Weighted-average life

In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life,^[1][2][3] is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid.

In a formula,^[4]

${\displaystyle {\text{WAL}}=\sum _{i=1}^{n}{\frac {P_{i}}{P}}t_{i},}$

where:

• ${\displaystyle P}$ is the (total) principal,
• ${\displaystyle P_{i}}$ is the principal repayment that is included in payment ${\displaystyle i}$, hence
• ${\displaystyle {\frac {P_{i}}{P}}}$ is the fraction of the total principal that is included in payment ${\displaystyle i}$, and
• ${\displaystyle t_{i}}$ is the time (in years) from the calculation date to payment ${\displaystyle i}$.

If desired, ${\displaystyle t_{i}}$ can be expanded as ${\displaystyle {\frac {1}{12}}(i+\alpha -1)}$ for a monthly bond, where ${\displaystyle \alpha }$ is the fraction of a month between settlement date and first cash flow date.