Tham khảo tài liệu 'prentice hall frank fabozzi bond markets analysis_10', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 464 CHAPTER 19 Liability Funding Strategies CF 1 - H 2 CFZ 2 - H 2 CF n - H 2 1 y 1 y 2 1 y where CF cash flow of the portfolio at time period t H length in years of the investment horizon or liability due date y yield for the portfolio n time to receipt of the last cash flow The immunization risk measure agrees with our earlier graphic analysis of the relative risk associated with a barbell and a bullet portfolio. For the barbell portfolio portfolio A in Exhibit 19-10 the portfolio s cash flow payments are widely dispersed in time and the immunization risk measure would be high. The portfolio cash flow payments for the bullet portfolio portfolio B in Exhibit 19-10 are close to the liabil- ity due date so the immunization risk measure is low. Notice that if all the cash flows are received at the liability due date the immu- j nization risk measure is zero. In such a case the portfolio is equivalent to a pure discount security zero-coupon security that matures on the liability due date. If a portfolio can be constructed that replicates a pure discount security maturing on the liability due date that portfolio will be the one with the lowest immunization risk. Typically however it is not possible to construct such an ideal portfolio. The objective in constructing an immunized portfolio then is to match the portfolio s duration to the liability s duration and select the portfolio that minimizes the immunization risk. The immunization risk measure can be used to construct approximate confidence intervals for the target yield and the target accumulated value. Zero-Coupon Bonds and Immunization So far we have dealt with coupon bonds. An alternative approach to immunizing a portfolio against changes in the market yield is to invest in zero-coupon bonds with a maturity equal to the investment horizon. This is consistent with the basic principle of immunization because he duration of a zero-coupon bond is equal to the liability s duration. However in practice the yield on .
