CFA Level I · CFA Level I Exam · Fixed-Income Bond Valuation: Prices and Yields
A 5-year annual-pay bond with a 5% coupon and face value of 100 has a yield to maturity of 5%. If the yield rises to 6% and then instead falls to 4% (from 5%), the changes in price are most likely:
The price falls about 4.21 when the yield rises to 6% and rises about 4.45 when it falls to 4%. The price-yield curve is convex, so equal yield moves produce a larger price gain than loss.
- Aa fall of 4.21 and a rise of 4.45Correct
- Ba fall of 4.45 and a rise of 4.21
- Ca fall of 4.21 and a rise of 4.21
Explanation
At 5% the price is 100. At 6%: 5 x 4.2124 + 100/1.3382 = 21.06 + 74.73 = 95.79, a fall of 4.21. At 4%: 5 x 4.4518 + 100/1.21665 = 22.26 + 82.19 = 104.45, a rise of 4.45. The price-yield relation is convex, so a yield decline raises price more than an equal rise lowers it.
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