In the US, most bonds are generally semi-annual coupon paying bonds, so we calculate the semi-annual yield and then calculate the bond-equivalent yield (annualized) by simply doubling the semi-annual yield. This is done when the bonds have semi-annual coupon payments.
However, not all bonds pay semi-annual coupon, especially there are many non-US bonds that pay coupon annually and hence will have the annual yield that is calculated by the compounding rules.
The bond-equivalent yield of a semi-annual coupon bond and the annual yield from an annual-pay bond cannot be directly compared. To make them comparable, we need to convert the annual yield from the annual-pay bond into bond equivalent yield, which is done using the following formula:
BEY of annual-pay bond = 2 x [(1+ yield on annual-pay bond)0.5 -1]
What the above formula does is first calculates the semi-annual yield and then applies the convention of doubling it to arrive at the bond equivalent yield.
Let’s take an example. Let say that an annual coupon paying bond has a yield of 6.5%. The bond-equivalent yield will be calculated as follows:
BEY = 2*(1.065^0.5 – 1) = 6.398%
Note that BEY will always be lesser than the effective annual yield or the YTM of annual pay bond because BEY doesn’t consider the effect of compounding.
Alternatively you could also convert the BEY of a semi-annual pay bond into YTM on annual-pay basis by using the formula:
YTM on annual-pay basis = (1+BEY/2)2 – 1
So, if BEY is 6%, then YTM on annual-pay basis will be:
YTM (annual-pay basis) = (1+6%/2)^2 – 1 = 6.09%
Again note that YTM on annual pay basis is more than Bond-equivalent Yield.