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On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market

Published online by Cambridge University Press:  09 June 2010

David H. Goldenberg  and
Raymond J. Schmidt
David H. Goldenberg
Affiliation:
Lally School of Management, Rensselaer Polytechnic Institute, Troy, NY 12180.
Raymond J. Schmidt
Affiliation:
Lally School of Management, Rensselaer Polytechnic Institute, Troy, NY 12180.
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Abstract

This paper derives and numerically simulates maximum likelihood estimators for the drift in several important diffusion price models. The time series convergence properties of these estimators are compared to those of standard estimators including the geometric and arithmetic means. Merton (1980) demonstrated that it is difficult to efficiently estimate the drift in a log-normal diffusion model. We qualify and strengthen his result by noting that his estimator is the maximum likelihood estimator and by applying our simulation results. However, we also demonstrate that it is possible to efficiently estimate the drift in other useful diffusion price models. In particular, by asking just how much time is needed in order for the maximum likelihood estimators of the drift in different diffusion processes to converge, these results qualify and quantify Black's (1993) statement that “we need such a long period to estimate the average that we have little hope of seeing changes in expected return."

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 31 , Issue 4 , December 1996 , pp. 605 - 631
Copyright
Copyright © School of Business Administration, University of Washington 1996

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