# How to Calculate Yield on a Bond Equivalent Basis

by Ryan Menezes

A bond's coupon specifies its annual rate of return. Yet the actual amount that you receive depends on how frequently the bond pays its coupon. If a bond pays its coupon semi-annually, you will receive returns after six months that you can reinvest. After a year, you'll have higher returns than if the interest had not been compounded. The equivalent yield of a bond with compounded returns is the yield of an bond of equal actual value that pays its coupon annually.

1. Divide the number of days in a year by the number of days before the bond reaches maturity. For example, if the bond reaches maturity in 91 days, divide 365 by 91, which gives an answer of slightly more than 4. This means the bond pays its coupon four times a year.

2. Divide the bond's yield by the number of times that it pays each year. For example, if the bond has a yield of 8 percent, divide 0.08 by 4. This produces 0.02.

4. Raise this periodic return rate by the number of times that the bond pays out during the year. Continuing with the example from the previous steps, raise 1.02 to the power of 4, which is 1.082.

5. Subtract 1 from the result from Step 4. With this example, you will get 0.082, or 8.2 percent. This is the bond's equivalent yield, which is slightly more than its stated yield of 8 percent.

#### Tip

• If the bond assumes a financial year of 360 days, as Treasury notes do, then use calculate using 360 for the number of days in a year, instead of 365 in Step 1.