# Correct definition of Bond Equivalent Yield?

Just reviewing some notes and I keep seeing different definitions for BEY. Some say it is: 6-month HPY x 2 Others say: HPY x 365/t Anyone see the same thing or am I missing something?

Actually, there’s 2 different definitions of BEY as you mentioned, and you must be careful because it may both appear in the exam. In corporate finance, the BEY is used to measure short-term discount securities and is calculated as they said: HPY x 365/days In Quantitative methods, and maybe in fixed income, the BEY is calculated differently: BEY = effective semi-annual yield x 2

I thought both are same yields, just the different way of calculating it. no?

I don’t think they are the same. BEY in quant includes compounding. Ie you calculate the effective semi-annual yield (using compounding) then multiply by 2.

I think theres one formula for LT bonds - semiannial yield times two And another for short term instruments in working capital management - HPY * 365/t

Doesn’t holding period yield includes compounding as well, as you are calculating this yield by using the final amount you are going to receive from this investment and the money you have invested?

JonnyKay, the BEY is used for both short term and long term bonds, it’s a convention in US financial market, according to CFAI books. sgupta0827, the effective semi-annual yield should be used because HPY is not valid for the formula if the holding period is not exactly 6 months long.

@quangnguyen82 Could you provide more insight into the 6 month rule for HPY? I haven’t seen it anywhere, or point me to LOS.

sgupta0827, actually there’s no 6 month rule as you mentioned. The HPY is not valid for the formula if you see this example: Suppose we hold a security for 3 months and then we sell it to get a three-month return of, I suppose, 3%, this is our HPY. To calculate the BEY, we cannot use this HPY because it is not equal the semi-annual yield (it’s a three-month yield, not a six-month yield). For this reason, I said that the HPY is only valid if the holding period is equals exactly 6 months or 1/2 year.

But HPY can be used to calculate EAY and that in turn can be used to calculate BEY. I am not sure what should be the compounding for HPY as that is calculated on return but EAY is definitely annual compounding and BEY is semiannual compounding, if I understand it correctly. That is the reason we can convert these yield back and forth because if you want to compare the return of a bond with short term security how would you calculate them? By converting only, like you do or tax exempt and taxed bonds. That is the reason I am insisting that these yields are not different, just a different way of calculating it.

Let’s work it with numbers. Say a 3-month investment yields 5%. BEY (corp fin method) = HPY x 365/t = .05 x 365/90 = 20.27% BEY (quant method) = semi annual discount rate x 2 = ((1.05^2)-1) x 2 = 20.5%