for a 3 year Bond, bond price at the first node in year 2 is calculated as:
Corriculum has it as:
({0.5[(face value of upper node + coupon) + (face value of lower node + coupon)]} / 1 + Rf) + coupon
Schweser has it as {0.5[(face value of upper node + coupon) + (face value of lower node + coupon)]} / 1 + Rf
Which one are we to follow? definitely the value you derived from differ with the two formula’s due to the addition of the coupon.
Did CFAI made a mistake, from my view, I think Schweser is correct, considering the Corriculum Derivative calculation of bond price, which is similar to Schweser’s calculation, but in contrast to CFAI Fixed income calculation.
I believe that the two methods give the same answer. By the same answer, I mean we will get the same value of the bond now. However, the value of the bond at each nodes are different.
For example, imagine we want to value a 2-year coupon bond.
CFAI discount the principal and the coupon at time T=2 to time T=1, and then add the coupon at time T=1 to get the value of the bond at node T=1. Then they discount the value at note T=1 to now and then add the coupon at T=0 (which is 0) to get the value of the bond.
Schweser/Wiley discount the principal and the coupon at time T=2 to time T=1 to get the value the the bond at node T=1. Then they add the coupon at node T=1 to the value at node T=1 and then discount it to time T=0 to get the value of the bond.
So the two methods are basically the same. The only difference is the value of the bond at the nodes. I recommend using the CFAI method, because they may ask us to calculate the value of the bond at a node and if we use the other method we will get a wrong answer.
I was gonna stick to that policy but then topic tests Krishna and Desna used different methods. Will do it in Excel later to see if indeed they give same bond value in the end (kind of sceptical about it).
True indeed! The solution turns out simpler than I thought.
The next caveat is when final period cash flows are discounted before we even start the backward induction process. Did you see the Krishna topic test?
As you can see there are two value now - 99.206 and 100.551, which have been reconciled using both methods.
The difference is that at Year2 we discounted 103.20 and only then moved back to Year1, as with the attached diagram.
The diagram in my previous post starts out with 103.20 and ends up with a value 100.551.
I believe the key is what rates we are using. With forward rates we get 100.551 and with spot/par rates we get 99.206. Isn’t this something significant to remember? See Krishnan case if you haven’t yet.
I actually got this in my notebooks when i first did it in April. Now I understand. It is just the answers having short cuts in presenting the calculation. Krishnan is exactly the same as other questions.
Instead of Vuu = 0.5*(103.2/1.0621+103.2/1.062) they just did Vuu = 103.2/1.0621
What i can take out is that you stick with the CFA formula (formula 1 when the bond has an embedded option, while we stick with the Schweser method we dealing with straight bond.)
I struggled with Desna’s binomial tree question only because I didn’t read the question properly and I was trying to compute the value using every node in the tree, when I should have started at T=2 for a 3 year bond (if I recall correctly).
For binomial trees, I follow the same procedure every time and it’s never failed me unless I made some other silly mistake.
I take the coupon, multiply it by 2 then hit STO 0 on my calculator. Then it’s Node 1 + Node 2 + RCL 0 / 2, then divide the result by 1+ the rate in the tree for the prior period node. If working with a callable or putable bond I simply check the result against the call/put prices and write down the appropriate price at that node and continue on. Rinse and repeat.
