Essays in Memory of Albert Ando
Edited by Lawrence R. Klein
Chapter 9: A Three-Factor Yield Curve Model: Non-Affine Structure, Systematic Risk Sources and Generalized Duration
9. A three-factor yield curve model: non-aﬃne structure, systematic risk sources and generalized duration* Francis X. Diebold, Lei Ji and Canlin Li 1. INTRODUCTION We assess and apply the term-structure model introduced by Nelson and Siegel (1987) and re-interpreted by Diebold and Li (2005) as a modern three-factor model of level, slope and curvature. Our assessment and application has three components. First, we ask whether the model is a member of the recently popularized aﬃne class, and we ﬁnd that it is not. Hence the poor forecasting performance recently documented for aﬃne termstructure models (e.g. Duﬀee, 2002) in no way implies that our model will forecast poorly, which is consistent with Diebold and Li’s (2005) ﬁnding that it indeed forecasts quite well. Second, having clariﬁed the relationship between our three-factor model and the aﬃne class, we proceed to assess its adequacy directly, by asking whether its level, slope and curvature factors capture systematic risk. We ﬁnd that they do, and that they are therefore priced. In particular, we show that the cross-section of bond returns is well explained by the sensitivities (loadings) of the various bonds to the level, slope and curvature state variables (factors). Finally, conﬁdent in the ability of our three-factor model to capture the pricing relations present in the data, we proceed to explore its use for bond portfolio risk management. Traditional Macaulay duration is appropriate only in a one-factor (level) context; hence we move to a three-factor generalized duration...
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