Visualizing the Duration of Assets

This is just a simple example comparing the durations of two different assets.  Investment 1 pays $1000 in year 1, $2000 in year 2, and $3000 in year 3; Investment 2 pays $3000 in year 1, $2000 in year 2, and $1000 in year 3.  At an interest rate of 8%, investment 1 is worth $5022.10 and investment 2 is worth $5286.29.

Obviously asset 1 is more risky because its larger payments come later.  This means that the bulk of its worth is subject to more interest rate fluctuation.  We would expect it to have a higher Duration than asset 2.  This is easy to verify; The Duration of Asset 1 is 2.28983 (DM = 2.12) and the Duration of Asset 2 is 1.6247 (DM = 1.50435).  Therefore, we’d expect asset 1 to be disproportionately affected by interest rate fluctuations, which is evident from the graph below.


The PV of the assets is almost the same at low interest rates, and investment 1 decreases in value more than investment 2 does when interest rates change.


About schapshow

Math & Statistics graduate who likes gymnastics, 90s alternative music, and statistical modeling. View all posts by schapshow

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