TIPS, the Dual Duration, and the Pension Plan

By defining “duration” as the sensitivity of an asset's price to changes in some other variable, one may characterize any asset as having an inflation duration, D_i, and a real-interest-rate duration, D_r. Unlike nominal bonds, for which D_i = D_r, inflation-linked bonds, such as Treasury Inflation-Indexed Securities (commonly called TIPS), have different values for D_i and D_r. Defined-benefit pension liabilities also have different values for D_i and D_r. Such liabilities can be modeled as bonds (or portfolios of bonds and equities or other assets) held short. Thus, by appropriately combining TIPS and nominal bonds, a manager can build a portfolio that has the same inflation duration and real-interest-rate duration as the liability stream. Equities also have different values for D_i and D_r, so the interaction of equities with TIPS and nominal bonds can be exploited in forming efficient pension portfolios—particularly in defeasing various liability streams.