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 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.
[5] WAL should not be confused with the following distinct concepts: WAL is a measure that can be useful in credit risk analysis on fixed income securities, bearing in mind that the main credit risk of a loan is the risk of loss of principal.
All else equal, a bond with principal outstanding longer (i.e., longer WAL) has greater credit risk than a bond with shorter WAL.
In particular, WAL is often used as the basis for yield comparisons in I-spread calculations.
WAL should not be used to estimate a bond's price-sensitivity to interest-rate fluctuations, as WAL includes only the principal cash flows, omitting the interest payments.
Instead, one should use bond duration, which incorporates all the cash flows.
The WAL of a bullet loan (non-amortizing) is exactly the tenor, as the principal is repaid precisely at maturity.
On a 30-year amortizing loan, paying equal amounts monthly, one has the following WALs, for the given annual interest rates (and corresponding monthly payments per $100,000 principal balance, calculated via an amortization calculator and the formulas below relating amortized payments, total interest, and WAL): Note that as the interest rate increases, WAL increases, since the principal payments become increasingly back-loaded.
For a coupon of 0%, where the principal amortizes linearly, the WAL is exactly half the tenor plus half a payment period, because principal is repaid in arrears (at the end of the period).
, and now one multiplies by the principal to get total interest payments."
To ease exposition, assume that payments are monthly, so periodic interest rate is annual interest rate divided by 12, and time
(time in years is period number in months, over 12).
Both of these quantities are the time-weighted total principal of the bond (in periods), and they are simply different ways of slicing it: the
sum counts how long each dollar of principal is outstanding (it slices horizontally), while the
counts how much principal is outstanding at each point in time (it slices vertically).
For instance, if the principal amortized as $100, $80, $50 (with paydowns of $20, $30, $50), then the sum would on the one hand be
This is demonstrated in the following table, which shows the amortization schedule, broken up into principal repayments, where each column is a
, so the WAL is: Similarly, the total interest as percentage of principal is given by