Calculation of BEY for treasury bill confused understanding the equation for review

CFA General
#1

I have a question related to the following equation for BEY

BEY= (F-P)/P x 365/n where n = days to maturity

Isn’t this just annualizing HPY?

To find BEY you must find semi annual yield and multiply 2.
So by using below equation

(1 + APR/m)^m = (1+ APR / n)^n

shouldn’t you convert the HPY to semi annual yield and multiply by 2 to obtain treasury bills’ BEY?

For example, let’s say you have a T-bill priced at 99 with 170days to maturity.

Using the first equation above, the BEY= 2.1687%

But by converting the HPY → semi annual yield—>x2 , I obtain 2.170%

(1 + APR/m)^m = (1+ APR / n)^n
(1+ HPY)^(365/170)= (1+ semi annual yield)^(1/2)
semi annual= 2.170%

thanks please help me out
Which is the correct method???

#2

I have no idea why they call your first formula BEY.

It isn’t.

But they’ve been doing it for years.

BEY is twice the semiannual effective yield, as you say.

#3

Thanks for replying.

So are you saying that although the math isn’t really accurate

this confusing equation :BEY= (F-P)/P x 365/n where n = days to maturity

it’s just the market’s convention for calculating T-bill yields?

#4

Yup.

It’s a perfectly valid yield calculation, but it’s not BEY (or EAY, for that matter).