Fund managers market their strategy products as that they are able to achieve consistent competitive performance through particular repetitive decision-making process; attribution is an extremely useful tool in verifying their claims to possess these investment skills.

*Fixed Income Attribution vs. Equity Performance Attribution*

Equity attribution is standardized – almost all methodologies focus on the value added from asset allocation and stock selection. By contrast, fixed income attribution is not standardized, as much of its returns are driven by structural risk factors, and the sources of risks also include yield-curve distribution, duration, optionality, convexity, currency, and credit spreads of the bond securities in the portfolio. Beyond that, fixed income portfolios and portfolio management styles are not homogeneous. In this sense, fixed income attribution by nature is a complex and mathematically demanding practice.

*Factor-Based Attribution*

Factor-based attribution is basically a regression analysis. It seeks to explain “R (portfolio) – R (benchmark),” and it statistically breaks down returns based on systematic factors. Due to strong mathematical relationship between changes in interest rates and price, fixed income portfolio can be particularly well analyzed with this approach. More importantly, for bonds, factor-based models help minimize the number of dimensions necessary to explain yield curve shifts.

Like most regressions, the principle of the factor-based fixed income attribution is that bond returns can be expressed as a linear combination of sensitivities to systematic factors and the returns associated with those systematic factors:

- Interest shifts: 3-factor representation, key rate representation
- Spread shift: flexible granularity
- Prepayments, optionality, etc.

Factor-based attribution is better applied to a multi-dimensional investment process, and it can better separate both intentional and unintentional sources of returns. Furthermore, this approach particularly handles derivatives fairly easily. However, compared with other methodologies, factor-based attribution substantially requires larger data, and more effort to relate results to market moves.

*Sector-Based Attribution*

Each bond security belongs to a given market, an issuer sector, each sector has a given maturity, and each sector has a rating. Given this thinking, it is essential to group bonds in a way that best represents the manager’s investment process. In a straightforward sector-based attribution model, durations of various sectors are the basis for yield curve exposure. Rather than using the bond portfolio’s yield curve exposures through arbitrary points, we should consider sector durations to represent the key rate durations of the portfolio. The primary reasons are:

- A portfolio’s yield curve distribution is a critical aspect of its structure and return attribution, so the values used to represent this curve distribution should be the result of observable decisions
- Portfolio managers pick bonds with specific durations to implement the strategy; therefore, each sector’s duration is the result of specific manager decisions and specific issue purchases.
- This approach reflects a bond manager’s thinking on sector allocation.

The basic data for the model includes: market value weighting, return, coupon, beginning price, beginning duration, treasury curve at beginning and end of performance period. With these sets of information, we can easily calculate par value weighting, treasury change at the point matching each sector duration, and spread change for each benchmark sector.

The limitation of this approach is that in reality, it may require access to all of the benchmark’s constituent bond holdings, which are often thousands or ten thousands of bonds.

*Component Returns Calculation*

- Income Effect: interest earned on market value invested (periodic coupon divided by price)
- Treasury Effect: price change from treasury change (-duration times Treasury change)
- Spread Effect: price change from change in spread (total return minus income effect minus Treasury effect)
- Spread change: spread effect divided by –duration
- Portfolio Spread Effect: -duration times benchmark spread change

*Time effect (Carry Effect)*

Some fixed income attribution methods only capture the dirty price return of a bond portfolio while does not capture physical cash flows. To mitigate this issue, we can incorporate an income approximation by adding the product of:

The portion of the year elapsed during the measurement period and the yield of the fixed income fund: − D×∆Y+∆T ×Y

- Rolldown – As a bond matures, the reference point on the yield curve will roll down to the left. In a steep yield curve environment, bond prices will increase as the bond matures and fall into portion of the yield curve with lower yield.
- Accretion – As a bond matures, its price will move towards par, which will result in accretion or amortization for premium bonds.

*Yield Curve Attribution*

Imagine that a portfolio manager’s trading decision is to bet on an anticipated steepening of the curve in the 2-5 year region, then an attribution scheme should be able to describe and measure any such steepening in precisely the same terms so that the returns generated from this decision can be allocated appropriately:

- Shift
- Twist
- Curvature

There are many different ways to assign numerical measures to these three effects, but however calculated, they should add up to the net change in the yield curve.

*Credit Attribution*

Credit attribution is the simplest way to identify returns added by changes in yield against an industry sector curve, after changes due to movements in the market reference curve have been removed. This analysis is adequate for a simple portfolio.

*Principal Component Analysis*

Principal component analysis (PCA) can be used to classify yield movements. To simplify, PCA is a process of forming a variance-covariance matrix from spot rate changes at N maturities selected. This approach is mathematically elegant and assigns returns where the user expects them. However, PCA is heavily dependent on the data set used to construct the base functions and the interval over which they are constructed. For investment consultants, the results and implications of a PCA are hard to explain to the investors without a background in mathematical statistics.

*Key Rate Durations*

Key Rate Durations method does not capture the cash flow distribution along the yield curve; instead, it treats every security as a bullet cash flow security. Therefore, it is not a preferred performance measurement by most portfolio managers.

*References:*

*1) **Credit Suisse Asset Management: Mary Cait McCarthy, September 2012*

*2) **The Journal of Performance Measures Spring 2011*