**Subject 5. Bond Equivalent Yield**

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Periodic bond yields for both straight and zero-coupon bonds are conventionally computed based on semi-annual periods, as U.S. bonds typically make two coupon payments per year. For example, a zero-coupon bond with a maturity of five years will mature in 10 6-month periods. The periodic yield for that bond, r, is indicated by the equation Price = Maturity value x (1 + r)

^{-10}. This yield is an internal rate of return with semi-annual compounding. How do we annualize it?

The convention is to double it and call the result the bond's yield to maturity. This method ignores the effect of compounding semi-annual YTM, and the YTM calculated in this way is called a **bond-equivalent yield** (**BEY**).

However, yields of a semi-annual-pay and an annual-pay bond cannot be compared directly without conversion. This conversion can be done in one of the two ways:

- Convert the bond-equivalent yield of a semi-annual-pay bond to an annual-pay bond.

- Convert the equivalent annual yield of an annual-pay bond to a bond-equivalent yield.

*Example*
- A Eurobond pays coupon annually. It has an annual-pay YTM of 8%.
- A U.S. corporate bond pays coupon semi-annually. It has a bond equivalent YTM of 7.8%.
- Which bond is more attractive, if all other factors are equal?

**Solution 1**
- Convert the U.S. corporate bond's bond equivalent yield to an annual-pay yield:
- Annual-pay yield = [1 + 0.078/2]
^{2} - 1 = 7.95% < 8% - The Eurobond is more attractive since it offers a higher annual-pay yield.

**Solution 2**
- Convert the Eurobond's annual-pay yield to a bond equivalent yield (BEY):
- BEY = 2 x [(1 + 0.08)
^{0.5} - 1] = 7.85% > 7.8% - The Eurobond is more attractive since it offers a higher bond equivalent yield.

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