7. However, certain modifications are needed when we analyze coupon bonds’ instead of zeros’ expected returns—and the approximation will be somewhat worse. We use each bond’s rolling yield to measure the horizon return given an unchanged yield-curve; this measure no longer equals the one-period forward rate. We also use the end-of-horizon duration and convexity, as well as the change in the constant-maturity rate of a constant-coupon curve at horizon, and we adjust the duration and convexity effects for the fact that the bond’s value increases to (1 + rolling yield/100) by the end of the horizon. Besides the approximation error of ignoring higher-order terms than duration and convexity effects, another source of error exists for coupon bonds: The reinvestment-rate assumptions vary across bonds. Recall that the calculation of the yield-to-maturity implicitly assumes that all cash-flows are reinvested at the bond’s yield-to-maturity. This fact may lead to exaggerated estimates of yield income for long-term bonds if the yield-curve is upward-sloping, a problem common to all expected-return measures that use the concept of yield-to-maturity. Even though our approach of using bond-specific yields does not ensure internal consistency of the reinvestment-rate assumptions across bonds, any inconsistencies should have a relatively small impact on the overall level of bonds’ expected returns.