particular data history and (in practice) data/software vendor. The shape of the modes may not match user expectations, and in practice it will be most unlikely that the portfolio will be managed and hedged with reference to these fundamental modes. A manager is more likely to view future curve movements in terms of a simple shift and twist. The great advantage of a factor-based approach is that it ensures that as much curve movement as possible is attributed to shift movement, and that twist and curvature motion are given as small values as possible. This allows apparently straightforward reporting, because hard-to-understand curve movements are always assigned small weights in an attribution analysis. However, this is at the cost of a distortion of the other results. On the other hand, a naïve interpretation of the terms shift, twist, curvature when applied to yield curve movements may well give rise to higher-order movements that are much higher than investors would expect. There are also problems in the exact definition of the terms shift and twist. Without fixing a twist point at the outset, there is no unique value for these terms in either a Nelson-Siegel or polynomial formulation. However, the location of this twist point may not match user expectations. For a deeper discussion of this point, see Colin (2005). Interest returns The first source of return in a fixed-income portfolio is that due to interest. The majority of securities will pay a regular coupon, and this is paid irrespective of what happens in the marketplace (ignoring defaults and similar catastrophes). For instance, a bond paying a 10% annual coupon will always pay 10% of its face value to the owner each year, even if there is no change in market conditions. However, the effective yield on the bond may well be different, since the market price of the bond is usually different from the face value. Yield return is calculated from where is the security's yield to maturity, and is the elapsed time. Towards the end of the bond's life we often see a pull-to-parity effect. As maturity approaches, a bond's price converges to its nominal amount, irrespective of the level of interest rates, and this may cause a bond's price to move in a different way to what would normally be expected. Roll return Roll return can occur when a yield curve is steeply sloped. In the absence of any