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
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 $c_i$.
