Estimating Real and Nominal Term Structures
Professor Peter Ritchken’s paper Estimating Real and Nominal Term Structures Using Treasury Yields, Inflation, Inflation Forecasts, and Inflation Swap Rates develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short-term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes.
Ritchken derived analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. He then estimated the model parameters using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. Findings showed that allowing for GARCH effects is particularly important for the real interest rate and expected inflation processes, but that longhorizon real and inflation risk premia are relatively stable.
Comparing model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004, but subsequently were valued fairly. Results indicate unexpected increases in both short run and longer run inflation — implied by our model — have a negative impact on stock market returns. An implication is that stocks are, at best, an imperfect hedge against inflation. This underscores the importance of inflation-linked securities as a means for safeguarding the real value of investments.