FRM Part I · FRM Exam Part I · Interest Rates
A 3-year bond with a face value of 100 pays a 4% annual coupon and is priced at par (100) at a yield of 4%. Its modified duration is about 2.775. Immediately after the yield rises to 5%, what is the bond's exact price (annual compounding)?
The exact price is 97.28. Discounting the cash flows of 4, 4 and 104 at 5% gives 3.81, 3.63 and 89.84. The duration-only estimate of 97.22 is lower because it ignores convexity, which adds a small positive amount to the price after a yield rise.
- A97.28Correct
- B97.22
- C96.00
- D98.00
Explanation
Price = 4/1.05 + 4/1.1025 + 104/1.157625 = 3.8095 + 3.6281 + 89.8384 = 97.28. The duration estimate is 100 x (1 - 0.02775) = 97.22, which understates the price because it ignores positive convexity. The 96.00 option applies a flat 1% drop per year of maturity, which is wrong.
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