is provided in Dynkin et al. (1998). Yield curve attribution A more widely used approach to fixed-income attribution is to decompose the returns of individual securities by source of risk, and then to aggregate these risk-specific returns over an entire portfolio. Typical sources of risk include yield return, return due to yield curve movements, and credit spread shifts. These sub-returns can then be aggregated over time and sector to give the overall portfolio return, attributed by source of risk. For a description of the mechanics of combining these sub-returns in a self-consistent manner, see Bacon (2004). Sources of return Over a given interval, the return of each security will be made up of return from various sub-returns (see below for explanations) return due to yield (equivalently coupon, or accrued interest, or running yield); return due to rolling down the yield curve; return due to movements in the reference yield curve; return due to credit shifts; other sources of return, such as option-adjusted spread (OAS), liquidity, inflation, paydown, etc. First principles versus perturbational attribution To calculate the return arising from each effect, we can reprice the security from first principles by using a pricing formula, or some other algorithm, before and after each source of return is considered. For instance, in calculating yield return, we might calculate the price of the security at the start and end of the calculation interval, but using the yield at the beginning of the interval. Then the difference between the two prices may be used to calculate the security's return due to the passage of time. This approach is simple in principle but can lead to operational difficulties. It requires accurate pricing formulae including, where relevant, ex-coupon, settlement, and country-specific conventions; security-specific data, such as day-count conventions and whether a bond has a non-standard first and last coupons; accurate inputs to these formulae, including market yields and other variable quantities such as the 90-day bank bill swap rate (BBSW) and consumer price index (CPI) factors for floating rate notes and inflation-linked securities, and regular updates for these quantities; a reconciliation function between existing performance measurement systems and the attribution system For these reasons, a pricing model-based approach to attribution may not be the right one where data sourcing or reconciliation is an issue. An alternative solution is to perform a Taylor expansion on the price of a security and remove higher-order terms, which gives Writing