Weighted Average Life - WAL

The weighted average life (WAL) is the average length of time that each dollar of unpaid principal on a loan, a mortgage or an amortizing bond remains outstanding. Calculating the WAL shows an investor, an analyst or a portfolio manager how many years it will take to receive half the amount of the outstanding principal.

The time weightings are based on the principal paydowns. A higher dollar amount means the corresponding time period has more weight in the WAL. For example, if the majority of the repayment amount is in 10 years, the weighted average life will be closer to 10 years.

The WAL gives investors or analysts a rough idea of how quickly the bond in question pays out returns. Since rational investors want to receive returns earlier, if two bonds were compared, the investor would select the one with the shorter WAL.

There are four steps involved in calculating an amortizing bond's WAL. Assume a bond makes one payment per year. Over the next five years, the bond's payments are $1,000, $2,000, $4,000, $6,000 and $10,000. The first step of the calculation is to take each of these payments and multiply them by the number of years until the payment occurs. In this example, these values would be:

Year 1 = 1 x $1,000 = $1,000

Year 2 = 2 x $2,000 = $4,000

Year 3 = 3 x $4,000 = $12,000

Year 4 = 4 x $6,000 = $24,000

Year 5 = 5 x $10,000 = $50,000

The second step in the calculation is to add these weighted amounts together. In this example, the total weighted payments equal $91,000. Step three is to add up the bond's total unweighted payments. In this example, the total is $23,000. The final step is to take the total weighted payments and divide this value by the total unweighted payments to get the WAL:

Weighted average life = $91,000 / $23,000 = 3.96 years

The largest payment is the final payment, so the WAL is close to the total five-year term of the bond. If, for example, the year two and year five payments were switched, the weighted average life would be much lower:

Year 1 = 1 x $1,000 = $1,000

Year 2 = 2 x $10,000 = $20,000

Year 3 = 3 x $4,000 = $12,000

Year 4 = 4 x $6,000 = $24,000

Year 5 = 5 x $2,000 = $10,000

Weighted average life = $67,000 / $23,000 = 2.91 years