Calculating forward rates

CFA Level II Fixed Income
#1

First and most important, after reading magician’s article about Spot and Forward rates I am sure that he’s the best teacher I’ve ever had, and I don’t even know him… THANKS.

I only have one question that arose at the bottom of the reading… it is clear to me that if you want to know the f(1,4), you divide the spot at maturity 5 by the spot at maturity 4 (which is, in essence, discount the 5-year spot 4 years back, right). Then, why if we want to know the f(2,3) we have to do the squared-root of the division? I don’t see why and I would like to understand the logic behind this, in order to know when to do what.

Thanks once again master!!

(1 + 2f3)2 1 + 2f3 2f3 = (1 + 2f3)2(1 + s3)3= (1 + s5)5(1 + s3)3= (1 + s5)5(1 + s3)3−−−−−−−−−⎷= (1 + s5)5(1 + s3)3−−−−−−−−−⎷ − 1

(1 + 2f3)2 1 + 2f3 2f3 = (1 + 2f3)2(1 + s3)3= (1 + s5)5(1 + s3)3= (1 + s5)5(1 + s3)3−−−−−−−−−⎷= (1 + s5)5(1 + s3)3−−−−−−−−−⎷ − 1

#2

Each of the spot rates and forward rates we calculate are _ annual _ interest rates. So (1 + 2f3) is a factor for one year, and (1 + 2f3)² is a factor for 2 years.

The calculation is:

(1 + s3)³(1 + 2f3)² = (1 + s5)^5

When we do the division, we get:

(1 + 2f3)² = [(1 + s5)^5]/(1 + s3)³

So you take the square root to get to:

1 + 2f3

#3

There you go, great once again.

Thanks for everything sir.

#4

My pleasure.

#5

Hello Magician,

I have been your follower like others. I am struggling with the way the reading has been explained in curriculum.

where can I find your article?

Many thanks,

with regards,

dealdone

#6

Well I did find the article on your website.

will go through it.

many thanks.

#7

You’re welcome.