Bond Duration & Convexity in 2 Minutes

This interview question asks for a clear, intuitive explanation of two core fixed income risk measures used in bond portfolios: duration and convexity. The candidate is expected to articulate what each concept represents economically, how they relate to a bond's price sensitivity to interest rate moves, and why practitioners care about them. In many buy-side, risk, and rates trading interviews, this style of question checks whether the candidate can connect balance-sheet or trading decisions to the underlying mechanics of bond pricing, hedging, and risk reporting.

Answering it well relies on comfort with present value ideas, comparative statics, and the link between yield changes and price movements. Good responses usually touch on how duration and convexity are estimated, how they scale for portfolio-level analysis, and how they're used in hedging, risk limits, and performance attribution. Interviewers listen for conceptual precision (not mixing up yield, price, and return), an understanding of linear versus nonlinear approximations, and an ability to translate the mathematics into practical language that traders, risk managers, or clients could act on.

What it tests

The core structure behind duration and convexity problems is the idea that a bond's price is a function of its future cash flows discounted at the prevailing yield, and that the sensitivity of this price to changes in yield can be understood through calculus. Duration is the first derivative of price with respect to yield (appropriately scaled), capturing the linear response—the immediate, proportional price change for a small yield shift. Convexity is the second derivative, measuring how this sensitivity itself changes as yields move, reflecting the nonlinearity in the price-yield relationship. The reason these measures work is that the present value formula for a bond is a sum of exponentials in yield, so its response to yield changes is governed by the rules of differentiation. This means duration and convexity are not just empirical rules but mathematically precise summaries of how cash flow timing and magnitude shape interest rate risk.