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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A callable bond exhibits negative convexity when yields fall to levels near the call price. Compared with the estimate from modified duration alone, how does the actual price change for a large decline in yields behave?

The actual price rise is smaller than the duration estimate. Negative convexity makes the second-order term negative, and the rising chance of being called caps price appreciation as yields fall, so the price still rises but by less than duration predicts.

  1. AThe actual price rise is greater than the duration estimate
  2. BThe actual price rise is smaller than the duration estimateCorrect
  3. CThe actual price rise equals the duration estimate because the call option offsets convexity
  4. DThe price falls because the call is likely to be exercised

Explanation

With negative convexity the second-order term 0.5·C·(Δy)² is negative, so it reduces the gain predicted by duration. As yields fall, the likelihood of a call increases and price appreciation is capped. The price still rises, but by less than the duration-only estimate.

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