The advantages of using excess returns to model the term structure

We advocate the use of excess returns rather than yields or log prices in analysing the risk neutral dynamics of the term structure. We show that under standard assumptions, excess returns are affine in the risk neutral innovations in the factors. This framework has several important advantages. First, it allows for an easy estimation of models that are more flexible than the AR(1). Indeed, we estimate models with more general dynamics, like ARFIMA(p, d, q), almost as easily as AR(1). Second, within our framework the dimension of the unrestricted model is the same for the AR(1) as it is for the richer models, and does not expand in line with the state vector as it does in a yield or log price framework. This makes it appropriate to test all of these risk neutral dynamic specifications against the same OLS unrestricted alternative. Our results for the US Treasury bond market show that the unrestricted model is preferred to the AR(1) by the Bayesian Information Criterion, but the opposite conclusion is reached for more flexible models. A final advantage of the excess returns framework is that the pricing errors are much lower than for the equivalent log price system.