Bond Price-Yield Relationship and Convexity

This question focuses on the shape of the bond price–yield curve and how a candidate connects basic fixed income intuition to a graphical representation. The setup is a standard coupon bond, with the candidate asked to sketch how its market price varies as yield-to-maturity moves across a range of values, and to describe the qualitative features of that curve. This style of question is common in fixed income and rates interviews, including sell-side desk roles and buy-side analyst positions, where understanding how prices respond to rate moves is fundamental.

Answering well relies on comfort with present value formulas, discounting, and the idea that yields and prices move in opposite directions. The interviewer is looking for the recognition that this relationship is nonlinear and for a clear, verbal explanation of why the curve is bowed rather than a straight line. Strong answers typically invoke duration and convexity language, connect to sensitivity of price to small yield changes, and may mention higher-order effects. Clarity of reasoning, not algebra, is what is being tested.

What it tests

The price-yield relationship for bonds is governed by the mathematical structure of present value: as yield increases, each future cash flow is discounted more heavily, causing the bond price to fall. This relationship is inherently nonlinear because the present value formula involves exponentials of the yield, so equal changes in yield do not produce equal changes in price. The curve's convexity arises because the rate at which price falls slows down as yield rises—each additional increment in yield reduces price by a smaller amount than the previous increment. This is a general property of discounting: the marginal effect of increasing the discount rate diminishes as the rate grows, resulting in a convex (bowed) curve. The convexity is a direct consequence of the second derivative of price with respect to yield being positive, reflecting the diminishing sensitivity of price to yield at higher yields.