Skip to content

FRM Part I · FRM Exam Part I · Interest Rates

A 10-year zero-coupon bond has an annually compounded yield of 5.0%. For a zero-coupon bond, modified duration is n/(1+y) and convexity is n(n+1)/(1+y)^2. Using duration and convexity, what is the approximate percentage price change if the yield falls by 50 basis points?

The price rises by about 4.89%. Modified duration is 10/1.05 = 9.524 and convexity is 110/1.1025 = 99.77. The duration term gives +4.76% and the convexity term adds +0.125%. Using Macaulay duration of 10 would overstate the gain.

  1. A+4.89%Correct
  2. B+4.76%
  3. C+4.64%
  4. D+5.00%

Explanation

Modified duration = 10/1.05 = 9.5238. Convexity = 110/1.1025 = 99.77. Change = 9.5238 x 0.005 + 0.5 x 99.77 x 0.005^2 = 0.04762 + 0.00125 = 4.89%. Duration alone gives 4.76%. Subtracting convexity gives 4.64%. Using maturity of 10 as duration gives 5.00%.

Did you get it right without looking?

One question tells you little. A timed set on Interest Rates shows your real accuracy, how long you take and where you lose marks.

Practise Interest RatesFree diagnostic mock

More Interest Rates questions