Amortizing Bond

A fully amortizing bond is priced as an annuity. Given a principal amount, a periodic coupon rate and a number of periods, the level payment is the principal divided by the present value annuity factor for that rate and term. Equivalently, the payment is the amount that, discounted at the periodic rate over all remaining periods, exactly equals the outstanding balance.

Each payment is then split mechanically. Interest for the period equals the beginning-of-period outstanding balance multiplied by the periodic rate. Whatever remains of the payment reduces principal, and the new balance carries into the next period. Because the balance falls, the interest charge falls each period and the principal component rises correspondingly, accelerating toward maturity. At the final payment the balance reaches zero, with no separate redemption of face value. A partially amortizing structure uses the same arithmetic but sizes the payment so a specified balloon remains outstanding at the end.

Most consumer and secured lending amortizes. Residential and commercial mortgages, auto loans, equipment leases and bank term loans all repay principal over their lives, which is why the securitized products built on them (mortgage-backed securities, auto ABS and equipment lease ABS) pass amortized principal through to investors rather than repaying a single face amount.

In the corporate bond market, amortization also appears through sinking fund provisions, where the issuer retires a stated portion of the issue each year by open-market purchase or by calling bonds at par, often selected by lottery. Project finance and infrastructure debt is typically amortizing because the underlying asset generates a finite stream of cash flows. Sovereigns and investment-grade corporates, by contrast, usually issue bullet bonds and refinance at maturity, accepting rollover risk in exchange for lower current debt service.

Valuation is unchanged in principle: discount each scheduled payment at the appropriate spot rate or at a single yield. What changes is the timing profile. Because principal is returned throughout the life of the bond, the weighted average time to receipt of cash flows is shorter than for a bullet of identical maturity, so Macaulay and modified duration are lower and price sensitivity to yield changes is smaller.

Credit exposure also declines as the balance amortizes, which is one reason amortizing loans support higher leverage against a given asset. Offsetting this, the investor receives cash sooner and must reinvest it, so reinvestment risk rises. Where borrowers may prepay, as in mortgage pools, actual principal timing is uncertain: analysts work with weighted average life under prepayment assumptions, and negative convexity emerges because prepayments accelerate when rates fall.

Candidates should be able to construct an amortization table for at least the first two or three periods: compute the level payment from the annuity factor, apply the periodic rate to the opening balance to isolate interest, subtract the residual as principal, and roll the balance forward. Questions frequently ask for the interest portion of a specific later payment or the balance remaining after a given number of payments, both of which follow from that recursion or from present-valuing the remaining payments.

Beyond arithmetic, be ready to compare an amortizing bond with a bullet and a zero-coupon bond of the same maturity on duration, reinvestment risk and credit exposure, to classify a structure as fully or partially amortizing, and to explain why securitizations of amortizing collateral require assumptions about prepayment speed before average life can be estimated.