Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

CFA Events Calendar

View full calendar

Recommended Discussions

See how our partners can help you ace your CFA exams.

Fixed Income security question

fmccrayfmccray OklahomaPosts: 8 Associate
Hello,
This question if for Level 1 in fixed income securities. I need help please.  :(
I am having trouble with the conversion from annual to semiannual and converting to quarterly. ( It is section 3.3 Yield measures for fixed-rates bonds. It is the formula for conversion based on periodicity i believe is what i don't understand.

I am assuming that (1.03) to the power of 2 is semiannual. Not sure about (1.03) to the power of 0.5 ( i have no idea why it is 0.5)

here is the question: A firm has issued a bond with YTM of 6% on a semiannual basis. What yield should be used to compare it with an annual pay bond and a quarterly pay bond?

AFor annual pay bond – 6.09%, for quarterly pay bond – 5.96%.
BFor annual pay bond – 6.15%, for quarterly pay bond – 5.90%.
CFor annual pay bond – 615%, for quarterly pay bond – 6.20%.

Explanation:

A is correct. A general formula to convert an annual percentage rate for m periods per year, denoted APRm, to an annual percentage rate for n periods per year, APRn, is

For annual pay bond: (1.03)2 - 1 = 6.09%
For quarterly pay bond: (1.03)0.5 - 1 =1.49%.
and for quarterly basis 1.49 * 4 = 5.96%  


Thank you,

Comments

  • The 6% number is the annual percentage rate (APR), which is just a convention that banks used. It is simply the interest rates received multiplied by the number of periods in a year. So 6% on a semiannual basis means you get paid 3% every 6 months. 

    The question is asking "If I have a bond that pays 6% on a semiannual basis, what is the equivalent APR I should shop for if I want an annual or quarterly pay bond?"

    To convert, you compound it accordingly to calculate annual and quarterly interest payments, then recalculate the APR.

    So if you're receiving 3% every 6 months,
    • to make it annual you'd compound it by 2 periods (6 months * 2): 1.03^2 -1 = 6.09%
    • to make it quarterly you'd have to compound it by 0.5 periods (6 months * 0.5): 1.03^0.5 -1 = 1.49%, which is 1.49% * 4 = 5.96%
    Bonus info: Because of the nature of compounding, frequent interest payments will always result in a lower APR. So without calculating you can already tell that C is wrong, because the quarterly pay bond APR is higher than the semiannual (6%).

    Hope that is clear, English is not my first language.
    perambulatorbarbtoksvfp92
  • fmccrayfmccray OklahomaPosts: 8 Associate
    This explanation is so helpful. English is not my first language either :). Thank you so so much.
Sign In or Register to comment.