Journal of Probability and Statistics
Volume 2011 (2011), Article ID 595741, 19 pages
Research Article

Drift and the Risk-Free Rate

1Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144-5591, USA
2School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA

Received 5 May 2011; Revised 27 June 2011; Accepted 2 July 2011

Academic Editor: Arjun K. Gupta

Copyright © 2011 Anda Gadidov and M. C. Spruill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is proven, under a set of assumptions differing from the usual ones in the unboundedness of the time interval, that, in an economy in equilibrium consisting of a risk-free cash account and an equity whose price process is a geometric Brownian motion on [ 0 , ) , the drift rate must be close to the risk-free rate; if the drift rate 𝜇 and the risk-free rate 𝑟 are constants, then 𝑟 = 𝜇 and the price process is the same under both empirical and risk neutral measures. Contributing in some degree perhaps to interest in this mathematical curiosity is the fact, based on empirical data taken at various times over an assortment of equities and relatively short durations, that no tests of the hypothesis of equality are rejected.