Calculate the Weighted Average Life

Calculate the weighted average life (WAL) for bonds, mortgages, and loans with precision.

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Annual Summary of Principal Repayment and Interest (First 10 Years shown)

Year	Principal Paid	Interest Paid	Remaining Balance

What is Weighted Average Life (WAL)?

The Weighted Average Life (WAL) is a critical financial metric used to measure the average amount of time that each dollar of unpaid principal on a loan, mortgage, or bond remains outstanding. Unlike the simple maturity date, which only tells you when the final payment is due, calculating the weighted average life provides a more realistic timeline of principal repayment, accounting for amortization and potential early prepayments.

Financial analysts, investors in Mortgage-Backed Securities (MBS), and portfolio managers use WAL to assess credit risk and interest rate sensitivity. A shorter WAL implies that principal is returned faster, reducing the lender's exposure to long-term market fluctuations. Conversely, a longer WAL indicates that capital is tied up for a more extended period.

Who Should Calculate Weighted Average Life?

• Bond Investors: To estimate the effective maturity of amortizing bonds.
• Mortgage Lenders: To understand the true duration of their loan portfolios.
• Corporate Treasurers: To manage debt schedules and liquidity planning.

Weighted Average Life Formula and Explanation

To accurately calculate the weighted average life, one must sum the product of each principal repayment and the time at which it is paid, then divide by the total original principal.

WAL = Σ ( P_t × t ) / Total Principal

Variable	Meaning	Unit
Pt	Principal repayment amount at time t	Currency ($)
t	Time elapsed since origination	Years
Total Principal	The initial loan or bond amount	Currency ($)
CPR	Constant Prepayment Rate (optional factor)	Percentage (%)

The calculation becomes complex when introducing the Constant Prepayment Rate (CPR). CPR assumes a fraction of the outstanding principal is prepaid annually, accelerating the reduction of the balance and shortening the WAL significantly.

Practical Examples of WAL Calculation

Example 1: The "Bullet" Bond

Consider a $100,000 corporate bond with a 5-year term that pays interest only until maturity (a "bullet" structure). Since 100% of the principal is repaid at year 5:

• Principal Repaid at Year 5: $100,000
• Weighted Calculation: ($100,000 × 5) / $100,000 = 5.0 Years.

For bullet bonds, the WAL equals the maturity term.

Example 2: The Amortizing Mortgage

Now consider a $100,000 mortgage at 4% interest for 30 years. The borrower pays principal every month. In the early years, payments are mostly interest. In later years, payments are mostly principal. Because principal is returned gradually over the 30 years, the WAL will be significantly less than 30 years—typically around 18 to 22 years depending on the rate. If the borrower makes extra payments (prepayment), the WAL might drop to 10 or 12 years.

How to Use This Weighted Average Life Calculator

1. Enter Principal Balance: Input the total face value of the bond or the current loan balance.
2. Set Interest Rate: Enter the annual coupon or interest rate. Higher rates typically lead to slower initial principal paydown in standard amortization, slightly lengthening WAL.
3. Define Term: Input the total number of years until final maturity.
4. Adjust Prepayment Speed (CPR): This is crucial. If you expect early payoffs (e.g., refinancing), increase the CPR. A 0% CPR means no early payments; 10-20% is common for mortgages in low-rate environments.
5. Analyze Results: Look at the "Weighted Average Life" figure. Compare this against the original term to see how much faster the capital is being returned.

Key Factors That Affect Weighted Average Life

Several variables influence the outcome when you calculate the weighted average life:

• Amortization Schedule: Loans that pay principal monthly (like mortgages) have a shorter WAL than "interest-only" loans with a balloon payment.
• Prepayment Rates (CPR): This is the single biggest factor. High prepayment rates dramatically reduce WAL because principal is returned years ahead of schedule.
• Interest Rate: On a fixed payment loan, a higher interest rate means a smaller portion of the early payments goes toward principal, which can slightly extend the WAL compared to a lower-rate loan.
• Payment Frequency: Moving from monthly to bi-weekly payments accelerates principal reduction, shortening the WAL.
• Loan Term: Naturally, a 15-year loan has a shorter WAL than a 30-year loan, but the ratio of WAL to Term is often higher in shorter loans due to the amortization curve.
• Default Risk: While not calculated here, defaults effectively stop principal payments or result in a lump sum recovery, altering the realized WAL.

Frequently Asked Questions (FAQ)

How is Weighted Average Life different from Duration?

WAL focuses strictly on the repayment of principal. Duration (Macaulay or Modified) measures the weighted average time of all cash flows (principal plus interest) and is used primarily to measure sensitivity to interest rate changes.

Why is WAL shorter than the maturity date?

Unless the loan is a zero-coupon or bullet bond, some principal is paid back before the final date. These early payments drag the "average" time down.

What is a good WAL for an investment?

It depends on your goals. If you want liquidity, a shorter WAL is better. If you want to lock in a yield for a long time, a longer WAL is preferable.

Does inflation affect Weighted Average Life?

Indirectly. High inflation often leads to higher interest rates, which slows down prepayments (lower CPR), thereby extending the WAL of existing mortgages.

Can WAL be negative?

No, time cannot be negative. The minimum WAL is effectively zero (immediate repayment).

How does CPR relate to PSA?

CPR (Constant Prepayment Rate) and PSA (Public Securities Association) are both benchmarks for prepayment speed. 100% PSA roughly equates to a CPR that ramps up to 6% over 30 months.

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