General approach to yield curve attribution
FIA employs a successive yield curve method for both approaches. To run attribution, the program uses a number of yield curves, each representing the effect of a progressive change in the curve when different sources of risk are added in. The effect of changes in each yield curve is then computed on the security’s return.
For instance, suppose we are modelling changes in the sovereign curve in terms of shift, twist and other types of curvature.
- The first curve is the level of the curve at the start of the calculation interval.
- The second curve is this initial curve plus the parallel shift that occurs over the calculation interval.
- The third curve is the initial curve, plus the parallel shift, plus the twist shift, over the calculation interval.
- The final curve is the curve at the end of the interval, which contains shift, twist and other effects.
The time at which each price is calculated is at the end of the interval. All time effects are calculated in the previous section, so we explicitly exclude time effects from this part of the calculation, which is specifically designed only to measure returns due to changes in the yield curve.
The sum of these changes (time and yield curve) is the overall change in the yield curve over the interval. Any discrepancy seen between the return calculated from these changing prices and the actual return will be due to credit, market noise, or other effects. Further changes due to movements in the credit curve, MBS repayment rates and other risk effects can be added in a similar manner.
Calculating parallel shift
Parallel yield curve shift is regarded as one of the major drivers of fixed income fund performance. There are good reasons for this. Principal component analysis (eg Phoa, 1999) shows that parallel curve shifts usually account for at least 90% of the return of managed bond funds from sovereign yield curve effects.
This is reflected in the widespread use of modified duration as a proxy for a security’s risk exposure to curve movements, where modified duration represents the sensitivity of the security’s return to parallel curve movements. However, there is no standardised, accepted way of calculating parallel shift.
FIA offers two ways to calculate the average level of the yield curve, and hence changes in its average level:
- Arithmetic average: A simple average of all yields is calculated. This is simple and widely used, but tends to amplify the effects of changes at the short end of the curve if there are more points supplied at the short end – which is often the case.
- Trapeziodal integration: Calculates the area under the yield curve, and divides by the difference between the largest and the smallest times. This is probably the most accurate way of measuring parallel shifts, as it removes sensitivity to variable sample spacing along the term structure.
Other types of averaging may be introduced in future.