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. Nominal bonds are generally considered to have one duration (the sensitivity of the bond's price to a change in its nominal yield or interest rate), but inflation-indexed bonds, such as Treasury Inflation-Indexed Securities (formerly, Treasury Inflation-Protected Securities, TIPS), may be regarded as having two durations: D i , the sensitivity of the bond's price to a change in inflation, and D r , the sensitivity of the bond's price to a change in real interest rates.For a nominal bond, whether a change in yield was caused by a change in inflation expectations or a change in the real interest rate does not matter; the effect on the bond's price is essentially the same either way. But for a TIPS bond, an increase in inflation does not affect the bond's price because the change in the cash flows in the numerator (of the equation for discounted cash flow analysis) is indexed to inflation and the discount rate in the denominator has also been increased by the same change in the expected inflation rate. Thus, the TIPS bond has an "inflation duration" of zero. A change in real interest rates, however, affects the price of a TIPS bond much as it does the price of a nominal bond, so a long-term TIPS bond has a long real-interest-rate duration—say, 15 years.The idea that an asset or stream of cash flows has two durations (an inflation duration and a real-interest-rate duration) can be extended to pension liabilities, equities, and so on. Defined-benefit pension liabilities also have this dual-duration characteristic; for liabilities with a full cost of living adjustment (COLA), the inflation duration is zero and the real-interest-rate duration is long. Thus, a portfolio of TIPS can be used to fund such a pension plan with almost no residual risk. The plan would be hedged in both inflation duration and real-interest-rate duration.Most pension plans do not have a full COLA, and many have no formal COLA provision, yet they are exposed to inflation risk (that is, they have a nonzero inflation duration) because their benefit formulas are based on final salary, which for active employees is determined by wage inflation between the present time and the date of retirement. For example, we found that a stylized one-participant plan with no COLA and with the participant expecting to retire in 10 years has an inflation duration of about 7.6 "years" and a real-interest-rate duration of 17.5 "years." The inflation and real-interest-rate risks of such a plan can be eliminated with a portfolio of nominal U.S. T-bonds and TIPS that is engineered to have the same inflation and real-interest-rate durations as the pension liability. A portfolio of purely nominal bonds cannot accomplish this result.Typical pension managers find, however, that a mix of nominal bonds and TIPS does not have a high enough expected return to be attractive. They seek to increase expected return by moving farther out on the efficient frontier—adding equities and other risky assets. Dual-duration matching can nevertheless be preserved in this context if one has an estimate of the inflation and real-interest-rate durations of equities. Like TIPS and pension liabilities, equities have a relatively short inflation duration (because companies try to pass price increases on to consumers) and a long real-interest-rate duration. Thus, equities are, like TIPS, a natural hedge of these risks in the pension plan and, as one moves out on the efficient frontier, tend to displace TIPS (more than they displace nominal bonds) in efficient asset/liability portfolios.