FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01
A 50 million bond portfolio has a modified duration of 6.0 and a convexity of 70. Yields rise by 150 basis points in parallel. What is the dollar value of the convexity adjustment to the duration-based price estimate?
The convexity adjustment is +393,750. It equals 0.5 times 70 times 0.015 squared, which is 0.7875% of the 50 million portfolio, and it offsets part of the 4.5 million duration-only loss.
- A+39,375
- B+393,750Correct
- C+787,500
- D+4,106,250
Explanation
Convexity term = 0.5*70*(0.015)^2 = 0.007875, or 0.7875% of value. Multiplying by 50,000,000 gives +393,750. The +787,500 option omits the 0.5 factor. The +4,106,250 option is the total estimated loss (duration loss of 4.5m less 0.39375m) in magnitude and is not the adjustment. The +39,375 option misplaces a decimal.
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