# Understanding periodicity

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

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.

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

Hi Ernest,

Thanks for stating the obvious.