Amortizing Bonds: Weighted-Average Life Is Not Duration

What is weighted-average life for an amortizing bond?

Weighted-average life summarizes when principal is repaid: multiply each principal repayment by its time from the stated measurement date, sum those products and divide by the principal being repaid. Coupon interest is excluded from this principal-timing measure. The MSRB glossary presents an average-life calculation using bond-years. Preserve the timing origin and units so a figure measured from issue is not compared without adjustment to remaining life measured today.

An amortizing structure reduces outstanding principal through scheduled repayments rather than returning everything in one final bullet. The final maturity remains relevant, but it no longer states when every unit of principal comes back. Ask whether the schedule is fixed, subject to sinking-fund selection or dependent on borrower behavior. Those differences affect what the reported average life can legitimately describe and how stable it may be.

Reconcile coupons against the remaining balance

Specify whether interest accrues on the opening balance, an average balance or another contractual base. For a simple opening-balance schedule, principal repaid at a period's end no longer earns coupons in later periods. Applying the original face amount to every coupon would overstate promised income. Separate interest and principal in the ledger before calculating total receipts or comparing the schedule with a future spending obligation.

Do not infer this schedule from the word amortizing alone. A pool, tranche or sinking-fund bond can allocate principal differently from a simple deterministic loan. Investor.gov's mortgage-backed-securities description explains that principal and interest are distributed according to structure, with differing prepayment risks. That is a warning to read the allocation rules, not permission to treat all amortizing securities as the same product or calculation.

Reperform a synthetic three-year schedule

Assume USD 1,000 original principal, annual interest at 6% of opening principal and repayments of USD 200, USD 300 and USD 500 at the ends of years one, two and three. Opening balances are USD 1,000, USD 800 and USD 500. Coupons are USD 60, USD 48 and USD 30. Total scheduled receipts are USD 1,138, comprising USD 1,000 returned principal and USD 138 interest, with no reinvestment.

Weighted-average life is (200 times 1 plus 300 times 2 plus 500 times 3) divided by 1,000, or 2.3 years. Final maturity is three years. These are synthetic cash flows, not a security's terms or a return calculation. The USD 1,138 total does not establish profit without the purchase price, costs and payment realization, and it does not discount receipts to a common valuation date.

Why is average life different from duration?

Weighted-average life uses undiscounted principal amounts as weights. Macaulay duration uses present-value weights for the modeled cash flows, including coupons. Modified duration then connects a specified yield convention to a local price sensitivity. A principal-timing statistic cannot substitute for that derivative. Two securities can share average life while differing in coupons, discounting, optionality and price response, so matching this one statistic does not establish equivalent exposure.

Average life also need not be the date by which half the principal has been repaid. It is a weighted mean, not a median. Inspect the cumulative repayment schedule when the question is how much cash arrives by a deadline. In the synthetic example, the full schedule answers that question directly; compressing it into 2.3 years discards information needed to assess the timing of an actual obligation.

Keep scheduled and expected repayments distinct

If borrowers may prepay, the remaining principal path can depend on behavior and market conditions. An expected average life then needs a prepayment assumption rather than only the legal final maturity. Earlier principal return can shorten the receipt horizon and reduce future interest; slower repayment can extend exposure. Those are cash-flow changes, not just different discount rates applied to an otherwise fixed schedule.

Ask which prepayments, defaults and recoveries the projection includes, and retain each scenario's principal reconciliation. A smooth average-life figure can conceal divergent repayment paths. Do not claim to forecast mortgage behavior from this deterministic teaching example, and do not add a default loss to a projection that has already reduced receipts for the same impairment without understanding the construction. Separate payment uncertainty from a pure no-default repricing exercise.

Review the model boundary before using a ladder

The site's ladder contains bullet rungs, not amortizing securities. Any decomposition must preserve every coupon and repayment under consistent discounting. Matching final maturity or total principal is insufficient, especially with prepayment or tranche rules. Inspect the resulting schedule before assuming the structures are equivalent.

Check principal conservation, nonnegative balances, coupon bases and timing origin. Returned principal is not yield, and average life is not duration. Keep scheduled and behavior-dependent paths distinct. This ledger is educational, not an implemented amortizing-security calculator or a recommendation to fund a liability.

Primary references

1. MSRB: Glossary of Municipal Securities Terms, public full text, average-life calculation
2. SEC Investor.gov: Mortgage-Backed Securities and Collateralized Mortgage Obligations, public product description