Fixed Income: Reading 44 - Practice Problem number 10

[Mark666]

Hello,
I have a question regarding Fixed Income: Reading 44 - Practice Problem number 10. The session is called: The arbitrage Free Valuation Framework.
How to use the Schweser method to make a binominal tree when interest rate in Year 0 is not given?
If you look at exercise 10, the year 0 rate is not given. In all the Schweser exercises, Year 0 is always given. So how would you use the Schweser method to arrive at the right answer?
Thank you

 

[krokodilizm]

First, there is no Schweser method that is different from other curriculums. The question established 2 methods in the beginning of the questions and Q10 says to use Method 2, i.e. binomial tree.
The interest rates given are forward rates. Forward rates look into the future. So there is no rate for Y0. All you have to do is discount cash flows up to Y1 and that would be the forward price.

 

[S2000magician]

With all due respect, there are forward rates starting at year 0. They happen to equal the corresponding spot rates.

 

[krokodilizm]

S2000magician wrote:
With all due respect, there are forward rates starting at year 0. They happen to equal the corresponding spot rates.

Can you please make a reference to the question above because it gets a bit confusing. The answer discounts the cash flows for Y3, Y2 and Y1. Where does Y0 fit in?

 

[Mark666]

krokodilizm wrote:
First, there is no Schweser method that is different from other curriculums. The question established 2 methods in the beginning of the questions and Q10 says to use Method 2, i.e. binomial tree.
The interest rates given are forward rates. Forward rates look into the future. So there is no rate for Y0. All you have to do is discount cash flows up to Y1 and that would be the forward price.

The way the CFAI calculates a binominal tree is:
0.5 x ((1000+50)/1.05) + 50
Schweser does 0.5 x ((1000+50)/1.05)
I am confused about the +50 in the CFAI.
Also, the only difference I could see is that CFAI does not give year 0, the spot rate.
Schweser exercises provides the Year 0 spot rate.
You do get rates in Year 0.

 

[S2000magician]

krokodilizm wrote:

S2000magician wrote:With all due respect, there are forward rates starting at year 0. They happen to equal the corresponding spot rates.

Can you please make a reference to the question above because it gets a bit confusing. The answer discounts the cash flows for Y3, Y2 and Y1. Where does Y0 fit in?

If it’s discounting the cash flows from year 1, it’s discounting them to year 0. The rate used is the 1-year spot rate, or the 1-year forward rate starting today: they’re the same rate.