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.