Premium
Markov Chains and Regression toward the Mean
Author(s) -
Kolb Robert W.,
Rodriguez Ricardo J.
Publication year - 1991
Publication title -
financial review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.621
H-Index - 47
eISSN - 1540-6288
pISSN - 0732-8516
DOI - 10.1111/j.1540-6288.1991.tb00373.x
Subject(s) - markov chain , econometrics , interval (graph theory) , mathematics , regression , statistics , set (abstract data type) , stationary distribution , regression analysis , distribution (mathematics) , economics , combinatorics , computer science , mathematical analysis , programming language
Abstract Using the theory of stationary Markov chains, we uncover a previously unknown property of the behavior of betas. Specifically, if the cross‐sectional distribution of betas is stationary over time, then the set of firms that remain in an arbitrarily chosen beta interval between one period and the next will not regress toward the mean. This surprising result occurs in spite of the well‐known fact that the set of all the firms in the interval will exhibit the regression tendency. Our empirical tests indicate that betas behave in remarkable accordance with this prediction.