Explain what drives the return on a bond portfolio when benchmark yields change

When benchmark yields move, the percentage price change is approximately −(modified duration × Δy) + ½ × convexity × (Δy)². Duration gives the first-order loss when yields rise; convexity adds a positive second-order term for option-free bonds, so larger moves favour more convex portfolios. Curve changes are usually described by level (a parallel shift), slope (steepening or flattening) and shape or curvature (a butterfly move). Return also includes rolling yield (carry, before any financing cost): the coupon income plus rolldown as a bond ages along an upward-sloping curve. Callable bonds and mortgage-backed securities have negative convexity: they gain less when yields fall and lose more when yields rise than comparable option-free bonds. The trap is relying on duration alone for large moves.