Toward a theory of marginally efficient markets

https://doi.org/10.1016/S0378-4371(99)00077-1Get rights and content

Abstract

Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as favorable games, in the sense that there is a small probabilistic edge that smart speculators can exploit. We propose to identify this probability using conditional entropy concept. A perfect random walk has this entropy maximized, and departure from the maximal value represents a price history's predictability. We propose that market participants should be divided into two categories: producers and speculators. The former provides the negative entropy into the price, upon which the latter feed. We show that the residual negative entropy can never be arbitraged away: infinite arbitrage capital is needed to make the price a perfect random walk.

Introduction

One of the fundamental pillars of Modern Economics is the efficient market hypothesis (EMH). Its essential meaning is that if the market price were predictable, then these opportunities would be exploited to make a gain so that such opportunities would disappear in a competitive and efficient market. Indeed, this proposition is very plausible and has a long history. Bachelier, almost a century ago [1], has had the vision that the market prices should behave like a random walk. Contemporary economists have gone great lengths to formalize the random walk concept, reaching the high-water mark when Samuelson mathematically “proved” that properly anticipated prices are random walk [2]. Empirical observations, however, are much less convincing. Many authors have indeed found that market prices may contain some profit pockets. The proponents of EMH generally label such observations as “anomalies” without significance.

On the other hand, if the competitive markets are indeed so efficient as the proponents of EMH would like them to be, then we are facing the enormous paradox: there is a huge industry (Wall Street!) trying hard to anticipate market moves using essentially past information. These institutions can hardly be accounted for in the orthodox economics. The fact that people can cling to EMH so long is that there is so far no rival alternative convincing enough to oust the elegant, simple assumption. After all, prices in competitive markets have to be rather efficient. In this work we show that the basic arguments of the random walk are generally valid, i.e. market prices are not very predictable. It is the small inefficiency margin which contains all the interesting dynamics.

What is wrong in the naive EMH is that it implies that if there are arbitrage opportunities, they would disappear instantly upon speculators’ action. We emphasize that arbitrage opportunities in general are represented by probabilities. Though they are favorable in the probabilistic sense, they are not riskless. To profit from such opportunities speculators would need large capital and bear certain risk. Thus this favorable probability is the speculators’ edge. Upon increased participation of speculators, this marginal probability would shrink, but never disappear. This is so because with the diminished marginal probability, it is even harder to make a profit. Still larger capital is needed and risk incurred is also larger. To make this favorable marginal probability disappear, infinite capital is needed and the return per capital invested would diminish to zero.

Therefore, it is this marginal probability which keeps the market competitive and dynamic, such that it is attractive to all participants. Speculators work harder to outguess the market, if they make profit by exploiting their probabilistic edge, the market will be more efficient, but never be so in the absolute sense. So a competitive market can keep its marginal probability low, thanks to the fierce competition of the participants.

We propose the alternative of marginally efficient markets (MEM) to replace the sterile EMH. Instead of regarding the anomalies as mere annoyance, we show in the following sections that it is in this marginal region many interesting things take place.

Section snippets

Market inefficiency and probabilistic edge of speculators

Modern version of EMH is formulated in three versions: strong form, semi-strong form, and weak form. For a review we refer readers to a recent comprehensive volume [3]. Here we show a few examples suggesting that even the weak form does not hold, with varying degrees of violation. The weak form of EMH states that using the past price alone, you cannot predict the future price movements. Strong and semi-strong versions allow other information besides the price history itself. Fama [4] was the

Market participants, market dynamics

Many studies have been done on optimization of positive returns from markets, neatly summarized in portfolio theory [9]. It is rarely mentioned in the literature that in order for “smart” investors to make money someone must lose it in the first place. Standard portfolio theory deals with how to get the best portfolios, without giving hint of the global picture where buyers and sellers are both considered. If an investor, convinced of the optimal portfolio theory, buys the stocks by the

