FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01
A bond has key rate durations of 0.5 at the 2-year point, 3.0 at the 5-year point, and 4.5 at the 10-year point, and none elsewhere. The 2-year rate rises 20 bp, the 5-year rate rises 10 bp, and the 10-year rate falls 30 bp. Using key rate durations, what is the approximate percentage price change?
The bond's price rises about 0.95%. Multiplying each key rate duration by its yield change gives 0.10%, 0.30%, and -1.35%, summing to -0.95%. The price change is the negative of this sum, so the large fall in the 10-year rate outweighs the other increases.
- A+0.95%Correct
- B-0.95%
- C+1.75%
- D+0.35%
Explanation
Change = -Σ KRD*Δy = -(0.5*0.20% + 3.0*0.10% + 4.5*(-0.30%)) = -(0.10% + 0.30% - 1.35%) = -(-0.95%) = +0.95%. The -0.95% option has the sign flipped. The +1.75% option ignores the sign of the 10-year move (-(0.10+0.30+1.35)).
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