Power laws of wealth, market order volumes and market returns

Abstract

Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue that 'fair play' for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α ∼ 3/2. In particular we relate it to the average number of individuals L depending on the average wealth: α ∼ L/(L − 1). Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β ∼ α ∼ 3/2. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ ∼ 2α ∼ 3. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for β and[Gopikrishnan et al. 1999] for γ).

Inelastically scattering particles and wealth distribution in an open economy

“…It can be easily verified [54] that the functionΦ 1 (x) = (1+ √ 2x)e − √ 2x is a solution of (7). Inverting the Laplace transform we obtain the corresponding wealth distribution Φ 1 (w) = 1 √ 2π w −5/2 exp(− 1 2 w ) which has similar form as obtained in previous studies [13,21,22]. However, in this case the value of ǫ is negative, which contradicts our assumption of wealth increase, while for ǫ > 0 the above idea leading to the functionΦ 1 (x) does not work.…”

“…There are few agents having wealth below w max . This suggests that the intuition formalized e. g. in [11,13], that the exponent is "tuned" by the low-wealth behavior of the distribution, may be in work quite generally. Here, the free parameters are apparently the wealth production and exchange, but in reality these parameters may be themselves tuned by a mechanism which fixes the position of the maximum of the wealth distribution, i. e. the lowest wealth compatible with survival.…”

Market Statistics of a Psychology-Based Heterogeneous Agent Model

“…Some previous explanations for the existence of inverse-cubic pricereturn decays [54,18] are predicated upon the fact that the distribution of agent sizes follows a Pareto law with known exponent. However, the above results show that the same exponent can be observed in a model with all agents of equal size.…”

Power Laws in Economics: An Introduction

“…The power law distribution of firms might actually explain the power law distribution of stock market crashes. In Stanley (2003, 2006), we develop the hypothesis that stock market crashes are due to large financial institutions selling under pressure in illiquid markets (see also Levy and Solomon 1996;Solomon and Richmond 2001). This may account not only for large crashes, but also for the whole distribution of mini-crashes described by the power law.…”