Fixed Income, CFAI Reading 36, Q10, page 102

CFA Level II Fixed Income
#1

I am not understanding the interest rate tree given for Q10 for CFA reading 36. It starts with year 1 i=1%, year 2 rh=4% rl=2%, year 3 rhh=6% rhl=5% rll=3%

So the question asks to value a 3 year 6% annual coupon bond using the tree. My understanding of valuing is the same as the blue box example 3 on page 82-83. So year 3 is maturity hence we will receive principal and interest, which we should discount by the year 2 rate to give the PV for year 2. T the solution solves for year 2 present values by discounting by the t=3 rates from the binomial tree. So am totally confused by the binomial tree is stated.

It’s probably something really simple that I am missing, but I just am unable to understand the question and make the correlation to the blue box example.

Would appreciate any help on this.

#2

Sup dude.

They give you the one year forward rates

value at time 0 uses year 1 rate to discount

value at time 1 uses year 2 rate to discount

value at time 2 uses the 3 year rate to discount

You’re gonna get the principal and coupon at the end of year 3, so to get the value at t2 you need to use the year 3 rates, yo.

Just remember, you’re looking for V0, not V1

#3

With all due respect, you have all of these rates wrong.

To get the value at time 0 you use the 1-period forward rate at time 0 to discount the time 1 values.

To get the values at time 1 you use the 1-period forward rates at time 1 to discount the time 2 values.

To get the values at time 2 you use the 1-period forward rates at time 2 to discount the time 3 values.

And so on.

Please be careful.

#4

Hi S2000, thanks for replying. What you have described is how I understand the binomial interest rate tree to work.

So what am I missing in regards to the way the question is stated?

#5

Two things:

First, the way they presented the rates is stupid: the rate they call “Year 1” is, in fact, the 1-year forward rate starting today and ending at year 1, which isn’t remotely the way an interest rate tree is normally presented. The headings should be Year 0, Year 1, and Year 2.

Second, I owe AnalystDude123 an apology: your description of the discount rates is consistent with the stupid table.

bimo: you’re not missing anything. They labeled the tree in a stupid manner, and it threw you, as well it should. I’ll write CFA Institute and ask them about that.

#6

Haha I got a little worried since I thought I completely messed up the answer once you replied. But I did check the book before posting and the rates were presented kind of counter intuitively in regards to other examples and schweser.

Edit: And I’m also aware that you use the forward rates to discount, but I tried tailoring my response in context of how they were presented in the question. Sorry if I caused any confusion!

#7

You didn’t cause any confusion. I didn’t look at the table before I replied, so I made the silly assumption that the table wasn’t presented stupidly.

#8

Many thanks for your help S2000, I was banging my head on that question for a couple of hours because I thought I wasn’t grasping a key concept about the binomial tree which would bite me in the behind the exam. I have now found relief lol.