Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 47, 4/8/6
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http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary
You are the investment actuary for a small insurance company that has a liability of
$10,000,000 payable as a lump sum in one year, and $5,000,000 payable as a lump sum
in ten years. Current interest rate is 6.41% for all maturities. You decide to invest your
company’s assets in one zero-coupon bond, whose Macaulay duration exactly matches
the Macaulay duration of the combined liabilities portfolio. Find the maturity of the
appropriate zero-coupon bond that your company will invest in as a result of your
decision.
A. 3.00 years B. 3.09 years C. 3.17 years D. 3.25 years E. 3.41 years
Solution.
The Macaulay duration of the liabilities portfolio is
10, 000, 000
5, 000, 000
1!
+ 10 !
1.0641
1.064110 " 3.00.
10, 000, 000 5, 000, 000
+
1.064110
1.0641
The Macaulay duration of the zero-coupon bond must be the same. Since for a zerocoupon bond its Macaulay duration equals its maturity, the maturity desired is 3 years
exactly.
Answer A.
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