A 20-year bond priced to have an annual effective yield of 10% has a Macaulay duration of 11. Immediately after the bond is priced, the market yield rate increases by 0.25%. The bond's approximate percentage price change, using a first-order Macaulay approximation, is X.

Calculate X.

• –2.22%
• –2.47%
• –2.50%
• –2.62%
• –2.75%

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

[[math]]P(0.1025)\approx P(0.10){\Biggl({\frac{1.10}{1.1025}}{\Biggr)}}^{11}=0.97534P(0.10). [[/math]]

Therefore, the approximate percentage price change is 100(0.97534 – 1) = –2.47%.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.