BOND MATH: The Theory Behind the Formulas

Accurate Implied Forward Rates

Equation 5.2 provides an excellent, and easy-to-calculate, approximation for the implied forward rate (Rate_{A × B}) that connects a shorter-term rate (Rate_{0 × A}) to a longer-term rate (Rate_{0 × B}). For now, we'll stay with bond yields so the relevant time periods continue to be AYears and BYears. Money market rates will require some special attention because of the unique manner in which they are quoted—recall the add-on rates and discount rates and 360-day years in Chapter 1.

An accurate formula for an implied forward rate that includes compounding and the specific periodicity (PER) for the yields is based on the expression shown in equation 5.3.

The first term is the proceeds per unit invested for AYears assuming ...