# EAY, BDY, MMY relationship

Can someone explain their relationship with eachother?

For example: If the money market instrument is sold at a discount what is the relationship between the 3 above? I.e which is biggest and which is smallest?

Thanks

BDY = (is the difference divided by the FACE VALUE ) x 360/t

MMY = (the difference divided by PRICE) x 360/t

keep in mind, the difference divided by price is = Holding Period Yield

EAY = (1 + HPY) ^ (360/t) - 1

to remember the sizes jjust remember MBE (Member of the order of the British Empire)

with M < B < E

M= money market yield; B= Bond equivalent yield and E = effective annual yield

As for bank dicount yield, it’s not directly comparable, you’d need to convert it to money market yield or something else that uses HPY for it to be comparable

Maybe these articles I wrote will help a bit:

Mikap – I believe the EAY is 365 not 360

It is.

Hey bud, easiest way to remember their relationship is to remember that they all have HPY/HPR in common, and are just manupulations of that number to get a stated annualized return based on one of those particular metrics. If you have one return, just do the reverse of its typical formula to get back to HPY/HPR, and then re-apply another formula to see what the comparative for a different metric is (i.e. go from BEY to HPR to BDY)