Weighted-average life

In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, 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,

where:

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.

In loans that allow prepayment, the WAL cannot be computed from the amortization schedule alone; one must also make assumptions about the prepayment and default behavior, and the quoted WAL will be an estimate. The WAL is usually computed from a single cash-flow sequence. Occasionally, a simulated average life may be computed from multiple cash-flow scenarios, such as those from an option-adjusted spread model.

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