The Matching of Assets and Liabilities

In the British actuarial journals most papers on immunization examine the theory as it applies to the valuation of the assets and liabilities of an insurance company or a pension fund. The papers deal primarily with valuation and little with how to determine investment strategy. This paper investigates how the concepts of asset-liability matching can be used to shape investment strategy.A general model for matching assets and liabilities is developed. Three aspects of the investment problem are discussed: initial investment strategy, reinvestment strategy, and asset liquidation strategy. Reinvestments and disinvestments are handled by an investment-year method. Explicit provision is made for different new-money rates in each future year.The model is defined by specifying (1) the schedule of interest and principal payments for representative investment instruments comprising the initial portfolio, (2) the expected net cash outflows of the pension fund or other block of business, (3) rollover rates for reinvestments, and (I) a set of patterns of future new-money interest rates. An investment strategy is defined to be a specific allocation of investable funds among the representative instruments. The model solves for a region of strategies that result in a nonnegative total fund value at the end of the investment horizon for each interest rate pattern in the set described in item 4.Conventional immunization theory is identified as a special case of the general model in which each interest rate pattern represents an immediate and permanent change in the level of interest rates from the current level. The problem of establishing the interest guarantee for a deposit fund is discussed as an example where conventional immunization theory fails but the general model does not.