Because mortgages are more likely to be prepaid rather than paid off on schedule, mortgage maturity (date the final mortgage payment is due) is not a good measure for the time length of a mortgage.

A more suitable measure is the Weighted Average Life (WAL). It is the weighted average time for principal repayment, that is, the average time it takes for every dollar of principal to be repaid. The time weights are based on the principal payments, i.e., the years with more principal payments will have a higher weight.

Average life is a better measure of length than mortgage maturity.

For a bullet (non-amortizing loan), the Weighted Average Life will be the same as its tenor because the full principal is repaid at maturity.

For a loan with a given maturity, WAL increases with the increase in coupon. This happens because with a higher coupon, the principal payments are further delayed in time. If the coupon was 0, and the loan was amortizing linearly, then WAL will be exactly half of the loan tenor plus half a period. Half a period is added because the payments are made in arrears. So for a 30 year 0% loan, paying monthly, the WAL is 15 1/24 years.

The average life estimate is heavily dependent on prepayment assumptions. We need to make an assumption about the prepayment rate, and estimate the WAL, which will be the simulated average life. Faster prepayment translates to a shorter average life.

## Calculating Weighted Average Life

Let’s take a simple example to understand how WAL can be calculated.

Assume a $10,000 mortgage with a maturity of 30 years and coupon of 6%. The monthly payments will be $59.96

For this loan, the WAL will be calculated as follows:

Let’s analyze this calculation. The numerator represents total interest payments, while the denominator represents annual interest payments. You can look at this mortgage as equivalent to a 19.31 bullet (non-amortizing) loan at 6% per annum. Both loans will generate the same interest cash flow. Since the WAL of the 19.31 years bullet loan is 19.31, the WAL of our mortgage will also be 19.31, i.e., the principal will be repaid in 19.31 years.

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