Asset-Liability Portfolio

Study guide: Exam FM-2

An asset-liability portfolio is the combined position of an institution's assets and the liabilities they are held to fund, valued together. Its surplus — the present value of the asset cash flows A_t less that of the liability cash flows L_t — is what asset-liability management protects against changes in the interest rate i.

S(i) = \sum_{t} v^t \left(A_t - L_t\right) = PV_A(i) - PV_L(i)

• Cash Flow Matching (dedication): choose assets whose cash flow on each date exactly equals the liability cash flow due that date, which protects the surplus against any movement in interest rates
• Redington Immunization: equal present values, equal modified durations (Duration Matching), and asset Convexity greater than liability convexity — all three are required; it protects against small changes in i
• Full Immunization (single liability): equal present values, equal durations, and one asset cash flow before and one after the liability — the surplus is positive for any immediate change in i
• Banks, insurers and pension funds manage their assets and liabilities together because their net worth — the surplus — fluctuates with the interest rate (Immunization is the general name for the duration-based strategies)

Simple ALM An insurer has a liability of 50{,}000 due in exactly 4 years at i=5\%. Describe a cash-flow-matched portfolio.

Answer Purchase a 4-year zero-coupon bond with face value 50{,}000 at a cost of 50{,}000(1.05)^{-4} = 41{,}135.12 The bond's single cash flow exactly matches the liability, so the surplus is zero at every interest rate: the position carries no interest rate risk.