What is convexity (simple definition)
– Convexity describes the curvature of the relationship between a bond’s price and its yield (interest rate). It shows how a bond’s duration (a measure of price sensitivity) itself changes as yields move. In plain terms: duration approximates the immediate percent price change for a small move in rates; convexity shows how that sensitivity steepens or flattens for larger moves.
Key terms (short definitions)
– Yield: the return an investor earns by holding a bond.
– Coupon: the periodic interest payment the bond makes, usually expressed as a percentage of face value.
– Term to maturity: the time until the bond repays principal.
– Duration: an estimate of how much a bond’s price will change in percent for a 1 percentage-point (1%) change in yield; higher duration = greater price sensitivity.
– Convexity: how duration itself changes as yields change; a second-order measure of interest-rate sensitivity.
– Positive convexity: as yields fall, price increases accelerate; as yields rise, price declines decelerate.
– Negative convexity: the opposite profile; price gains are limited as yields fall and losses can accelerate as yields rise (common in many mortgage-backed securities).
How convexity works (conceptual)
– The price–yield relationship for a fixed-rate bond is not a straight line; it’s curved. Duration assumes a straight-line (linear) relationship and is useful for small rate moves.
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– Since the price–yield curve is curved (not a line), duration gives a linear (first-order) approximation that is accurate only for small yield moves. Convexity is the second-order term that corrects the duration estimate for larger yield changes. Mathematically, the percent price change ΔP/P for a small parallel shift in yield Δy can be approxim