The paper explores the relationship between fixed income excess returns and maturity differentials. In a quest to quantify this relationship, we go beyond testing the monotonicity of excess returns, by exploring the functional form of excess returns' dependence on the maturity differential. Essentially, the paper tests whether the monotonicity of excess returns is linked to maturity differential in a linear or nonlinear fashion. The findings suggest that a quadratic relationship fits the data adequately, and therefore imply that excess returns exhibit sensitivity both to maturity differential and also to their location on the yield curve. Thus, although excess returns increase monotonically with maturity they do so at a decreasing rate.