The Fundamental Law of Active Portfolio Management

Journal of Investment Management, Vol. 4, No. 3, Third Quarter 2006

Posted: 3 Oct 2006

See all articles by Harindra de Silva

Harindra de Silva

Analytic Investors, Inc.

Steven Thorley

BYU Marriott School of Business

Roger G Clarke

Ensign Peak Advisors

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.

Keywords: Portfolio management, fundamental law, transfer coefficient

Suggested Citation

de Silva, Harindra and Thorley, Steven and Clarke, Roger G, The Fundamental Law of Active Portfolio Management. Journal of Investment Management, Vol. 4, No. 3, Third Quarter 2006. Available at SSRN: https://ssrn.com/abstract=934440

Harindra De Silva (Contact Author)

Analytic Investors, Inc. ( email )

555 West 5th Street
50th Floor
Los Angeles, CA 90013
United States
213-688-3015 (Phone)
213-688-8856 (Fax)

Steven Thorley

BYU Marriott School of Business ( email )

616 TNRB
Brigham Young University
Provo, UT 84602
United States
801-378-6065 (Phone)
801-378-5984 (Fax)

Roger G Clarke

Ensign Peak Advisors ( email )

60 East South Temple
4th Floor
Salt Lake City, UT 84111
United States

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