Beyond Single-Factor Affine Term Structure Models
37 Pages Posted: 22 Mar 2002
Date Written: January 2002
This paper proposes a new approach for testing the hypothesis of a single priced risk factor driving the term structure of interest rates. The method does not rely on any parametric specification of the state variable dynamics or the market price of risk, and simply exploits the constraint imposed by the no arbitrage condition on instantaneous expected bond returns. Using a Kolmogorov-Smirnov type test, we find that a general single factor term structure model is rejected by a dataset of Spanish Treasury bills and bonds. In particular, historical expected returns on bills and bonds maturing in the short term are lower than those consistent with expected returns on long term bonds under the single-factor hypothesis. We find that a nonparametric two-factor model where the state variables are taken as the level and slope of the yield curve partially accounts for this bias, although the model underestimates medium-term expected returns. Finally, a three-factor model that includes curvature risk greatly improves the fitted term structure of expected returns across all maturities. These results suggest that the significantly lower premium detected by the test in short term treasuries is probably due to their role as a hedge against two additional sources of risk: The risk of long term bond yields rising relative to short yields (slope risk), and the risk of medium-term yields rising relative to both short term and long term yields (curvature risk).
Keywords: nonparametric estimation, term structure of interest rates
JEL Classification: E43, C14
Suggested Citation: Suggested Citation