The Impossibility of Stationary Yield Spreads and I(1) Yields under the Expectations Theory of the Term Structure

It is a widely encountered misconception that the vector of spreads between longer-term interest rates and the short rate is stationary under the Expectations Theory (ET). By considering a complete term structure of maturities it is shown that the ET determines the conditional mean of the VAR process followed by the yield curve. We prove that under this process, the zero-coupon yield curve is I(2), immediately casting doubt on the empirical usefulness of the ET. Furthermore, the yield spreads are shown to be a non-stationary, cointegrated I(1) process. This result invalidates many existing approaches to evaluating and formally testing the ET. Finally, time series features of yield curve data simulated under the ET are compared with those of actual US Treasury zero-coupon yield curves.