Fixed Income Topic Test Desna Problem #4

CFA Level II
#1

Aside from this topic test being really difficult (1/6). I had an issue with the CFAI answer for the binomial interest rate tree problem #4. I assume I am missing something obvious, but I don’t understand their calculations.

For example, why isn’t V(u,u) calculated as .5*(102.8+102.8)/1.0456 = 98.317?

And then why do they only add $2.80 at each of the preceding nodes instead of $5.60?

Thanks in advance.

#2

I don’t have access to the test, but for the second question I’ll venture the guess that the coupon is paid semiannually, not annually; therefore, each 6 months you get half the coupon.

#3

Unfortunately, it specifies annual payments. Thanks for the thought, though! Love your site.

#4

Oh, well. I tried.

Thanks for your endorsement.

#5
  1. They are doing what you are saying. However you need to add the coupon received at that period at the end which is not discounted.

2.)

Using a different set of benchmark bond values, Maalouf constructs the calibrated binomial interest rate tree shown in Exhibit 2. He shows Fujioka how to value a three-year, option-free, fixed-rate bond with a 2.8% coupon rate, annual payments, and a face value of 100 using this interest rate tree.

2.8% coupon, annual payments = 2.8 coupon 1x per year

2.8% coupon, semi-annual payments = 1.4 coupon 2x per year.

The curriculum does a funky job with the formulas explaining how to discount. I thought Wiley did a better job, but in the end you get the same answer. Luckily I have a background in FI or I would have been lost :confused:

#6

This is really a notation issue. Their V(x,x) includes the current node CF whereas everywhere else I’ve seen it’s only the PV of the future CFs.

I did indeed get the same answer doing it “my way”.

Thanks

#7

Yup, you will be receiving the CF on that date so you need to include it in the value.

#8

Yes, I understand that, thanks.

Open up your Wiley fixed income book to a binomial interest rate tree problem and tell me if their “V(u,u)” includes the CF that occurs at that time/node. You will see what I mean.

It’s just a notation issue.

#9

remember that

0.5 * 2.8 + 0.5 * 2.8 = 2.8 nonetheless

so a short cut would be to take (0.5 * Node 1 value + 0.5 * Node 2 Value)/(1+r) + 2.8

or even better

0.5 * [(Node 1 + node 2) / (1+r)] + 2.8 –

all shoiuld give you the same value

#10

Yes, I understand that, thanks.

It’s just a notation issue.

#11

Yeah I thought it was weird that Wiley presented it differently than the curriculum did. Confusing when you are trying to look at EOC answers and topic tests. I preferred how they did it but transitioning to CFAI was weird.

#12

Actually, they both (and Kaplan) say that V(x,x) is equal to the PV of future cashflows with C being the coupon/current period CF.

The only time I’ve ever seen V(x,x) being equal to PV future CF + C is in this one answer explanation from CFAI.

#13

Can someone comment on the below?

#14

If it’s a 3-year bond, we use only the current, year 1, and year 2 forward rates.

A fig for the year 3 rates.

#15

Can you provide a pathwise valuation for th above mentioned bond using the given interest rate tree Tx

#16

For Vuu= 102.80/1.0456 simple as that