Revision as of 18:16, 20 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>2.73</li><li>3.04</li><li>3.34</li><li>3.40</li><li>3.65</li></ul> {{soacopyright | 2023 }}")
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AAdmin
Nov 20'23

Exercise

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.

AAdmin
Nov 20'23

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.

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