Calculator help / FRA / What am I doing wrong???

I keep coming up w/ the wrong value of FRAs even though I’m setting up the equations correctly. What am I doing wrong???

no-arbitrage FRA rate = 6.01% for a 3 x12 FRA

45 days into FRA, what is the value of the FRA assuming a $10,000,000 notional sum, new FRA rate of 5.98% and a 315-day Euribor of 5.95%?

numerator: 10 million x (.0598 - .0601) x 270 / 360 = -2,250

denominator: 1 + (.0595 x 315 / 360) = 1.0521

numerator / denominator = -2,250/1.0521 = -2,138.58

But the answer is -2,195.14

Are you sure about the 6.01% and 5.98% rates?

Nothing else stands out.

I thought the formula for valuing a FRA used the initial FRA rate set at the start as follows for valuing on day “g”:

Vg(0,h,m) = 1 / 1+L(h-g)(h-g/360) - 1+FRA(0,h,m)(m/360) / 1+L(h+m-g)(h+m-g/360)

So shouldn’t the question provide the new 45 day LIBOR rate too (h-g) = (90-45)

And shouldn’t the 1+FRA be the initial 5.98% FRA rate - not the new 6.01%.

…or am I completely missing something?

I’m sure the formula you are using is to value a FRA at expiry, not at a point in time before expiry.

EDIT: Actually I guess if they give you the new FRA rate explicitly then the above may be a moot point.



This is Wiley practice question 25 for reading 47.

I would think it’s an error, except my calculation for the value of the FRA is off on every question. - Close enough to guess the answer, but not good enough otherwise.

And how about if you use the formula below:

Vg(0,h,m) = 1 / 1+L(h-g)(h-g/360) - 1+FRA(0,h,m)(m/360) / 1+L(h+m-g)(h+m-g/360)

Does that result in a correct answer? It is taken from the curriculum page 33-35 of Volume 6, the Derivatives book.

Bloody hell. You know how to read that formula? IMPRESSIVE!

If I apply the formula, my calculation is still off but I’m closer…

Here’s the input:

FRA(0,90,270) = .0601; $10 million notional contract

g = 45 days; h = 90 days; m = 270 days

h-g = 45 days. L(h-g) = .0555

h+m-g = 315 days. L(h+m-g) = .0595

Vg(0,90,270) = 1 / 1 + [L(h-g) x 45/360] - [1 + (FRA(0,90,270) x 270 / 360)] / [1 + (L(h+m-g) x 315/360]

= 1/(1 + .0555x45/360) - [1 +(.0601x270/360)]/[1 +(.0595x315/360)]

= 1/1.0069 - (1.0451 / 1.0521)

=(.9931 - .9933) x $10 million notional contract = 2,000

I’m still kind of upset that the value I calculated is off. I think it has to do w/ rounding.

If those are the figures provided, without rounding it comes to:

(0.993110297 - 0.993358284) x 10mill = -2479.87

That is quite far away from the answer given as -2195.14.

Seems like we’re missing something…

Are you able to reproduce all the question details/info here? (without plagiarising I’m not sure if that is possible ;))

This is an item set question. The first question is:

The no-arbitrage FRA rate for the 3 × 12 FRA is closest to: Answer = 6.01

The second question is:

Suppose 45 days later, the 45-day Euribor is 5.55% and the 315-day Euribor is 5.95%. Given the notional principal of $10m, the value of the long position is closest to:

  1. −2,250
  2. 5,731.34
  3. −2,195.14

Answer = C

Jeez I’m stumped then…Given th einfo provided I would have calculated it as I outlined above.

Either Wiley have got it wrong, or someone is going to come along and make us both look very silly :wink:

Does it explain their working behind their answer anywhere?

I’m intrigued…

Their answer calculation is shown in my original post. I thought I was just doing something funny w/ my calculator. Anyway, I can’t come up w/ their answers in the reading examples or problem sets.

Thanks so much for taking the time to work through this problem.

No problemo, sorry I couldn’t actually be of any help haha

I ran into the same issue, calculated the same answer you did, and I’m convinced there’s an error. I’m almost positive that the net value to the long at t=360 is -2,250. If that assumption is correct, the annualized interest rate you would need to use to discount it to t=45 in order to get -2,195.14 is 2.8562%. Definitely not the market rate of 5.95%.

The examples in the study guide work out just fine though (I had to use 5 or 6 decimals for most of them).

@penguin. I think you are right about the -2,250. It appears that they are trying to trip up people that forget to discount. I am using Schweser and running into a similar situation. I have been expanding out to 6 decimals. Still not getting an exact match but it gets within the ball park.

I have a similar problem. did you try the problems in the CFAI books?