The Influence of the Bias of the Jensen's Alpha Coefficient Estimator on Interpreting the Parameters of the Classical Market-Timing Models

Joanna Olbryś

doi:https://doi.org/10.59139/ps.2011.01-02.3

Joanna Olbryś Politechnika Białostocka Przegląd Statystyczny. Statistical Review, vol. 58, 2011, 1-2, pages: 42-59 Published online: 30 June 2011 DOI https://doi.org/10.59139/ps.2011.01-02.3

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ABSTRACT

Jensen’s alpha coefficient was introduced in 1968 as a measure of the manager’s ability to forecast future security prices (M.C. Jensen, The performance of mutual funds in the period 1945 – 1964, „The Journal of Finance”). The paper concluded that the performance measure ? may be positive for two reasons: 1) extra returns earned on the portfolio due to the manager’s ability and/or 2) a positive â estimator bias. In 1977, D.Grant (Portfolio performance and the „cost” of timing decisions, „The Journal of Finance”) stated that Jensen’s original work contained a mathematical error and a conceptual problem. He propounded a new equation which differed from that of Jensen in both direction and magnitude of the â estimator bias. Grant’s new approach caused serious confusion about the subject as some authors now quote after Jensen and some after Grant. Consequently, the conclusions concerning managed mutual funds’ portfolios performance are often ambiguous. The aim of this paper is to resolve this ambiguity and to determine which alpha coefficient interpretation is correct. The paper contains a proof of Jensen’s equation. We also present the examples of the classical T-M and H-M market-timing models in the case of Polish equity open-end mutual funds and test their stability in the period Jan 2003-Dec 2010.

KEYWORDS

Jensen’s alpha coefficient, selectivity, classical market-timing models

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