An introduction to attribution
1.1 Securities, portfolios and risk
1.1 SECURITIES, PORTFOLIOS AND RISK
The aim of a managed fund is to invest in appropriate financial instruments so that the fund’s value is maintained, or increased, over time. In this context, value can either be tracked in absolute terms or measured relative to a reference entity called a benchmark.
For convenience, the securities in a fund are usually grouped into entities called portfolios. One can then talk of the return of the portfolio as a whole, rather than the returns of its constituent assets.
1.2 TYPES OF RISK
Managed funds that hold assets such as cash, equities, investment trusts and derivatives are usually managed via stock selection and asset allocation decisions. Informally, a stock selection decision is which securities to hold, while asset allocation decisions are how much of each security to hold.1 Stock selection decisions apply at the security level, while asset allocation decisions are made by varying the relative weights of subsets of holdings between the portfolio and the benchmark.
In addition, many funds also hold fixed income securities, which supply exposure to additional sources of market risk such as yield, interest rate risk, credit risk and inflation.
Lastly, exposure to securities that are denominated in overseas currencies generates exchange rate risk, which may be hedged and controlled using securities such as forwards.
Almost every investment portfolio has exposure to multiple concurrent risks, which occurs when
- the securities that make up the portfolio are inherently exposed to multiple risks. For instance, a corporate bond generates simultaneous returns from yield, sovereign curve risk and credit risk;
- the manager deliberately uses multiple risks as part of an investment strategy.
It is up to the manager to decide to which risks they want to be exposed, and to implement suitable investment strategies that put these decisions into practice.
Just as importantly, the manager should be able to hedge their portfolio so that it is not exposed to other, unwanted risks. For instance, an equity manager may decide to take only stock selection decisions, and not to have any asset allocation exposures. In this case, the fund’s asset allocation return should always be zero, and the attribution report will verify that this decision was implemented successfully.
Asset allocation hedges are relatively easy to implement, as they simply require that each portfolio sector weight is equal to the corresponding benchmark sector weight. Other types of hedge, such as immunisation of the portfolio against non-parallel yield curve shifts, can be much more difficult to implement and may require considerable expertise and investment in risk-management tools.
1.3 RETURN AND ATTRIBUTION
A statement of the fund’s overall return will show the aggregate sum of the returns from each investment decision, decomposed by time or by market sector. What it will not show are the fund’s returns, decomposed by risk. The purpose of attribution is to disentangle this single return into the multiple returns generated by each risk. In other words, attribution measures which of your investment decisions about the portfolio’s underlying risks worked, and which did not. This is critical business intelligence for anyone involved in selecting, managing or marketing investments.
The ability to run attribution presupposes an ability to run accurate performance calculation. There is little use in being able to decompose the return of a security or a portfolio if that return is wrong.
Fortunately, accurate reporting of results can usually be assumed. The introduction of the Global Investment Performance Standards (GIPS) has ensured comparability of portfolio returns between managers and against benchmarks.
The capability to run attribution puts the manager in full control of their investments. Running attribution shows the following:
- the manager’s skill at identifying and managing risks;
- where the manager took risks;
- when the manager took risks;
- how well the manager’s hedging strategies worked.
Without this information, the manager is effectively flying blind. They may be making profits, but it is probably not clear where or why, and this lack of transparency will make it difficult or impossible to isolate the manager’s core investment strengths.
This is the true value of attribution. It allows the manager to ensure that a portfolio is following the manager’s investment strategy, to verify that no unexpected risks are driving returns down and to take remedial action if necessary. As a result, attribution is generally recognised as an important requirement for any investment institution.
1.4 STRATEGY TAGGING
Many portfolios implement simultaneous investment strategies by dividing their investments into different subportfolios, each designed to profit from a particular perceived market opportunity. These can vary in complexity from the simple (go long Russia) to the complex (volatility plays, yield curve barbell trades and the like). The overall return of the portfolio is generated by the return of all its underlying strategies, and the decomposition of a portfolio’s returns by investment strategy (as distinct from market sector or risk) is generally called strategy tagging.
In principle, the calculation of returns from each strategy is straightforward, and only requires standard performance measurement tools. If one regards the holdings assigned to each strategy as a separate subportfolio, then the return of that subportfolio will show the value added by the strategy.
In practice, few managers have successfully implemented strategy tagging systems. The difficulties are largely due to workflow issues and the mechanics of logging individual trades against the correct strategy.
