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We construct a factor model of the yield curve and specify time series processes for these factors, so that the innovations are mutually orthogonal. At the same time, the factors are such that they assume clear, intuitive interpretations. The resulting “intelligible factors” should prove useful for investment professionals to discuss expectations about yield curves and the implied dynamics. Moreover, they allow us to distinguish announced changes of the monetary policy stance versus monetary policy surprises, which we find to be rare. We identify two such events, namely September 11, 2001, and the Fed reaction to the sub-prime crisis of 2007.

For people who are required to form expectations about complex objects, such as the term structure of interest rates, it is useful to reduce the dimensionality of the problem with the help of a few factors that describe the object. Ideally, these factors should have two properties. Firstly, they should have an interpretation that is easy to understand. For instance, when we talk about the yield curve, the short rate is an interpretable factor, and the slope or the long rate, too, are interpretable factors. We can discuss our expectations about these things and it is clear what it means. Secondly, the factors should be driven by processes that have innovations that are mutually orthogonal. It is difficult to form expectations about the long rate and the slope separately if the long rate and the slope are driven by shocks that are not independent from each other. In this paper, we say that factors that fulfill these two requirements of being interpretable and having mutually and serially orthogonal innovations, are intelligible. The literature on the term structure of interest rates has produced a plethora of factor models, which can be divided into three lines. The first consists of models that start with a specification of some stochastic process for the short rate. They then derive the dynamics of the term structure by imposing arbitrage-freeness. Early representatives in this line of research are Pye, 1966 and Vasicek, 1977, and Cox et al. (1981). These models have been extended to multi-factor models where yields depend on the factors in an affine fashion. Duffie and Kan (1996) and Dai and Singleton (2000) are two prominent examples in this domain. In these models, the factors are typically some abstract entities with no clear economic interpretation. The second line consists of general equilibrium models that explain the term structure from first principles. The classic reference here is Cox et al. (1985). They explicitly derive an equilibrium term structure process as a function of the preferences of a representative utility maximizer and an assumed process of kk factors that describe the production possibilities of the economy. These kk factors have macroeconomic interpretations by construction. This model, therefore, is an early representative of the macro-finance literature that explores the relation between asset prices in general–or in this case, the term structure in particular–with observable or latent macroeconomic variables. The modern version of this literature (e.g. Ang and Piazzesi, 2003, Rudebusch and Wu, 2008 and Mönch, 2008) is much less explicit about the general equilibrium underpinnings of the model. It takes up the idea that the short rate depends on a set of macroeconomic variables and imposes arbitrage-freeness to derive the implications for the relation between the term structure and these macroeconomic factors. By using exogenous variables to estimate the model, they achieve a better fit of the yield curve compared to the models with unspecified factors. The third line of the literature consists of purely descriptive, empirical factor models. These models describe the term structure with the help of a few factors in order to facilitate communication about it. This literature is motivated more by the needs of the practitioner than by the interests of the economic theorist. A classic early reference to this type of literature is Litterman and Scheinkman (1991), who apply principal component analysis to yield curve data. This analysis generates orthogonal factors by construction. Typically, three factors suffice to describe the yield curve, and the corresponding loadings suggest an interpretation as ‘level’, ‘slope’, and ‘curvature’. Another early contribution in this domain is Nelson and Siegel (1987). These contributions are completely static in the sense that they model the yield curve at a particular point in time. They do not, however, contain information about the dynamics of the yield curve and can therefore not be used for forecasting. Their main advantage over the theory-based models is their better fit. Like Litterman and Scheinkman (1991), Bliss (1997) used the first three principal components to describe the term structure, but he was the first to analyze the dynamics of these factors using a vector autoregressive (VAR) specification. Diebold and Li (2006) have done the same with the Nelson–Siegel factors. They show that this combination of a set of easily interpretable factor loadings together with a simple stochastic process yields better forecasting performance than the dynamic theory-based models. The drawback is, of course, that it is not guaranteed that the model is arbitrage-free. Moreover, the factor innovations in