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Abstract:
Active portfolio management is typically conducted within constraints that do not allow managers to fully exploit their ability to forecast returns. Constraints on short positions and turnover, for example, are fairly common and materially restrictive. Other constraints, such as market-capitalization and value-growth neutrality with respect to the benchmark or economic-sector constraints, can further restrict an active portfolio's composition. We derive ex ante and ex post correlation relationships that facilitate the performance analysis of constrained portfolios. The ex ante relationship is a generalized version of a previously developed "fundamental law of active management" and provides an important strategic perspective on the potential for active management to add value. The ex post correlation relationship represents a practical decomposition of performance into the success of the return-prediction process and the "noise" associated with portfolio constraints. We verify the accuracy of these relationships with a Monte Carlo simulation and illustrate their application with equity portfolio examples based on the S&P 500 Index as the benchmark.

Portfolio Management: portfolio construction, rebalancing, and implementation, Portfolio Management: investment policy

Abstract:
Long/short ratios like 130/30 are an increasingly common way for the investment management industry to describe portfolios that are released from the long-only constraint. The ratio of a portfolio's long and short positions to net notional value is often the primary description of the strategy, replacing more traditional measures such as active risk. Unfortunately, managers and their clients may not understand the underlying parameters associated with the value of the long/short ratio, beyond the general recognition that the size of the extensions (e.g., 30 percent) and active risk are positively related. We develop a mathematical model to identify the factors that determine the size of the long/short extension, and illustrate the relationships using historical data on the S&P 500 benchmark, as well as current data on a variety of domestic and international equity benchmarks. The model confirms the basic intuition that the size of the long/short extension increases with the active risk target chosen by the manager, and decreases with the estimated costs of shorting. In addition, the model shows that the expected short extension for an unconstrained portfolio depends on average security risk, average pair-wise security correlation, the security weight concentration of the benchmark, the number of investable securities, and the assumed accuracy of security return forecasts. The model provides important perspectives on long/short strategies as the investment management industry continues to move away from more traditional long-only portfolios.

Portfolio Management, Short Selling, Portfolio Optimization

Abstract:
The strategic perspectives and terminology of the fundamental law is a common framework in the practice of active portfolio management. For tractability, fundamental law theory depends on the simplifying assumption of a diagonal covariance matrix of security returns, though the matrices supplied to numerical optimizers are fully populated. We extend the fundamental law of active management to allow for a full covariance matrix and show that the resulting ex-ante (expected) and ex-post (realized) return equations are exact in contrast to the approximate equality of previous derivations. The exactness of ex-post equations allows for performance attribution of realized returns that completely decomposes the return. Because the various fundamental law parameters we define incorporate all the information in the covariance matrix, they should also provide better ex-ante insights as to the sources and limitations of risk-adjusted active return. In addition to the generalization of the fundamental law, we describe a full covariance matrix alpha generation process and add some comments to the concept of implied breadth. The mathematics and practical application of the full covariance matrix fundamental law parameters are illustrated using an EAFE benchmarked portfolio with the 21 countries as individual securities.

Portfolio management, fundamental law, transfer coefficient

Abstract:
The reported study operationalized the fundamental law of active management in the context of a factor-based performance attribution system. The system incorporates factor payoffs in the linear regression framework that many portfolio managers and external reviewers use to judge what is being rewarded in the market. The study indicates that parameters of the fundamental law can be used to approximate and interpret the results of the regression-based performance attribution system. The procedure is illustrated by the use of security holdings, returns, and factor exposure data for two portfolios benchmarked to the S&P 500 Index for April 1995 to March 2004.

Portfolio Management, Portfolio Construction, Rebalancing and Implementation, Equity Strategies, Hedge Fund Strategies, Alternative Investments, Hedge Fund Strategies

Abstract:
The cross-sectional variation of U.S. stock returns has been unusually high in the past few years. The wide dispersion in security returns has led to correspondingly wide dispersion in fund returns. For example, the cross-sectional standard deviation of returns on actively managed domestic equity mutual funds was 24 percent in 1999, compared with only 5 percent in 1996. We argue that the wide dispersion in fund performance is a natural result of increased security return dispersion and has little to do with changes in the informational efficiency of the market or the range of managerial talent. The dramatic increase in return dispersion warrants a reexamination of traditional methodologies for measuring fund performance that implicitly assume constant dispersion. We show how performance benchmarking can be extended to incorporate the information embedded in return dispersion, as well as the benchmark mean return, by correcting fund alphas with a period- and asset-class-specific measure of security return dispersion.