# Derivatives Topic Test Whitney

For question 4 shouldn’t they divide the swap rates with 4? The answer uses the annual swap rates but these are with quarterly payment.

correct. you have to divide the rate by 4

It’s actually question 5 not 4. The one with the EUR HK\$ fixed for fixed currency swap. But yes they seem to have made an error.

Which swap rates should be divided by 4 and why? 90 Days have already passed, so it is 1 less payment. If you expand the bracket (2.9552 = 0.992704+0.985076+0.977422), by doing this, you multiply the annual swap rate by the 3 remaining discount rates to obtain each of the quarterly payments. There’s no need to divide any rates in this case.

Solution for reference:

€25,000,000 ´ [0.023181(2.9552) + 0.977422] – 285,500,000/HK\$/€9.96 ´ [0.018550(2.9632) + 0.980152 = €26,148,162 - €29,671,343 = €3,523,181

Hi ClownFiesta,

I’m just looking at a BB example with the same way of solving so I realize that I must be wrong but now I don’t understand it.

The present value factors are calculated from to de-annualized rates. So the swap rate should be de-annualized as well, not?

Because if the total interest payment for a year is 2.318% x the notional

we will pay only 1/4 of it each quarter. And each quarterly interest payment should be multiplied with the relevant discount factor.

What am I missing???

I have in front of me the Schweser book and the curriculum. I studied from Schweser but there CANNOT BE difference in such a calculation, yet there seems to be.

The way Schweser explains it:

The cash flow for the fixed leg:

annual swap rate x 90/360 x notional

multiplied by the discount factor each quarter

+ the notional multiplied by the last disocunt factor

You are correct in saying the present value factors are deannualized.

If you look at the first portion 0.023181(2.9552), you multiply the fixed swap rate by the sum of the discount factors.

I can restate the above like this 0.023181( 2.9552 )=(.023181) (0.992704+0.985076+0.977422)

So what I am saying now is, I multiply the swap rate by each individual discount factor in order to find the amount I would pay per \$ of the notional. This in essence de-annualizes the annual swap rate to each of the quarterly payments. Then i simply multiply that by the notional to find the total value of interest payments.

In this same topic test for question 4 they use the calculation explained by me:

annual swap rate / 4 x sum of the discount factors + notional x last discount factor.

At one question they calculate with de-annualized rate in the other with annualized? This can’t be correct!!!

Sorry what I’m saying is:

you have a quarterly cash flow. That is annual interest rate divided by 4 multiplied by notional. This is the exact cash flow that you will receive in the future every quarter.

In order to have the value today you discount each cash flow with the relevant (de-annualized) discount factor. In this we agree.

Where I cannot agree is the cash flow.

with very simple numbers.

The notional is 10 million. The interest rate is 4% per annum paid quarterly.

What is my quarterly cash flow? 0.04 x 90/360 x 10 million.

How CFAI calculates in this example (Question 5 of Whitney TT and BB example 16 in Reading 40) is they calculate the quarterly cash flow as 0.04 x 10 million. This CANNOT be right or I’m totally insane.

I have just looked at the errata on the website.

BB 316 IS WRONG! Yes the quarterly cash flow is annual interest rate / 4 x notional.

OMG!

Unfortunately we don’t have errata for the topic tests (at least I don’t know of it).

Still now I would feel more comfortable if someone would agree with my way of explaining…

can you send me the link of that revised change?

It’s a different formula.

In question 4 you are calculating the current value of the fixed bond.

If look closely at the formula you are multiplying the \$1 notional coupon by the remaining discount factors not the fixed rate.

and the answer should be around 3,624,511. is that what you get?

The questions are similar in my reading. In both cases there is a fixed payer. 4 is a fixed for floating in USD, 5 is a fixed EUR for fixed HK\$.

I am multiplying the whole cash-flow in front of me with the relevant discount factors.

OK I’m lost. I will continue it tomorrow.

It’s on CFAI website / Candidate Resources / Level II Errata

3,625,943

I was rounding a bit.

But esencially:

I don’t agree with the official solution in two numbers. I bolded out the swap rates from the official answer, instead of which I used

0.0058 and 0.00464 the two rates divided by 4 (i.e. x90/360)

€25,000,000 ´ [0.023181 (2.9552) + 0.977422] – 285,500,000/HK\$/€9.96 ´ [ 0.018550 (2.9632) + 0.980152 = €26,148,162 - €29,671,343 = €3,523,181

Sorry to bump this, but i agree with you Moosey. I’m wondering why they used the yearly payment instead of quarterly. Surely its a mistake? Did you find out any more since you posted?

Hi all,

didn’t have time to read everything carefully, but they should have used 0.04/4 * Notional. The cash flows each quarter are 1/4 of the annual CF which is given by the annual rate.

I’m pretty sure it’s a mistake, since I found the errata of blue boxes No. 15 and 16 where they committed (and corrected) the same mistake, the topic test must be a mistake, as well.