What is 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. Breaking Down Weighted Average Life – WAL

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 most 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 loan or deposit 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.

Weighted Average Life Calculation Example

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.

• 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

Using Weighted Average Life – WAL

WAL is one of the more useful analytic tools one can calculate. That is because it is not only how many years it will take to receive half the amount of the outstanding principal, but also it is the ratio of fees and costs to balances on a percentage basis plus more. Here are a few examples:

• Amortizing Loan Origination expenses: For example, if you have \$2,500 of loan origination expenses and your WAL is calculated, as previously, at 2.91 years then you should recognize \$859 (\$2,500/2.91) of that expense this year
• Coupon Yield Adjustments: From the prior example, if you divide the \$859 expense recognition by the principle balance of the loan you will calculate the impact on yield as a percent change those fees impart on the underlying loan coupon rate.
• Counter the Income Distortions of CECL: The pending CECL regulations require the institution to recognize loan losses at the origination of the loan. This can cause most loans to seem highly unprofitable early in their lives until they earn enough income to cover those losses. Using the WAL is an excellent method to smooth those losses over the life of the asset by showing the true life-time economic value.
• Determining Loan Loss Reserve level:   If you multiply the outstanding balance of a portfolio of loans times the loan loss provision (LLP) times the WAL the result will be the appropriate amount of reserves you should be holding for the portfolio.
• Determining Loan Loss Reserve Coverage: This is just the opposite of the prior calculation.   Take the Loan Loss Reserves and divide by the portfolio balance divided by the WAL provides the Loan Loss Provision you have reserved for. Now compare that to the portfolio’s actual Loan Loss Provision to see if you are too high or too low.
• Understanding the Relative Mismatch between your Assets and Liabilities: The difference between the WAL of your Assets and the WAL of your liabilities is a solid indicator of embedded interest rate risk on your current balance sheet.
• Forecasting “Future Costs” for loan/deposit pricing: One of the common mistakes made when cost+ pricing of loans is to use “average costs” from the profitability system. That approach fails to recognize that those are historical costs which may not reflect future costs. The WAL is an excellent tool to “inflation adjust” those historical costs so that they reflect future costs.
• Assigning Funds Transfer Pricing (FTP) Rates: If you are interested in learning more about please FTP see Kohl’s information on the subject. However, for this discussion, the WAL number can be used to determine what rate, based on the WAL term, to assign to a loan or deposit from a historical FTP yield curve.
• Assigning Liquidity Transfer Pricing (LTP) Rates: LTP is of create interest to regulators because of the liquidity issues associated with the last banking crisis. The WAL is a key parameter to calculating and assigning a liquidity premium for non-HQLAs

As you can see, the WAL calculation is very useful and should be a part of every financial analytics toolbox.