A trucking company with assets and liabilities needs to choose between various ten-year par value bonds each with 8% annual effective yield rate and annual coupons. The bonds have varying face values and varying coupon rates. The company wants to analyze the effects of face value and coupon rate changes on Macaulay duration of these bonds, in order to choose an investment strategy that immunizes its position. Determine which of the following statements is true about the separate effects of face value and coupon rate changes on the duration of these bonds.

• Macaulay duration increases as face value increases, and increases as coupon rate increases.
• Macaulay duration increases as face value increases, and decreases as coupon rate increases.
• Macaulay duration remains constant as face value increases, and increases as coupon rate increases.
• Macaulay duration remains constant as face value increases, and remains constant as coupon rate increases.
• Macaulay duration remains constant as face value increases, and decreases as coupon rate increases

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

Solution: E

A change in face value multiplies all cash flows by the same amount. Therefore, there is no change in the duration. If the coupon rate increases, the coupons become larger, but the redemption value stays the same. This causes payments prior to redemption to receive more weight relative to the payment at redemption and thus the duration will decrease.

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