ABSTRACT Consider a fixed‐income portfolio whose duration is equal to the length of a given investment horizon. It is shown that there is a lower limit on the change in the end‐of‐horizon value of the portfolio resulting from any given change in the structure of interest rates. This lower limit is the product of two terms, of which one is a function of the interest rate change only, and the other depends only on the structure of the portfolio. Consequently, this second term provides a measure of immunization risk. If this measure is minimized, the exposure of the portfolio to any interest rate change is the lowest.