Bond Taxation and the Shape of the Yield‐to‐Maturity Curve

EMPIRICAL STUDIES1 HAVE FOUND a wide variety of shapes of bond yield to maturity curves (showing yield to maturity versus maturity) for coupon-bearing bonds. It is widely believed that zero coupon bond yield curves will have similar shapes. The relationship between yield curves for zero coupon bonds and couponbearing bonds is important because the majority of the theoretical work on bond pricing is developed for zero coupon bonds, but virtually all bonds (with maturities exceeding one year) are coupon-bearing bonds. This paper will analyze the relationship between the yield curves for couponbearing bonds and zero coupon bonds in a world with differential taxation of coupons and capital gains. The relationship between coupon-bearing and zero coupon yield curves (and forward rates) is quite complex in the general case. To provide some insights into the relationships, this paper will examine two special cases: (1) level before-tax zero coupon yield curves, and (2) level after-tax zero coupon yield curves; it will be assumed in both cases that tax rates and bond coupon levels will be the same for all maturities. When before-tax zero coupon rates are constant for all maturities, it will be shown that the yield curve for coupon-bearing bonds will rise with maturity. When; after-tax zero coupon rates are constant, the yield curve for non-par bonds will take on a wide variety of shapes and the yield curve for par bonds will be flat, consequently a shift in the level of after-tax zero coupon rates will alter the shape of the yield curve. Because many of the non-par coupon-bearing yield curves will slope upward as zero coupon rates change, there will be a tendency to observe upward sloping yield curves for coupon-bearing bonds, unless non-par bonds are continuously replaced by par bonds. Thus, taxation per se can create an upward bias in observed yield curves. These results indicate that (except for the case where the yield curve for par bonds is flat) coupon-bearing bond yield curves cannot be used to make inferences about the shape of zero coupon yield curves even in the case where bonds of different maturity have the same coupon level and the same tax rates. In the more general case where actual coupons vary with maturity and tax rates differ by maturity, it will be shown that no inferences at all should be made. Consequently, existing empirical work testing theories of the behavior of zero coupon bonds, but employing coupon-bearing bond data, must be regarded with considerable reservation.