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Nov 20'23
Exercise
A common stock pays a constant dividend at the end of each year into perpetuity.
Using an annual effective interest rate of 10%, calculate the Macaulay duration of the stock.
- 7 years
- 9 years
- 11 years
- 19 years
- 27 years
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: C
The size of the dividend does not matter, so assume it is 1. Then the duration is
[[math]]
\frac{\sum_{t=1}^{\infty}tv^t}{\sum_{t=1}^{\infty}v^t} = \frac{(Ia)_{\overline{\infty}|}}{a_{\overline{\infty}|}} = \frac{\ddot a_{\overline{\infty}|}/i}{1/i} = \frac{1/(di)}{1/i} = \frac{1}{d} = \frac{1.1}{0.1} =11.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.