Amortizing Bond

Fixed Income · basic · CC-BY-4.0

An amortizing bond is a fixed income instrument in which the principal outstanding declines over the life of the bond through periodic repayments of principal embedded in each coupon payment, reducing interest payments over time as the outstanding balance decreases. Mortgage-backed securities (MBS) are the most prominent example of amortizing structures, though auto loans, equipment trusts, and some corporate debt also employ amortizing designs.

Key takeaways

Each payment in an amortizing structure includes both an interest component (coupon rate × outstanding principal) and a principal component, with the split shifting over time—early payments are interest-heavy, later payments are principal-heavy.
The average life of an amortizing bond (the weighted average time to principal repayment) is shorter than its final maturity and is the standard duration measure used for MBS and ABS comparison.
Prepayment risk is the primary analytic challenge for amortizing bonds: when rates fall, borrowers refinance, returning principal earlier than expected (extension risk arises when rates rise, slowing prepayments).
Yield for amortizing bonds is quoted as a spread over a matched-maturity Treasury based on their projected average life, accounting for expected prepayment behavior under a standard prepayment model (PSA).
The pricing of amortizing bonds requires modeling the prepayment function—typically using the PSA prepayment model or more sophisticated econometric models—to project the expected cash flow schedule.

Explanation

Unlike bullet bonds that return all principal at maturity, amortizing bonds return principal in installments throughout the bond's life. This structural difference has profound implications for duration, reinvestment risk, and cash flow predictability. A standard 30-year fixed-rate mortgage amortizes completely over its term: the monthly payment is sized so that the outstanding balance reaches zero at month 360, with each payment combining interest (declining over time) and principal (increasing over time).

The amortization schedule is calculated using the annuity formula. For a mortgage or loan with outstanding balance B, interest rate r (monthly), and remaining periods N, the monthly payment P = B × r / (1 - (1+r)^(-N)). Interest payment in period t = B_t × r; principal payment = P - Interest_t; new outstanding balance = B_t - Principal_t. This declining balance structure means that interest accruals decrease over time, making later-period cash flows predominantly principal repayment.

For fixed income portfolio management, amortizing bonds introduce complexity that bullet bonds lack. Duration calculation must account for the changing principal balance—the modified duration of an amortizing bond is shorter than a bullet bond of the same coupon and maturity because principal is returned earlier. Convexity can be negative for mortgage-backed securities due to prepayment optionality: when rates fall, prepayments accelerate, shortening duration precisely when investors want longer duration (duration shrinkage); when rates rise, prepayments slow, extending duration when investors prefer shorter duration (duration extension). This 'negative convexity' must be compensated by a spread over Treasuries.

The prepayment model is the central analytical tool for valuing amortizing bonds. The Public Securities Association (PSA) prepayment model provides a standard benchmark: 100 PSA assumes prepayments ramp from 0.2% CPR (constant prepayment rate) per annum in month 1 to 6% CPR by month 30, then remain constant. Actual prepayments are expressed as a percentage of PSA—'150 PSA' means prepayments are 1.5× the standard model. More sophisticated models use regression-based approaches incorporating current mortgage rates (refinancing incentive), loan age (burnout effect), seasonal patterns (home sales peak in spring), and borrower characteristics.

Formula

Monthly Payment = B × r / (1 - (1+r)^(-N))
where B = Outstanding Balance, r = Periodic Interest Rate, N = Remaining Periods
Average Life = Σ (t × Principal_t) / Total Principal

Example

A $500,000 30-year fixed-rate mortgage at 6.5% generates a monthly payment of $3,160.34. In the first month, interest is $500,000 × 0.065/12 = $2,708.33 and principal is $3,160.34 - $2,708.33 = $452.01. In month 120 (year 10), the outstanding balance has declined to approximately $440,000; interest is $440,000 × 0.065/12 = $2,383.33 and principal is $777.01. By month 300 (year 25), the outstanding balance is approximately $140,000; interest is $757 and principal $2,403. A bond investor owning a pool of such mortgages receives these aggregate cash flows, which decline in total dollar terms as prepayments reduce the outstanding pool balance—typically requiring the investor to reinvest principal returns at current (potentially lower) rates.

Amortizing Bond

Key takeaways

Explanation

Formula

Example

Related terms