Question on monthly compound rate

[sridhar]

David:

I am watching Market B, Part 1 on fixed income bonds episode. I refer to pages 47 & 48 of the screencast PDF.

On both pages, you ask the same question: "What is the monthly compound rate that corresponds to a market rate of 6%."

Seems like you are asking the identical question with the same market rate of 6%. Yet you derive two different answers because you are using slightly different formulas. Looks like the one on page 47 is correct and 48 is not.

On the other hand, there must be some nuance I am missing. What gives?

The computation on page 47 corresponds to the AIM you present on page 46. But the stuff of 48 has me befuddled.

--sridhar

 

[David Harper CFA FRM]

Hi sridhar,

Yes, did you notice i mentioned i didn't like the term "market rate?" This is exactly why!

P 47, the slide i spoke to, echoes Tuckman's formula, and therefore implicity assume a bond-equivalent basis
p 48 (i don't think i spoke to that? right? didn't i try to skip it?) show 6% as an annual rate

Neither of these is wrong !?

The key to this is understanding that Tuckman is always dealing in semi-annual compound frequency.
So, his market rate = 6% is the same as when Fabozzi says (and which i much prefer)
"The bond-equivalent rate = 6%"
A bond-equivalent rate of 6% means: 3% every six months; i.e., it is a semi annual return.

so, 6% on a bond-equivalent basis (ie., Tuckman) means the EFFECTIVE ANNUAL YIELD/RATE (EAY/EAR) = 1.03^2 = a bit higher than 6%

on p 48, that is a plain old annual rate. On page 48 (not Tuckman), a 6% annual rate = 6% EAR.

both can be translated into monthly compound frequency. But they start at different places. To see this, note we can reverse their different monthly compound rates:

p 47: [1+(5.9263%/12)]^6 = 1 + 3% semiannual, which is 6% bond-equivalent and 6.09% EAR
p 48: [1+(5.5841%/12)]^12 = 1 + 6% annual, which is 6% annual and 6% EAR

I hope that clarifies. The AIM is well-crafted. I actually fault Tuckman for imprecise language around the term "market rate" in Chapter 4. His 5% is a semi-annual rate but this relationship to imprecise market rate/annual/EAR is not shown.

David