Adjusting yields for periodicity, doubt, schweser page 46 (2022) and

CFA Level I
#1

Atlas corp bond is quoted with a YTM of 4% on a semiannual basis.

So for every 6 months, the yield is 2%

Effective annual yield on semi annual coupon bond would be

1+0.4/2^2 = 4.04%

For quarterly pay bond, we’d use ^0.5 since 0.5*4(quater) = 2 and get an answer of 0.995 and that times four is 3.98%

By this logic, if we divide by 1 and use ^ as 1, we get an answer of 4% i.e. for annual.

So shouldn’t 4% be annual, 4.04 be semi annual and 3.98 be quarterly?

In Schweser it says, 4.04 on annual basis, 4.00 on semiannual, 3.98 quarterly.

Example of page 46, schweser 2022. For reference.

#2

They are referring to the number of times interest is compounded over the year and how to get to the equivalent rate.

To use your example above, compounding semi-annually at 4% is equivalent to compounding annually at 4.04%. For the quarterly rate, the equation to solve is as follows:

(1 +QR/4) ^4 = (1 +4%/2)^2
(1+QR/4) ^ 4 = 1.02^2
(1+QR/4) ^ 4 = 1.0404
1+ QR/4 = 1.0404 ^ (1/4)
QR = 4 * [1.0404 ^0.25 - 1]
QR = 4 * 0.009950494
QR = 0.039801975

#3

Thanks for the response. I get it now!