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: is the (total) principal, is the principal repayment that is included in payment , hence is the fraction of the total principal that is included in payment , and is the time (in years) from the calculation date to payment . If desired, can be expanded as for a monthly bond, where 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. WAL should not be confused with the following distinct concepts: Bond duration Bond duration is the weighted-average time to receive the discounted present values of all the cash flows (including both principal and interest), while WAL is the weighted-average time to receive simply the principal payments (not including interest, and not discounting). For an amortizing loan with equal payments, the WAL will be higher than the duration, as the early payments are weighted towards interest, while the later payments are weighted towards principal, and further, taking present value (in duration) discounts the later payments. Time until 50% of the principal has been repaid WAL is a mean, while "50% of the principal repaid" is a median; see difference between mean and median. Since principal outstanding is a concave function (of time) for a flat payment amortizing loan, less than half the principal will have been paid off at the WAL. Intuitively, this is because most of the principal repayment happens at the end.