A Risk Minimizing Strategy for Portfolio Immunization
证明，当固定收益投资组合的久期等于投资期限时，其期末价值变化存在一个下限，该下限由利率变化和组合结构决定，后者可作为免疫风险的度量，最小化该度量可降低利率变动对组合的影响。
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.