The Impact of Yield Changes on the Systematic Risk of Bonds

While the literature in finance is replete with studies on stock betas, bond betas have, to this day, not attracted much attention. This is quite understandable because much of the finance literature addresses stock betas in the context of the single period Capital Asset Pricing Model (CAPM). In the single period model, the risk-free rate (if it exists) is assumed to be constant over the period in question. Since the interest rate is fixed and investors are required to hold these default-free bonds over the entire period, interest rate risk, and, consequently, systematic risk for bonds do not exist. However, if the constant risk-free rate assumption is relaxedand investors are allowed to trade “intra period,” (say continuously), Merton [4] has argued that an Intertemporal Capital Asset Pricing Model can be derived. Using Merton's framework, Jarrow [3] has recently derived a systematic risk measure for bonds. The primary intent of this paper is to investigate the effect of yield changes on the systematic risk of bonds. As we will demonstrate, the impact of yield changes on bond betas depends on several (sometimes complex) relationships between yields, duration, and bond prices. We derive conditions under which bond betas increase/decrease and show that the elasticity of duration with respect to yields and the sign of the initial beta of a bond will determine the manner in which yield changes affect bond betas.