A railroad company is required to pay 79,860, which is due three years from now. The company invests 15,000 in a bond with modified duration 1.80, and 45,000 in a bond with modified duration Dmod, to Redington immunize its position against small changes in the yield rate. The annual effective yield rate for each of the bonds is 10%.

Calculate Dmod.

• 2.73
• 3.04
• 3.34
• 3.40
• 3.65

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

Solution: B

The present value of the assets is 15,000 + 45,000 = 60,000 which is also the present value of the liability. The modified duration of the assets is the weighted average, or 0.25(1.80) + 0.75Dmod. The modified duration of the liability is 3/1.1 and so Dmod = (3/1.1 – 0.45)/0.75 = 3.04.

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