Understanding periodicity

CFA Level I Fixed Income
#1

Dear all,

I understand that there is a similar thread on this but I hope you can consider the following hypothetical question regarding periodicity:

A bond has a YTM of 5% quoted on a _ semi-annum _ bond basis.

Required:

  1. Effective Annual Yield (" EAY") of the bond
  2. (i) Convert the bond to quarterly bond basis and (ii) re-determine it’s EAY.

My Answer:

________________________________________________________________________________________

For 1:

EAY= ( 1+ 0.05/2)^2 - 1 = 5.0625%

________________________________________________________________________________________

For 2:

(i) Conversion : (1 + 0.05/2)^0.5 - 1 = 1.2423%

The revised nominal annum rate will be 1.2423% x 4 = 4.9691%. This however is not the EAY of the bond but the annual rate for the bond which is now paying quarterly coupon i.e. quoted on a _ quarterly bond basis _.

(ii) EAY= (1 + 0.04969/4)^4 - 1 = 5.0625 %

_________________________________________________________________________________________

Additional Question:

  1. Can I say that for a quarterly pay bond ( periodicity of 4 ), the YTM is often quoted on a quarterly bond basis? Likewise for semi-annual pay bond ( periodicity of 2 ), the YTM is quoted on a _ semi-annum bond basis _?
  2. Are there any instances whereby a company quote a semi-annum pay bond on a quarterly bond basis?

Thank you very much!

Cheers,

Ernest

#2

The use of periodicity in CFA text can be misleading. In my opinion, “frequency” of annual coupon payments shall be used here.

The periodicity of a quarterly-pay bond shall be "a quarter (3 months) and its frequency shall be 4. The periodicity of semi-annually pay bond shall be "semi-annual (6 months) and its frequency shall be 2.

#3

Hi Asuka.

I agree totally with you regarding the misleading part. I guess sometimes we just have to be flexible with the wording; and it varies depending on the context of the question.

Ernest

#4

Hi Ernest,

Thanks for stating the obvious.