Bond Equivalent Yield Formula?

CFA Level I
#1

I have seen 2 formulas for bond equivalent yield.

Which one is the correct one?

BEY=2*effective semi annual yield

BEY=(Discount/Price)*(365/T)

Are the two formulas same? Please explain.

#2

They both are the same equation stated in different ways. If the bonds pays semiannual then 365/t is the same as multiplying by 2. Are you sure on the “discount/price” part? I don’t recall seeing that phrase. Isn’t (HPY )* 365/t?

#3

How are the two same?

I still don’t get it. In the case of 2*effective semi annual yield the (365/t) is in exponent while in the other formula, we simply multiply by (365/t). How can the two give same results mathematically?

Yes (discount/price)*(365/t) and HPY*(365/t) are the same thing.

HPY=(face value-price)/price.

face value-price is discount

So, HPY=discount/price

1 + EAY = (1 + HPY)365/t

1 + EAY = (1 + HPY)365/t

#4

They’re not (remotely) the same.

#5

thanks … I believe I have completely misinterpreted the meaning of the “holding period yield”. I am deleting my second comment and striking out my first. My apologies to anyone I confused!

#6

Although it turns out that I, myself, have turned out to be confused by these two equation, I may be able to sort this bit out for you. I’m not sure if this is what you mean when you say “365/t is in the exponent” but I will explain where I think the confusion on that matter is coming from.

sometimes when you solve for BEY you must first take an effective annual yield to derive the semiannual yield. Since you are taking an annnual yield and converting to a 6month, you are essentually raising the annual yield to the power of 1/2. It looks like this:

semiannual yield =[(1+ EAY)^(t/365)] - 1

making the BEY = 2* [(1+EAY)^(t/365) - 1]

notice that the exponent is t/365 … NOT 365/t

#7

Then, why do we have 2 formulas for the same thing?

#8

Yes, thank you for correcting me. It is t/365. I am still confused though between the two. I’ll try to figure it out.

#9

We dont.

We have two formulae with the same name for different things.

Why? Got me! It’s stupid.

#10

Bond equivalent yield is just another way of saying a stated interest rate compounded semi annually.