BOND MATH: The Theory Behind the Formulas

Periodicity Conversions

A commonly used bond math technique is to convert an annual percentage rate from one periodicity to another. In the bond market, the need for this conversion arises when coupon interest cash flows have different payment frequencies. For example, interest payments on most fixed-income bonds are made semiannually, but on some the payments are quarterly or annually. Identifying relative value necessitates comparing yields for a common periodicity. In the money market, the need for the conversion arises when securities have different maturities. The 1-month, 3-month, and 6-month LIBOR have periodicities of about 12, 4, and 2, respectively, depending on the actual number of days in the time period.

The general periodicity conversion ...