IOs and whole mortgages are driven by the same prepayment option, but they respond differently because they own different cash flows. When rates fall sufficiently to trigger refinancing, the loan ends early. For an IO, that event destroys the asset: all future interest payments disappear, so the present value falls when rates fall into refinancing territory, giving the IO negative duration. A whole mortgage owns both the interest and the principal. When prepayment occurs, the interest stream ends but principal is returned at par immediately rather than at maturity. Whether the mortgage exhibits negative duration or negative convexity depends on the trade-off between two competing effects: the loss of future interest payments versus the benefit of receiving principal back early to reinvest at higher present values.

Consider a $100 mortgage at 6% with 30 years remaining. At par, the interest stream ($6/year for 30 years) has a present value of roughly $83, while the principal ($100 in 30 years) contributes only $17. When rates fall moderately to 4.5%, the interest stream PV rises to about $98 and principal to $27, giving a total value around $125 without prepayment. But as refinancing becomes attractive—say 50% likely—the expected value drops to roughly $113 (a blend of $100 from prepayment and $125 from continuation), still showing positive duration. When rates fall further to 3%, however, the dynamics shift. Without prepayment, the interest stream alone would be worth $118 and the total mortgage $159. But if prepayment is now 90% likely, the expected value collapses to about $106—a decline from $113 despite rates falling from 4.5% to 3%. This is negative duration: the loss of $118 in interest present value, weighted by rising prepayment probability, exceeds the gain from discounting principal at lower rates. The mortgage price actually falls as rates fall because the valuable interest cash flows are being destroyed faster than the principal component benefits from lower discount rates. If rates continue to 2% with refinancing certain, the price becomes stuck at $100 regardless of further rate movements—zero duration in this region.

The magnitude of this effect depends critically on time remaining. For the same mortgage with only 5 years left, the interest stream at 3% rates is worth just $27 rather than $118, so prepayment destroys far less value. The principal acceleration (receiving $100 now versus $86 discounted for 5 years) becomes relatively more important, making negative duration less likely. Instead, the mortgage exhibits negative convexity: price still rises with falling rates, but the rate of increase diminishes as prepayment looms.

The prepayment option exercises in both cases; the difference is that it always eliminates the IO’s entire value, while for the mortgage it creates either negative duration or negative convexity depending on how much interest cash flow remains to be lost versus how much the principal acceleration is worth. Short-duration or low-coupon mortgages generally exhibit negative convexity but retain positive duration, while negative duration is usually is a special, local phenomenon that arises in long-dated, high-coupon loans as rates enter the refinancing region.