Asset/Liability Matching (Five Moments)

It is well known that re-investment risk can be greatly reduced to the assets which are assigned to support liabilities are “matched. ” In particular matching two properties of the asset and liability cash flows, the dollar duration (DDl) and dollar convexity (DD2). can provide a significant reduction in re-investment risk. This paper provides a rigorous mathematical treatment of the asset/liability matching problem. This paper initially shows that DDl and DD2 are the first two moments of a set of cash flows (DDn). By means of a Taylor expansion of the present value of a set of cash flows, the paper then shows why matching individual moments of an asset flow with the corresponding moments associated with a liability flow can reduce re-investment risk, DDn. Finally, for every cash flow and pair of interest rates, there exists a characteristic time T. Even if the flow is originally priced to yield the first interest rate, and it is the second interest rate that prevails, the initial yield rate can be achieved by selling the flow at time T. The paper shows how this relates to asset/liability matching, and how T call be expressed in terms of the generalized moments.