Krzys’ Ostaszewski, http://math.illinoisstate.edu/krzysio/
Author of the Course FM manual available at:
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
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May 2005 Course FM/2 Examination, Problem No. 6, and Dr. Ostaszewski’s online
exercise 286 posted November 6, 2010
John purchased three bonds to form a portfolio as follows:
• Bond A has semi-annual coupons at 4%, a duration of 21.46 years, and was purchased
for 980.
• Bond B is a 15-year bond with a duration of 12.35 years and was purchased for 1015.
• Bond C has a duration of 16.67 years and was purchased for 1000.
Calculate the duration of the portfolio at the time of purchase.
A. 16.62 years
B. 16.67 years
C. 16.72 years
D. 16.77 years
E. 16.82 years
Solution.
Duration of a portfolio (be it Macaulay duration or duration) is a market-value-weighted
average of the durations of its individual pieces, thus the duration of this portfolio is:
980
1015
⋅ 21.46 +
⋅12.35 +
980 + 1015 + 1000
980 + 1015 + 1000
1000
+
⋅16.67 ≈ 16.7733.
980 + 1015 + 1000
Answer D.
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Exercises from the past actuarial examinations are copyrighted by the Society of
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