A particular difficulty is that some trades may involve one security but multiple strategies. For instance, if Strategy A requires the purchase of 500 bond future contracts, while Strategy B requires the sale of the same number of contracts, then the net result is that no physical trade need be made; yet each strategy requires a dummy trade, and the deal entry system should allow such trades to be recorded.
Strategy tagging is closely related to attribution but does not require any of its underlying machinery. Some managers regard strategy tagging analysis as more valuable than attribution analysis.
1.5 TYPES OF ATTRIBUTION
Attribution techniques fall neatly into two well-defined categories:
- equity attribution;
- fixed income attribution.
Each category has its own algorithms, literature and jargon. The conventional view is that equity attribution is mostly about the Brinson algorithm, while fixed income attribution is mostly about yield curves. While not strictly true, this is a useful distinction, and the book follows the same pattern.
1.5.1 Equity attribution
Equity attribution is usually driven by asset allocation and stock selection decisions. Individual equity returns are driven by both corporate and macroeconomic factors. From the attribution analyst’s perspective, there is no direct relationship between these market factors and security prices, and various statistical tools, such as factor analysis, can be used to find the core drivers of return, if required. Such topics are outside the scope of this text.
1.5.2 Fixed income attribution
The price and return of fixed income securities are driven by a combination of structural and market factors. Typically, these include:
- the cash flows of the security, including any guaranteed payments to the owner, such as coupons and repayment of principal;
- the risk-free yield curve;
- credit curves, where appropriate;
- the resulting yield of the security;
- other minor effects such as roll-down, convexity and paydown;
- security-specific factors, such as the creditworthiness and financial strength of the issuer.
In most cases the relationship between a security’s return and the change in its underlying curve(s) is well understood. The factors that drive performance can then be described as the sum of different movements in these curves, such as parallel shift, changes at a particular maturity and global movements in a credit curve.
Fixed income attribution decomposes the return of individual securities into return from each factor, and then recombines these returns over the portfolio so that their total contribution to return may be measured.
Fixed income portfolios can also generate excess return by varying their interest rate risks against benchmark at the sector or aggregate level. The effect this duration allocation decision has on the portfolio’s outperformance may then be measured. The topic is covered in detail in Chapter 14.
1.6 BOOK STRUCTURE
The book is divided into five sections. Part 1 concentrates on equity attribution, while Parts 2 to 5 cover fixed income attribution. The threads come together again occasionally, as when we discuss mixed and hybrid attribution techniques, which can be applied to both types of security, but generally the techniques required for fixed income and equity attribution are quite different.
Part 1 is a self-contained guide to equity attribution.
Chapter 2 covers the basics of performance measurement.
Chapter 3 examines the Brinson model, including attribution on nested allocation decisions.
Chapter 4 is about currency attribution and the Karnosky-Singer model for hedged portfolios.
Chapter 5 describes the rationale and techniques underlying smoothing of portfolio returns.
Part 2 introduces the concepts behind fixed income return.
Chapter 6 provides an overview of how a bond is priced and how its returns can be decomposed in terms of fixed income-specific factors. This material acts as an introduction to the concepts of fixed income attribution, and provides context for Part 3.
Chapter 7 covers the role of the yield curve as a fundamental driver of fixed income returns.
Chapter 8 is about ways in which movements in underlying market drivers can be translated to attribution returns, including first-principles pricing and the perturbational equation.
Part 3 describes, in detail, the sources of risk that drive the returns of fixed income securities, which include:
carry return (Chapter 9);
sovereign or risk-free curve return, and the ways in which movements in the yield curve can be decomposed and described (Chapter 10);
sector and credit curve return (Chapter 11);
other sources of return such as convexity, roll-down and pay-down (Chapter 12);
mixed or balanced attribution, in which top-down allocation returns are combined with bottom-up fixed income effects (Chapter 13);
macro-level allocation decisions (Chapter 14).
Part 4 describes how to perform attribution on the main fixed income security types:
bonds (Chapter 15);
money market securities (Chapter 16);
inflation-linked securities (Chapter 17);
futures (Chapter 18);
sinking securities, including MBS and amortising debt (Chapter 19);
swaps (Chapter 20);
options and callable bonds (Chapter 21);
collateralised and securitised debt (Chapter 22).
Part 5 covers some practical aspects of attribution:
popular attribution models (Chapter 23);
tools and techniques for attribution reporting (Chapter 24).