dates. In practice, the Nelson-Siegel function has the advantages that it is well-behaved at long maturities, and that its parameters can be set to model virtually any yield curve (see Nelson and Siegel [1987]). Factor-based attribution A factor-based model of yield curve movements is calculated by deriving the covariance matrix of yield shifts at predefined maturities, and calculating the eigenvectors and eigenvalues of this matrix. Each eigenvector corresponds to a fundamental model of the yield curve, and each eigenvector is orthogonal, so that the curve movement on any given day is a linear combination of the basis eigenvectors. The eigenvalues of this matrix then give the relative weights, or importance, of these curve shifts. [Phoa (1998)]. Factor models use a large sample of historical yield curve data and construct a set of basis functions that can be linearly combined to represent these curve movements in the most economical way. The algorithm always attributes as much of the curve movement to the first basis function, then as much as possible to the second, and so on. Since these functions roughly correspond to our shift and twist motions, this approach attributes almost all of the curve change to these two modes, leaving a very small contribution from higher modes. Typical results attribute 90% of curve movements to shift changes, 8% to twist, and 2% to curvature (or butterfly) movements. However, the issue that these basis functions may be different from those in which the risk decisions were expressed is not widely appreciated. Since conventional risk analysis for fixed-income instruments usually assumes a parallel yield shift across all maturities, it would be most convenient if a parallel motion mode turned out to dominate the other modes, and in fact this is more or less what occurs. While a factor-based decomposition of term structure changes is mathematically elegant, it does have some significant drawbacks for attribution purposes: Firstly, there is no agreement as to what these fundamental modes actually are, since they depend on the historical dataset used in the calculation (unlike, say, a parallel curve shift – which may be defined in purely mathematical terms). Each market, over each analysis interval, will therefore produce a different set of fundamental modes and hence different attribution decompositions, and so it may be impossible to compare sets of attribution results over longer intervals. By deciding to use such an approach, one is implicitly locked into a