# Valuing a Forward Rate Agreement - Schweser vs CFAI

I’m having trouble with the CFAI derivatives EOCs for FRAs, specifically question 9 on page 48 in reading 48, forwards.

Firstly 9B

((1.0595 / 1.0570(180/360)) - 1) x (360/180) = 0.0612

How are CFAI rounding this to get 0.0603? I’ve tried rounding up the compenant parts of the calculation but can’t get to 0.0603. The difference seems fairly inconsequential but when you’re calculating value based on \$10m principal it could have a large impact.

Then 9C

I can’t reconcile the method that I learned in the schweser summary to the method CFAI use in this example.

With the schweser method of calculating the new price of the FRA, calculating the interest difference and then discounting from the loan expiry date PV i get a completely different answer. Where am I going wrong?

new FRA price = ((1.0615(315/360) / 1.059(135/360)) - 1) x (360/180) = 0.0624

interest difference (using CFAIs answer from B) = (0.0624(180/360) - 0.0603(180/360)) x 10m = \$10,500

discounted interest difference = 10,500/ 1.0615(315/360) = \$9,965.73

CFAI get \$8100 using a different method which looks like a more formulaic version of schwesers logical explanation based on the ‘right to borrow at’ method.

Is the difference just down to the previous rounding issues?

Many thanks

Assuming that the

new FRA price = ((1.0615(315/360) / 1.059(135/360)) - 1) x (360/180) = 0.0624

was only a typo (it actually should be((1+0.0615*(315/360)… etc, I do not know how you came up with these results. I am using Schweser’s method as well, and I have the same results with CFAI. Most probably it is an issue of your calculator, because Texas is known to have some rounding issues. The methodology you are using is correct though, and I would advise you to do the same calculations with a scientific calculator (use the windows one) to check if you will get the same results.

Ah yes, I got the notation wrong. I think it should be:

new FRA price = ((1.0615^(315/360) / 1.059^(135/360)) - 1 x (360/180) = 0.0624

interest difference = (0.0624*(180/360) - 0.0603*(180/360)) x 10m = \$10,500

discounted interest difference = 10,500/ 1.0615^(315/360) = \$9,965.73

I’ve tried this on the Texas BA II Plus, on excel and on a casio scientific but still get \$9,965.73. I’m at work so can’t try the microsoft calculator, I’ll definitely try it at home.

Where does my answer start to diverge from yours? Is it when calculating the new FRA rate, the interest difference or the discounted interest difference?

Many thanks for your help.

doh! was ^ instead of *