Suppose that the yield to maturity on a Eurodollar bond is 7.8%.What is the bond-equivalent yield?

What will be an ideal response?

Because Eurodollar bonds pay annually rather than semiannually, an adjustment is required to make a direct comparison between the yield to maturity on a U.S. fixed rate bond and that on
a Eurodollar fixed-rate bond. Given the yield to maturity on a Eurodollar fixed-rate bond, its bond-equivalent yield is computed as follows:

bond-equivalent yield of Eurodollar bond = 2[(1 + yield to maturity on Eurodollar bond)1/2 – 1].

If the yield to maturity on a Eurodollar bond is 7.8%, then the bond-equivalent yield is:

2[(1.078)1/2 – 1] = 0.0765355 or about 7.6534%.

Notice that the bond-equivalent yield will always be less than the Eurodollar bond's yield to maturity.

To convert the bond-equivalent yield of a U.S. bond issue to an annual-pay basis so that it can be compared to the yield to maturity of a Eurodollar bond, the following formula can be used:

The yield to maturity on an annual-pay basis would be:

[1 + (yield to maturity on bond-equivalent basis / 2)]2 – 1.

For example, suppose that the yield to maturity of a U.S. bond issue quoted on a bond equivalent yield basis is 7.65355%.

The yield to maturity on an annual-pay basis would be:

[1 + (0.0765355 / 2] 2 – 1 = [1.0382678] 2 – 1 = 0.0780 = 7.80%.

The yield to maturity on an annual basis is always greater than the yield to maturity on a
bond-equivalent basis.