Asset-Liability Matching: Redington and Full Immunization

Redington Immunization Revisited

Redington immunization protects against small parallel shifts in the yield curve. The three conditions are: (1) present value of assets equals present value of liabilities, (2) first moments match (duration equality), (3) the second moment of assets exceeds that of liabilities (convexity condition). Mathematically, if h(i) = PV_A(i) - PV_L(i), we need h(i0) = 0, h'(i0) = 0, and h''(i0) > 0 at the current yield i0. This ensures h has a local minimum at i0 with h(i0) = 0, so h(i) >= 0 for i near i0.

Full Immunization

Full immunization protects against any parallel shift, not just small ones. For a single liability at time T, full immunization requires asset cash flows at times T - a and T + b (for a, b > 0) such that: (1) PV(assets) = PV(liability) and (2) Duration(assets) = T. With two asset cash flows straddling the liability, the convexity condition is automatically satisfied, and the surplus function h(i) >= 0 for all i, not just near i0.

This stronger guarantee comes from the mathematical structure: h(i) is a convex function with a minimum of zero, so it cannot become negative.

Cash Flow Matching (Dedication)

Cash flow matching (dedication) exactly matches each liability payment with a corresponding asset cash flow at the same time. This eliminates all interest rate risk since there are no reinvestment decisions. The cost is usually higher than Redington immunization because it constrains the asset choice more tightly. On Exam FM, problems may ask you to compare the cost of dedication versus immunization, or to construct a dedicated portfolio using zero-coupon bonds of various maturities.