From the September 2013 issue of Futures Magazine • Subscribe!

Measurement matters: Measuring trading performance

Jensen’s Alpha 

Jensen’s alpha follows directly from the single- factor market model, which links the expected return of an investment to the amount of beta risk incurred. 

Jensen’s alpha is a direct measure of the absolute amount by which an asset is estimated to outperform, if positive, the return on efficiently priced assets of equal systematic risk in a single-factor market model. It is tempting to describe the return in the context of the capital asset pricing model (CAPM), but strictly speaking, no asset offers a nonzero alpha in a CAPM world, because all assets are priced efficiently. In practice, expected returns on the asset and the market, as well as the true beta of the asset, are unobservable. So Jensen’s alpha is typically estimated using historical data as the intercept (a) of the following regression equation:

Rt- Rf = a + b(Rm,t- Rf)+εt

where Rt is the return of the portfolio or asset in period t, Rm,t is the return of the market portfolio in time t, a is the estimated intercept of the regression, b is the estimated slope coefficient of the regression and εt is the residual of the regression in time t. 

The error term εt estimates the idiosyncratic return of the portfolio in time t, b is an estimate of the portfolio’s beta and a is an estimate of the portfolio’s average abnormal or idiosyncratic return. Because the intercept, a, is estimated, it should be interpreted subject to levels of confidence.  Positive levels of alpha show outperformance, meaning that the manager has earned a greater amount of return than justified by the amount of risk undertaken.  Conversely, negative alpha measures underperformance, where the return on the investment was lower than expected for the amount of risk incurred.  

Other popular performance measures exist, and some firms use those unique to the firm. In practice, a variety of performance measures should be explored, each of which is selected to view performance from a relevant perspective.

Mark J.P. Anson, Ph.D., CFA,  has headed up several asset management firms, including Nuveen Investments, Hermes Pension Mgmt. and British Telecom Pension Scheme, as well as was CIO of the California Public Employees’ Retirement System. He also is on the board of the Chartered Alternative Investment Analyst (CAIA) Association. Donald R. Chambers, Ph.D., is the associate director of programs at CAIA and a professor of finance at Lafayette College. Keith H. Black, Ph.D., CFA, is the director of curriculum for CAIA. Hossein B. Kazemi, Ph.D., CFA, is a professor of finance at the Isenberg School of Management at the University of Massachusetts, Amherst. He also is a CAIA managing director. 

This piece is an exerpt from “CAIA Level I: An Introduction to Core Topics in Alternative Investments, Second Edition,” Wiley, 2012.

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