Callable Bonds and Yield Calculations for Exam FM

Callable Bonds

A callable bond gives the issuer the right to redeem the bond before maturity at specified call dates. The call price may differ from the par value. When computing the price to guarantee a minimum yield, an investor must consider the worst-case scenario across all possible call dates.

The rule for callable bonds on Exam FM: if the bond is bought at a premium (price > redemption value), assume the issuer will call at the earliest possible date (worst case for the investor, as the premium is lost sooner). If bought at a discount, assume the bond is called at the latest date (worst case, as the discount benefit is deferred).

Yield Rate Determination

The yield rate (or yield to maturity) is the interest rate i that makes the price equal to the present value of future cash flows: P = Fr * a-angle-n(i) + C * v^n(i). Given P, F, r, C, and n, solve for i. This usually requires interpolation or a financial calculator because the equation is not solvable algebraically.

For Exam FM, linear interpolation is sufficient: if P(i1) > P_target > P(i2), then i is approximately i1 + (P(i1) - P_target) / (P(i1) - P(i2)) * (i2 - i1).

Current Yield vs. Yield to Maturity

The current yield is the annual coupon divided by the current price: CY = Fr / P. This ignores the capital gain or loss at redemption. The yield to maturity accounts for all cash flows including the redemption. For premium bonds, YTM < coupon rate < CY is impossible; instead coupon rate > CY > YTM. For discount bonds, YTM > CY > coupon rate. Understanding these relationships helps check your answers on Exam FM.