the Diebold–Li model are not independent of each other. In other words, in the Nelson–Siegel model, one cannot discuss level innovations independently from slope innovations because these innovations are statistically not orthogonal. This jeopardizes interpretability. One can still use these models for forecasting, but the meaning of shocks to the individual factors is unclear. In this paper, we address this issue. We construct a factor model in the tradition of the third line of research, but impose orthogonality of the factor innovations in addition to a clear interpretation of the loadings, i.e. we restrict our factors to be intelligible. More concretely, our loadings, which can be identified as ‘long’, ‘short’, and ‘curvature’ factors, follow a VAR process with mutually independent and serially uncorrelated innovations. In other words, we construct the factors in such a way that the innovations to our short factor, for instance, are uncorrelated with innovations to the other two factors. In addition to the imposed intelligibility of the factors, our estimation reveals a dynamic structure which suggests a macroeconomic interpretation. We find that the curvature factor is a leading indicator of the short factor, while the long factor largely lives a life of its own. We will argue that this dynamic structure suggests that the curvature factor captures the intended (and communicated) medium term monetary policy stance, and the short factor captures surprise policy actions. We find that the curvature factor explains a much greater share of term structure movements than the other two factors. This is especially true for movements at the short end of the yield curve, which suggests that most monetary policy actions are well communicated by the Fed before they are actually executed. This interpretation relates our model to the macro-finance term structure literature. Indeed, our results confirm the finding of Mönch (2006) that curvature factor innovations are informative about the future evolution of the yield curve. Two remarks about the dominant role of the curvature factor are in order here. According to principal component analysis (Litterman and Scheinkman, 1991), a factor with a more or less constant loading on all maturities (the level factor) is traditionally considered to be dominant. Why is this not the case in our model? First, our model does not feature a level factor. Our long factor is constrained to have zero loading at zero maturity. Second, in our model the long factor, and maybe also the short factor, are more important than the curvature factor in describing the shape of the term structure at any given day. Yet, curvature is the main driver of the dynamics of the term structure as captured by the VAR. In this sense, curvature is the dominant factor affecting the changes of the term structure, through its influence on the other two factors.

In this paper, we show how to construct intelligible factors that describe the term structure of interest rates and its dynamics. We believe that such factors are useful for practitioners because they provide a parsimonious description of the yield curve (the interpretability aspect), and also provide a language to discuss innovations to the yield curve, because innovations to one factor are independent of innovations to other factors (the orthogonality aspect). The orthogonality property is important: what does it mean to discuss a possible level shock in the Nelson–Siegel model (which does not have orthogonal innovations), if we know that a level shock typically comes together with a slope shock? Our three factors do not only assume the interpretation as ‘long’, ‘short’, and ‘curvature’ that is imposed upon them by construction. We argue that they lend themselves also to interpretations related to monetary policy actions, due to the VAR structure of the factors. In this VAR, the curvature factor turns out to be a leading indicator of the short factor. We interpret this as saying that the curvature factor captures the communication of the Fed with regard to its future monetary policy stance. If the Fed indicates that it is likely to tighten monetary conditions, this induces market participants to expect higher interest rates in the medium term. In our model, such a communication is picked up as a positive curvature innovation. The short factor, on the other hand, captures surprise actions of the Fed. The fact that the short factor has only a minor effect on the term structure suggests that most monetary policy action is carefully communicated beforehand. We identify two exceptions to this rule, namely the September 11 shock, and the surprise reduction of the discount rate in the midst of the sub-prime crisis in 2007. Beyond helping us to interpret current events, the VAR that is contained in our model is also able to trace the dynamic effects of innovations to the three factors. This fact can be useful for several market participants. For instance, the model allows the central bank to quantify the immediate effects of its actions on the term structure, as well as the expected effects further down the road. Similarly, the model is potentially of value to bond portfolio managers. The model can be used to simulate the dynamics of the return distribution of bond portfolios, conditional on priors about factor innovations. This fact should be helpful to manage risk or optimize returns of a bond portfolio.