How to Convert a Bond Equivalent Yield to a Monthly Equivalent Yield
Certain investments, such as mortgage-backed securities, pay you monthly interest. When analyzing this type of investment, you can compare its yield, or return, to the yield on a U.S. Treasury bond, which pays interest semiannually. A Treasury bond’s bond-equivalent yield is its semiannual yield converted to an annual basis. The monthly-equivalent yield on an investment that pays interest monthly is the annual yield that accounts for monthly compounding, which is the effect of reinvesting the monthly interest payments. Converting the bond-equivalent yield to a monthly-equivalent yield helps you compare the potential returns of these investments.
Substitute the decimal form of a bond-equivalent yield into the formula 12 x [((1 + Y/2)^(1/6)) - 1], in which Y equals the bond-equivalent yield. For example, if you want to convert a bond-equivalent yield of 6 percent into a monthly-equivalent yield, substitute 0.06 into the formula to get 12 x [((1 + 0.06/2)^(1/6)) - 1].Step 2
Divide the bond-equivalent yield by 2 and add 1 to your result. In this example, divide 0.06 by 2 to get 0.03. Add 1 to 0.03 to get 1.03. This leaves 12 x [(1.03^(1/6)) - 1].Step 3
Raise your result to the 1/6 power and subtract 1 from that result. In this example, raise 1.03 to the 1/6 power to get 1.00494. Subtract 1 from 1.00494 to get 0.00494. This leaves 12 x 0.00494.Step 4
Multiply the remaining numbers and multiply that result by 100 to calculate the monthly-equivalent yield as a percentage. Continuing with the example, multiply 0.00494 by 12 to get 0.0593. Multiply 0.0593 by 100 to get a monthly-equivalent yield of 5.93 percent. This means that the annual yield of 5.93 percent on a security that pays interest monthly is the same as the annual yield of 6 percent on a bond that pays interest semiannually.
- In order for a monthly-equivalent yield to equal a bond-equivalent yield, the formula assumes you reinvest the monthly interest payments at the same interest rate and hold the investment until it matures. If either of these assumptions differs, the actual return might be more or less than the bond-equivalent yield.