Annualizing HPY: EAY vs. rMM

CFA Level I Quant
#1

Hi everybody,

I know all these formulas have been covered extensively already but I have a specific question regarding EAY and rMM.

Both formulas apparently annualize the HPY but you get the rMM by multiplying with 360/t whereas you get the EAY by using ^365/t.

Is that because rMM does not use compound interest and EAY does?

Jeez, all these seem so completely random to me…

Thanks!

#2

The money market yield gives you an annualize HPY based on a 360 days convention. The effective annual yield gives you the effective yield based on 365 days, taking into consideration compounding. Money market yield is not an effective yield as it does not take into account compounding, it simply annualizes HPY based on a 360 days convention.

#3

Thanks. I think I got it now.

So generally speaking, by multiplying I just get the annualized yield and by calculating the power (^) I get the annualized and compounded yield, correct?

#4

Yes,

Since you exponentiate the interest rate by a number of periods, it gives you the ‘‘interest on interest’’ effect. When you simply multiply, it gives you an annualized periodic rate or annualized yield as you said.

#5

Just wanna add important differences between rBD, rMM and EAY so that this could be more simplified

There are 3 flaws in rBD

  1. not the true return (discount/face value)

  2. No compounding only simple interest

  3. 360 days year

There are 2 flaws in rMM

  1. No compounding only simple interest

  2. 360 days year

rMM is a true return (discount/purchase price) but not in annualized yield

There are no flaws in EAY

  1. true return

  2. compounding

  3. 365 days year

#6

That’s good stuff. Thanks!