FRM Part I · FRM Exam Part I · Interest Rates
A three-year bond with a face value of 1,000 pays a 5% annual coupon and currently trades at par with a yield of 5%. If its yield rises immediately to 6%, what is the new price?
The new price is 973.27. Discounting coupons of 50 and the 1,000 principal at 6% for three years gives 133.65 plus 839.62. The price falls when yields rise, and the drop is not a simple linear 3% because of convexity.
- A973.27Correct
- B970.00
- C1,026.73
- D940.00
Explanation
Price = 50 × annuity factor + 1,000/1.06^3 = 50 × 2.6730 + 839.62 = 133.65 + 839.62 = 973.27. A linear 1% × 3 years drop (970) ignores the convexity of the price-yield relationship. 1,026.73 reverses the direction of the price change.
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