# 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.

HH

Hmmmm.

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

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

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?