Refresher Reading
Analysis of Active Portfolio Management
2021 Curriculum CFA Program Level II Portfolio Management and Wealth Planning
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The Markowitz (1952) framework of what was originally called modern portfolio theory (MPT) has now become the prominent paradigm for communicating and applying principles of risk and return in portfolio management. Much of the mathematics and terminology of mean–variance portfolio theory was subsequently combined with the notion of informational efficiency by Sharpe (1964) and other financial economists to develop equilibrium models, such as the traditional capital asset pricing model. Separately, the tools of MPT were applied by Treynor and Black (1973) to guide investors in their selection of securities when prices differ from their equilibrium values. The application of portfolio theory to active management was further developed by Grinold (1989) in “The Fundamental Law of Active Management” and by Black and Litterman (1992).
We summarize the principles of active portfolio management using the terminology and mathematics of the fundamental law introduced by Grinold (1989) and further developed by Clarke, de Silva, and Thorley (2002). Active management theory deals with how an investor should construct a portfolio given an assumed competitive advantage or skill in predicting returns. Thus, active management relies on the assumption that financial markets are not perfectly efficient. Although investors might ultimately care about total risk and return, when asset management is delegated to professional investors in institutional settings (e.g., pension funds) the appropriate perspective is risk and return relative to a benchmark portfolio. In addition to the principal–agent problem in delegated asset management, the availability of passively managed portfolios requires a focus on value added above and beyond the alternative of a low-cost index fund.
We assume an understanding of basic portfolio theory, including the mathematics of expected values, variances, and correlation coefficients, as well as some familiarity with the related disciplines of mean–variance optimization and multi-factor risk models. The following sections introduce the mathematics of value added through active portfolio management, including the concepts of active weights, relative returns, and performance attribution systems. The subsequent section compares the well-known Sharpe ratio for measuring the total risk-adjusted value added with the information ratio for measuring relative risk-adjusted value added. This section also makes a distinction between ex ante, or expected, risk and return versus ex post, or realized, risk and return and explains that the information ratio is the best criterion for evaluating active investors. We then introduce the fundamental law that describes how relative skill, breadth of application, active management aggressiveness, and the constraints in portfolio construction combine to affect value added. The remaining sections provide examples of active portfolio management strategies in both the equity and fixed-income markets, describe some of the practical limitations of the fundamental law, and provide a summary of the concepts and principles.
Learning Outcomes
The member should be able to:
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describe how value added by active management is measured;
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calculate and interpret the information ratio (ex post and ex ante) and contrast it to the Sharpe ratio;
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state and interpret the fundamental law of active portfolio management, including its component terms—transfer coefficient, information coefficient, breadth, and active risk (aggressiveness);
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explain how the information ratio may be useful in investment manager selection and choosing the level of active portfolio risk;
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compare active management strategies, including market timing and security selection, and evaluate strategy changes in terms of the fundamental law of active management;
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describe the practical strengths and limitations of the fundamental law of active management.
Summary
We have covered a number of key concepts and principles associated with active portfolio management. Active management is based on the mathematics and principles of risk and return from basic mean–variance portfolio theory but with a focus on value added compared with a benchmark portfolio. Critical concepts include the following:
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Value added is defined as the difference between the return on the managed portfolio and the return on a passive benchmark portfolio. This difference in returns might be positive or negative after the fact but would be expected to be positive before the fact or active management would not be justified.
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Value added is related to active weights in the portfolio, defined as differences between the various asset weights in the managed portfolio and their weights in the benchmark portfolio. Individual assets can be overweighted (have positive active weights) or underweighted (have negative active weights), but the complete set of active weights sums to zero.
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Positive value added is generated when positive-active-weight assets have larger returns than negative-active-weight assets. By defining individual asset active returns as the difference between the asset total return and the benchmark return, value added is shown to be positive if and only if end-of-period realized active asset returns are positively correlated with the active asset weights established at the beginning of the period.
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Value added can come from a variety of active portfolio management decisions, including security selection, asset class allocation, and even further decompositions into economic sector weightings and geographic or country weights.
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The Sharpe ratio measures reward per unit of risk in absolute returns, whereas the information ratio measures reward per unit of risk in benchmark relative returns. Either ratio can be applied ex ante to expected returns or ex post to realized returns. The information ratio is a key criterion on which to evaluate actively managed portfolios.
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Higher information ratio portfolios can be used to create higher Sharpe ratio portfolios. The optimal amount of active management that maximizes a portfolio’s Sharpe ratio is positively related to the assumed forecasting accuracy or ex ante information coefficient of the active strategy.
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The active risk of an actively managed strategy can be adjusted to its desired level by combining it with a position in the benchmark. Furthermore, once an investor has identified the maximum Sharpe ratio portfolio, the total volatility of a portfolio can be adjusted to its desired level by combining it with cash (two-fund separation concept).
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The fundamental law of active portfolio management began as a conceptual framework for evaluating the potential value added of various investment strategies, but it has also emerged as an operational system for measuring the essential components of those active strategies.
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Although the fundamental law provides a framework for analyzing investment strategies, the essential inputs of forecasted asset returns and risks still require judgment in formulating the expected returns.
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The fundamental law separates the expected value added, or portfolio return relative to the benchmark return, into the basic elements of the strategy:
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skill as measured by the information coefficient,
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structuring of the portfolio as measured by the transfer coefficient,
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breadth of the strategy measured by the number of independent decisions per year, and
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aggressiveness measured by the benchmark tracking risk.
The last three of these four elements may be beyond the control of the investor if they are specified by investment policy or constrained by regulation.
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The fundamental law has been applied in settings that include the selection of country equity markets in a global equity fund and the timing of credit and duration exposures in a fixed-income fund.
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The fundamental law of active management has limitations, including uncertainty about the ex ante information coefficient and the conceptual definition of breadth as the number of independent decisions by the investor.