# YTM vs. BEY

Hi all,

may someone please explain to me the difference between Bond-Equivalent-Yield (BEY) and the Yield-to-Maturity (YTM).

Let’s assume a 3-year bond with 5% coupon paying semi-annually at 104.
So:

PV = -104
FV = 100
N = 6
PMT = 2.5

CPT I/Y => .01791
This should be my internal rate of return (IRR).

Yielt-to-Maturity stated on an annual basis:
YTM = .01791 x 2 = .03582

The definition in the curriculum says:
“An annual rate having periodicity of two is known as the semiannual bond equivalent yield”.
So what is the difference between the YTM and this one? How would I calculate it?

Cheers

Bond equivalent yield (BEY) is simply a convention for quoting yields: it’s twice the semiannual effective yield. You could quote a yield as an effective annual yield (EAY), a quarterly nominal yield (four times the effective quarterly yield), a monthly nominal yield (12 times the monthly effective yield), a money market yield (MMY), a bank discount yield (BDY), a continuous yield, or whatever.

A bond’s YTM could be quoted using any of these conventions, but is most commonly quoted as a BEY because most bonds pay coupons semiannually (and the semiannual coupon rate is simply half the annual coupon rate). Much as the length of a hunk of rope can be quoted in inches, feet, millimeters, centimeters, yards, furlongs, miles, parsecs, ångströms, fathoms, parasangs, and so on.

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Thank you For example 3 year, 4% semi-annual bond at 102 and I want to state the YTM as a BEY:

1) calculation of the semi-annual effective yield:

N = 6
PMT = 2
FV = 100
PV = -102

CPT I/Y = 1.647 %

2) annualize to make it a BEY:

2 x 1.647% = 3.294%

If I want to state this BEY as an monthly nominal yield, I would just use the periodicity conversion:
(1 + .03294 / 2) ^ 2 = (1 + x / 12) ^ 12
solve for x = 3.272%

So it is not enough to say “calculate the YTM”!?

Looks good to me.

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