Negative entropy, a measure of market inefficiencies

If prices were a pure random walk, the variations would be a completely uncorrelated string of numbers. In physics and information theory [11] we would say that such a string of variables is completely disordered, or the entropy is maximized. On the other hand, if the price variations are somewhat correlated, then the entropy does not attain its maximal value. It is convenient to consider actual values of the price variation's entropy with reference to its maximal value. Any difference is

Persistent and anti-persistent walks

Persistent and anti-persistent walks (PW and APW) were first introduced by Mandelbrot. But his definition refers to long-range tendencies and the diffusion exponent are different from 12. Here we limit ourselves to short-range correlations, as it seems to be the case in the market prices. Many proponents of the random walk hypothesis (RWH) probably ignore the fact that being a random walk does not necessarily imply efficient markets. Short time correlations in prices can still arise and

Why market inefficiencies cannot be arbitraged away

The standard assumption in the mainstream economics is that if there is an arbitrage opportunity, “smart” investors would spot the chance and make a profit, thereby making the opportunity disappear in no time. It hardly occurs to people that in the competitive, fair markets the most frequent profit opportunities are only probabilistic in nature. To profit from probabilistic opportunities one has to bear risks. Moreover, the “smart” investor's capital is finite so also must be his impact on

Intrinsic illiquidity cost and market impact equation

In this section we digress a bit from the main line of this work to consider some implications of MEM to market dynamics. To understand what a small inefficiency can do to the market, first we need to discuss what are the implications of an efficient market. In the literature [14] much detailed mechanism is discussed.

The central point of this work is that markets are almost efficient with the inefficiency margin small. As a consequence any arbitrage opportunity without risk should be absent.

Summary and future work

In the above discussion we have tried to outline a novel approach to study dynamics of markets. The key ingredient is to recognize the important role played by the marginal inefficiency of the markets. We are led to view the market economies as a web of agents, quite like the food chain in ecology, connected through the markets. Two groups of agents (producers and speculators) live in symbiosis, the one injects “negative entropy” to make markets attractive; the other tries to exploit the

Acknowledgements

During the past few years I have benefitted from fruitful collaborations with D. Challet, G. Calderelli, M. Marsili, S. Maslov and F. Slanina.

References (18)

  • D. Challet et al.

    Physica A

    (1997)
  • L. Bachelier, Theory of speculation (reprint (1900)), in: P. Cootner (Ed.), Random Character of Stock Prices, MIT...
  • P. Samuelson

    Proof that properly anticipated prices fluctuate randomly

    Ind. Manage. Rev.

    (1965)
  • J.Y. Campbell, A.W. Lo, A.C. MacKinlay, The Econometrics of Financial Markets, Princeton University Press, Princeton,...
  • E. Fama

    J. Finance

    (1970)
  • R. Savit, R. Manuca, R. Riolo, preprint...
  • Y.-C. Zhang

    Europhys. News

    (1998)
  • N. Johnson et al., preprint...
  • E. Elton, M. Gruber, Modern Portfolio Theory and Investment Analysis, Wiley, New York,...
There are more references available in the full text version of this article.

Cited by (144)

  • Insights from the (in)efficiency of Chinese sectoral indices during COVID-19

    2021, Physica A: Statistical Mechanics and its Applications
    Citation Excerpt :

    Given this, the Chinese sectoral indices price fluctuations are somewhat correlated, it implies that the entropy does not attain its maximal value. Thus, the negative entropy can be considered a measure of predictability, reflecting the market’s inefficiency [17,19,37,38]. Our findings show that TELE, FOOD-DRUG-RET, HOUS-PERI, FOOD-BE-TOB, and CONS-STAP are closer to the lower boundary of the CECP (behavior closer to a random walk).

  • Exploring disorder and complexity in the cryptocurrency space

    2019, Physica A: Statistical Mechanics and its Applications
  • Capability satisficing in high frequency trading

    2017, Research in International Business and Finance
View all citing articles on Scopus

Based on presentations at the Econophysics meetings in Rome, March 1998, and Palermo, September 1998. To Appear in Palermo Proceedings (1999), Ed. R.N. Mantegna.

View full text