semiannual to quarterly

CFA Level I Fixed Income
#1

One of the problems asks to obtain the equivalent quarterly rate from 6% semiannual rate and I dont understand the logic given in the answer: 1.03^1/2-1=14.9% and then it uses this 14.9% to discount quarterly coupon payments!! Shouldn’t it be divided by 4 firstly, and then be used as a discount factor?! Or may it be just a mistake in the problem? And one off-topic question, probability of using ChiSquare test statistic formula is too low right? :slight_smile: thanks in advance

#2

You need to take compounding and the conventions of bond yield quotes into account:

Recall first of all that the semiannual rate is typically obtained by multiplying the 6-month effective rate by 2. If you want to obtain the quarterly effective rate, you need to calculate the 3 month effective rate and multiply that by 4. You proceed as follows:

  1. If the seminannual rate is 6% then the 6 month effective rate is 3%.

  2. The 6-month effective rate includes compounding in each period, thus to get the month rate, you cannot just divide by 2, but rather need to take the square root, => 1.03 ^(1/2)-1=1.49%=0.0149

  3. This quarterly rate then needs to be multiplied by 4 to get the annual rate.

The Chi Square qestions I encountered so far were pretty simple and typically computing the test statistic was half if not the entire battle. So even without putting much effort into it, just memorize it quick and you might have some easy points in the exam. Here it is by the way, write it down a couple times and you’ll remember :

Chi Square Test Statistic = (n-1)s^2/var

Greetings to the Caucasus by the way, my ancestors are from the area!!

#3

Watch yer decimals…

1.03 ^(1/2) - 1 = 0.0149 = 1.49%

#4

whoops, thanks!! I just copied from the original post without double checking the result (kind of sounds like a violation of Standard V(A) Diligence and Reasonable Basis)

I corrected my post.

Thanks again.

#5

Many thanks from Georgia guys! You are always welcome here :slight_smile:

#6

You are very welcome.

Thanks so much, hopefully some day…

#7

so from my understanding in situations like this, you would always take the annual yield and divide it by 2 to get the effective yield for six months and from there you would raise it by the power (or fraction of a power) in order to get it to quarterly periodicity correct?

Lets say the question wanted to find the annual rate for a monthly annual rate

you would take the 6 -> (6/2=3%) 1.03^(1/6) -1 = .00494 .00494*12= .05926 (5.926%)?

So my question is would everything first need to be computed to a 6-month effective rate and from there just convert it to either quaretly, monthly, etc?

#8

Correct. That is, typically you are provided with the bond equivalent yield, which is constructed by multiplying the 6 month rate by 2 (most bonds pay coupons semi-annually). So if not stated otherwise, I would proceed in that manner.