Abstract
What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.
Highlights
At least since Markowitz [1] initiated modern portfolio theory (MPT), it has often been maintained that the tradeoff between systematic risk and expected return is the most important theoretical element of financial economics, for example, Campbell [2]
Econophysicists generally consider financial economics to be primarily concerned with a core theory that is inconsistent with the empirical orientation of physical theory
This paper provides an etymology and history of the “classical ergodicity hypothesis” in 19th century statistical mechanics
Summary
At least since Markowitz [1] initiated modern portfolio theory (MPT), it has often been maintained that the tradeoff between systematic risk and expected return is the most important theoretical element of financial economics, for example, Campbell [2]. In contrast to natural sciences, such as physics, in the human sciences there is no assurance that ex post statistical regularity translates into ex ante forecasting accuracy Resolution of this quandary highlights the usefulness of employing a “phenomenological” approach to modeling stochastic properties of financial variables relevant to MPT. A modern interpretation of classical ergodicity is provided that uses Sturm-Liouville theory, a mathematical method central to classical statistical mechanics, to decompose the transition probability density of a one-dimensional diffusion process subject to regular upper and lower reflecting barriers This “classical” decomposition divides the transition density of an ergodic process into a possibly multimodal limiting stationary density which is independent of time and initial condition and a power series of time and boundary dependent transient terms. To illustrate the implications of the expanded class of ergodic processes available to econophysics, properties of the bimodal quartic exponential stationary density are considered and used to assess the ability of the classical ergodicity hypothesis to explain certain “stylized facts” associated with the ex post/ex ante quandary confronting MPT
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