FRM Part I · FRM Exam Part I · Stress Testing
A firm holds a bond portfolio worth USD 200 million with modified duration 5.0 and convexity 40. A stress scenario applies a parallel upward shift of 200 bp. Using the duration-plus-convexity approximation, what is the estimated portfolio loss?
The estimated loss is USD 18.4 million. The price change is minus 5.0 times 2 percent, which is minus 10 percent, plus the convexity gain of 0.5 times 40 times 0.0004, which is 0.8 percent, giving minus 9.2 percent of 200 million.
- AUSD 18.4 millionCorrect
- BUSD 20.0 million
- CUSD 21.6 million
- DUSD 19.2 million
Explanation
Percentage change = -5.0(0.02) + 0.5(40)(0.02)^2 = -0.10 + 0.008 = -0.092. Loss = 0.092 x 200 = 18.4 million. Duration alone gives 20.0 million. Subtracting the convexity term instead of adding gives 21.6 million.
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