hard · Quantitative Finance
A bond's price P is a function of its yield y. If the second derivative P''(y) is positive, how does the duration-based estimate of a price fall (due to rising yields) compare to the actual price change?
- The duration-only estimate is perfectly accurate no matter how large the yield move is.
- The duration-only estimate overstates the price fall because convexity works in the holder's favor.
- The price will actually rise, since positive P''(y) flips the yield-price relationship's sign.
- The duration-only estimate meaningfully understates the true magnitude of the price decline that occurs.
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