I have a pool of (mortgage) assets that pay cashflows as below. How could I correctly calculate the duration? Does it have a meaning in the sense of a vanilla/callable bond as the measure of price sensitivity?

Year CF

0 1

1 25

2 25

3 0

4 0

5 -5

6 0

7 -5

8 5


1 Answer 1


You can calculate the duration and use it as sensitivity measure, as you are used to.

That is because the npv of the cashflows is: $NPV = \sum_i [ c_i * \exp(- y_i * t_i ) ]$

With $c_i$ the fixed cashflow amount at time $t_i$.

From that it follows, that the derivative of the NPV with respect to a parallel shift of the yieldcurve is

$d(NPV)/dy = - \sum[ c_i * t_i * \exp(- y_i * t_i ) ]$

If you divide that by the NPV, you get the definition of the duration. You see the formulas are valid regardless of the sign or amount of the $c_i$.


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