What is weighted average life (WAL)?
The average amount of time that each dollar of unpaid principal on a loan, mortgage, or amortizing bond stays outstanding is known as the weighted average life or WAL. An investor, analyst, or portfolio manager may determine how long it will take to receive about half of the outstanding principal by computing the weighted average maturity (WAL). When calculating the credit risk of fixed-income instruments, the formula is helpful.
Understanding Weighted Average Life (WAL)
Weighted average life computations employ temporal weightings that are dependent on principal payments. Every payment on several loans, including mortgages, is divided into principal and interest installments. Only principal payments are considered in WAL, which tend to increase with time. Specifically, interest is applied chiefly to early mortgage payments, whereas principal is primarily used to loan balances nearing maturity.
Example of Weighted Average Life
The WAL of an amortizing bond is calculated in four stages. A bond pays out once a year. The bond will be paid $1,000, $2,000, $4,000, $6,000, and $10,000 over the next five years. Consequently, before the WAL calculation, the total value of the (unweighted) payments was $23,000.
To begin the computation, multiply each of these installments by the total number of years that remain before the payment is made. These values, in this case, would be:
- Year 1: $1,000 x 1 equals $1,000
- $4,000 / 2 x $2,000 = Year 2.
- Year 3: $12,000 x 3 x $4,000
- Year 4: $4 times $6,000 equals $24,000.
- $50,000 × 5 x $10,000 = Year 5.
The computation proceeds with the addition of these weighted sums. The total weighted payments in this scenario are $91,000. The bond’s entire unweighted installments are added together in step three. The sum, in this case, is $23,000. To get the WAL, the total weighted payments must be divided by the total unweighted payments as the last step.
Weighted life expectancy is 3.96 years ($91,000 / $23,000).
In this case, WAL is almost equal to 4.00, and after four years, only half of the $23,000 principle is paid off, with $13,000 remaining. Since the final payment is the greatest, the WAL is closer to the bond’s five-year period. But the weighted average life would be much less if the payments for years two and five were exchanged:
- Year 1: $1,000 x 1 equals $1,000
- Year 2 is equal to two times $10,000, or $20,000.
- Year 3: $12,000 x 3 x $4,000
- Year 4: $4 times $6,000 equals $24,000.
- Five years times $2,000 is $10,000.
- The weighted average life is 2.91 years ($67,00 / $23,000).
WAL provides a ballpark estimate of the bond’s rate of return payout to analysts or investors. If two bonds were evaluated, the investor with the shorter WAL would be chosen since reasonable investors prefer to get their profits sooner. Put another way, principal loss is the most significant credit risk associated with a loan, and a lower WAL suggests a greater chance of principal repayment in full.
Conclusion
- The weighted average life is used to calculate the remaining debt on a loan or mortgage.
- The computation is “weighted” because it considers the timing of principal payments; for instance, if almost all principal payments are paid over five years, WAL will be nearly five years.
- Loan interest payments are not taken into account in the weighted average life.
- Since a smaller WAL indicates a reduced credit risk, most investors will choose the bond with the smaller WAL.
