After 30 days Adams wants to value a $10 million short position in the 2x5 FRA. The 90-day forward rate in 30 days is now 4.14%, and the original price of the FRA was 4.3%. 120-day LIBOR has change4d to 3.92%. The current value of the $10 million FRA under this scenario is closest to: A. -3,948 B. -15,794 C. 3,948 D. 15,794 Answer posted below: The correct answer was C) (.043-.0414)*10m*(90/30)= 4,000 discount back 4,000/1.0392 /\ (120/360) = 3,948 ---- My question is why didn’t they use the formula for value of the FRA on day G like in the CFA Book, 1/1+L(h-g) (h-g/360) - 1+FRA (h,m) (m/360) / 1+L(h+m-g) (h+m-g/360)
I don’t understand why I can’t get the answer. I also don’t know why they used that formula as you pointed out. 1/1+.0414(60/360) - (1+.043(90/360))/(1+.0392(120/360)) which gives -.007913214 which is a gain to the short.
I am not aware of that formula but this is how i did it FRA-value-at-time-t0 = 0.043 FRA-futureValue-at-time-t60 = 0.0414 So the rates have fallen and SHORT should gain. To quantify the gain, (0.043 - 0.0414)*90/360 * 10m = 4000. This is the gain to short at the end of loan duration i.e at time-t150. We need to discount it back to find the gain at the FRA contract end date i.e. at-time-t60 /[1 + 0.0392/3] = 3948.4074 Does this sound correct to you?
That does sound correct and clearly gives the correct answer, however, now I have no idea when I’m supposed to use the FRA on day G formula. I didn’t see the formula in Schweser but the CFA text had several examples of it. When, if ever, would it be used? Any ideas? T/G
dinesh, that is the correct solution. I typically take the same path.
I used a more convoluted way to get to what Dinesh did, except I forgot he went short and chose A.
The complex formula in the CFA book does two things for you 1) It calcs the current 90-day LIBOR 30 days from now (R90 if you will) and 2) discounts the interest payment back to today. But in this case, we are already given the current R90 rate. All we have to do then is find the difference between the original FRA rate and the current rate, R90, and then discount it back by the current R90. The point of reference in the formulas is from the Long position, so in a short position, simply reverse the sign. Follow the Schweser notes method for this topic, much easier to understand.
I think is safe to say that there more simple (dinesh) way i better.