BOND MATH: The Theory Behind the Formulas

Credit Spreads and the Implied Probability of Default

Statements about corporate bond yields inevitably include the “assuming no default” caveat. That's because the yield to maturity indicates the highest rate of return the buy-and-hold investor can expect to obtain. When there is a risk that the issuer might default, a prudent investor should expect to realize a return lower than the yield to maturity. If we were to draw a probability distribution for outcomes on a 10-year corporate zero-coupon bond, it would look something like Figure 2.3.

Obviously, the best outcome is that there is no default. The issuer pays the bond holder the full par value at the maturity date, and the investor's realized rate of return is 5.174% (s.a.), given the assumed ...