Attribution is therefore an extremely useful tool in verifying a fund manager's claims to possessing particular investment skills.
If a fund is marketed as being interest-rate neutral while providing consistent returns from superior credit research, then an attribution report will confirm this claim.
Fixed-income attribution therefore provides a much deeper level of information than is available from a simple portfolio performance report.
Typically, such a report only shows returns at an aggregated level, and provides no feedback as to where the investor's true skills lie.
These sub-returns can then be aggregated over time and sector to give the overall portfolio return, attributed by source of risk.
It requires For these reasons, a pricing model-based approach to attribution may not be the right one where data sourcing or reconciliation is an issue.
The perturbation equation does require externally calculated risk numbers, but this may not be a major obstacle, since these quantities are readily available from the same sources as yields and prices.
Any discussion of fixed-income attribution therefore requires an appreciation of how changes in the curve are described, and their effect on the performance of a portfolio.
Briefly: To describe these movements in numerical terms, typically requires fitting a model to the observed yield curve with a limited number of parameters.
Another generalizing of Nelson-Siegel is the family of Exponential Polynomial Model[1] ("EPM(n)") where the number of linear coefficients is free.
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]).
While a factor-based decomposition of term structure changes is mathematically elegant, it does have some significant drawbacks for attribution purposes: 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.
Without fixing a twist point at the outset, there is no unique value for these terms in either a Nelson-Siegel or polynomial formulation.
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, in April 2005 General Motors debt was downgraded to non-investment, or junk, status by the ratings agencies.
As a result, the credit spread (or return demanded by investors for holding this riskier investment) rose by over 150 basis points, and the value of General Motors bonds accordingly fell.
This may be quite adequate for a simple portfolio, but for traders who are deliberately interest-rate neutral and are making all their returns from credit bets, something more detailed is probably necessary.
The lower the credit rating, the higher the spread, thus reflecting the extra yield premium demanded for greater risk.
Mortgage-backed securities (MBS) are substantially more complex to price than vanilla bonds, due to the uncertainties implied by the prepayment option included in the instrument's structure.
The modified duration of a bond assumes that cash flows do not change in response to movements in the term structure, which is not the case for an MBS.
It does not take into effect other risk factors, such as non-parallel yield curve shifts, convexity, option-adjusted spreads, and others.
Ho defines a number of maturities on the yield curve as being the key rate durations, with typical values of 3 months, 1, 2, 3, 5, 7, 10, 15, 20, 25 and 30 years.
This approach can easily be combined with the earlier decomposition into shift, twist and curvature components to give price changes due to these yield curve movement types.
They include While all these factors can be important in accounting for changes in MBS returns, in practice a particular user may only select a subset.
The reason is that a perturbational analysis requires the provision of risk sensitivity numbers for each factor, and in some cases these may simply not be available.
While benchmarks may have much greater uniformity of instrument type than managed portfolios, the sheer number of securities – and the data maintenance issues required to reprice each one, and to ensure that the correct coupon amount and timing is used when a coupon is paid – means that detailed benchmark modeling remains extremely difficult.
For some Asian benchmarks, illiquid markets can mean that accurate yield data is not published at all, which can make calculation of risks very difficult.
The sheer variety of the fixed-income markets, and the pace of innovation in this area, means that provision of an attribution capability from scratch will continue to present significant challenges.
In no particular order, issues to be faced include While there remain numerous challenges to solve, the state of fixed income attribution is much less murky than was the case even five years ago.