 0.05 > Rnew = *360/90 > InterestSaving = (Rcontract*90/360 - > Rnew*90/360)*notional > Loss = InterestSaving*Z150 > > Ans A? 15154.88290 +1
But see, what I don’t understand is, we are at day 30 now. So day 60 is 30 days from now. So don’t you want the 90 day rate 30 days from now, not the 90 day rate 60 days from now?
you are re-evaluating the FRA 30 days from contract initiation. Your original 90 days is 60 days away. and your original 180 days is now 150 days away… You have moved forward lock, stock and barrel 30 days forward. Based on the original forward rate (90-150) what should be the new 60-150 day contract worth because of the movement of the interest rates? Based on your original 90-180 days schedule you were getting some payoffs (read cash flows). Now what is the change in interest rate doing to those payoffs?
cpk123 Wrote: ------------------------------------------------------- > you are re-evaluating the FRA 30 days from > contract initiation. Your original 90 days is 60 > days away. and your original 180 days is now 150 > days away… > > You have moved forward lock, stock and barrel 30 > days forward. Based on the original forward rate > (90-150) what should be the new 60-150 day > contract worth because of the movement of the > interest rates? > > Based on your original 90-180 days schedule you > were getting some payoffs (read cash flows). Now > what is the change in interest rate doing to those > payoffs? LOL…CPK why the lock, stock and barrel reference in your response? I like the explanation though.
So it was originally a 3 X 6 FRA, with expiration on day 90 and settlement on day 180?That’s what tripped me up. I couldn’t figure out the terms of the FRA from the way it was worded.
3 x 6 FRA -> means your underlying is (6-3) months - 90 day Interest Rate. You sign up for the Loan in 3 months, and expiration is at 6 months.
the lock, stock and barrel reference - was how I tried to picture it. I am now 30 days and there. forget the zero time… you are at 30 days… is what I tell myself all the time