The paradigm in economics is about to change. The focus shifts away from the analysis of overall market structures in rational expectation equilibrium to the investigation of the interactive market process based on the market’s rules and regulations. Economic research realises the necessity of founding the analysis on the comprehensive market performance, taking the acting and interacting of individuals explicitly into account, like physics started to proceed from Newtonian physics to nuclear physics some 150 years ago.
The paper is organised as follows. In Section 2 the call for a model of the interactions between and among individuals at markets is substantiated. Reference is made especially to the results of Kurz (1997a). Section 3 points out how the distribution of the market participants’ intrinsic value estimates may be revealed. Empirical data are tabulated in Appendix A. Section 4 introduces random utility models and shows the appropriateness of their application to modelling the decision making in trading securities. The utility functions of the agents are specified. Appendices B.2 and B.3 formally describe the agent’s evaluation process in detail.
The analogy to portfolio theory’ s multifactor model underlines the relevancy to capital market theory. In Section 5 the multinomial logit model is applied. The actions’ execution probabilities give the transition probabilities of a Markov process imaging the stock market’s evolution. The details of the Markov state vector are presented in Appendix B.1. It can be shown that in this scenario the independence from irrelevant alternatives (IIA) property is fulfilled. Section 6 introduces entropy concepts and Section 7 applies these concepts to measuring both the activity efficiency of individuals (AEI) and the informational efficiency of capital markets (IEM) based on the Markov transition rates. Furthermore, capital market equilibrium is shown to be analogous to Bose-Einstein condensation and the so-called Grossmann and Stiglitz (1980) paradox is disentangled at an operational market microstructure level. Section 8 summarises the findings.
Contents
1 Introduction
2 Modelling the performance of individual agents
3 Deducing the distribution of intrinsic value estimates
4 Random utility maximisation and discrete choice models
4.1 Basic framework
4.2 Logit model
- 4.2.1 Independence from irrelevant alternatives
4.2.2 Extreme value distribution
4.2.3 Modelling of interactive market dynamics
4.3 CAPM and multifactor models as random utility approaches
4.4 The deterministic part of the utility function
- 4.4.1 Determining factors of trading decisions’ utility
4.4.2 Implementation of psychological attitudes
4.4.3 Evaluation of buy and sell actions
4.4.4 Evaluation of value adjustments
5 Catallactic interactions imaged by a Markov process
5.1 Stock market evolution as Markov process
5.2 Transition rates of Markov process derived from actions’ utility
6 Entropy and economic efficiency
6.1 Meanings of entropy
- 6.1.1 Entropy in physics
6.1.2 Entropy in information theory
6.1.3 Entropy and statistics
6.1.4 Entropy of selected probability distributions
6.2 Entropy and discrete choice.
7 Unconstrained maximum entropy identifies efficient markets
7.1 Master equation and Markov process provide probability distribution
7.2 Entropy and market efficiency
7.3 Entropy of the distribution of actions’ execution probability
- 7.3.1 Definition of activity efficiency of individuals
7.3.2 Definition of information efficiency of markets
7.3.3 Pure insider knowledge, minimum entropy and minimum information efficiency of markets
7.3.4 Pure ignorance, maximum entropy and maximum information efficiency of markets
7.4 Market equilibrium as Bose-Einstein condensation
7.5 Entropy and economic efficiency– two suggestions
- 7.5.1 Entropy and logit model’ s probability
7.5.2 Entropy and aggregation of individual decisions to collective decisions
8 Summary
Appendix A. Value estimates for 18 EuroStoxx50 companies
Appendix B. The KapSyn model in detail
B.1. The market condition vector
B.2. Agents’ decisions to buy and sell
- B.2.1. Rate of return and execution's feasibilities as the factors determining bids and asks
B.2.2. Establishing bid and ask offers
B.2.3. Determining permissible bid/ask amounts
B.2.4. Evaluation of buy and sell actions
B.3. Evaluation of value adjustments
Appendix C. Index of symbols
References
