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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

A 10-year zero-coupon bond is compared with a 10-year coupon bond of the same yield. Which statement about their duration and convexity is correct?

The zero-coupon bond has both higher Macaulay duration and higher convexity. All its cash flow arrives at maturity, so its duration equals 10 years, while the coupon bond returns part of its value earlier and therefore has a shorter, less convex profile.

  1. AThe zero-coupon bond has higher Macaulay duration and higher convexityCorrect
  2. BThe zero-coupon bond has lower duration but higher convexity
  3. CThe coupon bond has higher duration and higher convexity
  4. DBoth have the same Macaulay duration because maturities are equal

Explanation

A zero-coupon bond pays everything at maturity, so its Macaulay duration equals 10 years, exceeding that of the coupon bond. Its cash flows are also more concentrated at a distant date, giving higher convexity.

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