Weighted-average Life - Related Concepts

Related Concepts

WAL should not be confused with the following distinct concepts:

Bond duration

Bond duration is the weighted average of the times of the present values of all the cash flows (not distinguishing between principal and interest), while WAL is the weighted average of the actual amounts of the principal payments (disregarding 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. This is a common misunderstanding. Since for a flat payment amortizing loan, principal outstanding is a concave function (of time), at the WAL, less than half the principal will have been paid off. Intuitively, this is because most of the principal repayment happens at the end. Formally, the distribution of repayments is negative skewed: the small principal repayments at the beginning drag down the WAL (mean) more than they reduce the median.

Weighted-average maturity (WAM)

WAM is an average across several loans, and applied to pools of mortgages, instead of an average of principal repayments for a single loan. There is also a notion of WAL within pools of loans, quite similar to but technically different from WAM, and unrelated to WAL as discussed in this article.