Breakdown of the mean-field approximation in a wealth distribution model

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.Comment: 11 pages, 3 figure

Schumpeterian economic dynamics as a quantifiable minimum model of evolution

We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition mechanism existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to a generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets - which could be interpreted as Schumpeterian business `cycles'. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.Comment: 21 pages, 11 figure

Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior

Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. This work is a contribution to the building of a set of stylized facts about the traders themselves. Using the client database of Swissquote Bank SA, the largest on-line Swiss broker, we find empirical relationships between turnover, account values and the number of assets in which a trader is invested. A theory based on simple mean-variance portfolio optimization that crucially includes variable transaction costs is able to reproduce faithfully the observed behaviors. We finally argue that our results bring into light the collective ability of a population to construct a mean-variance portfolio that takes into account the structure of transaction costsComment: 26 pages, 9 figures, Fig. 8 fixe

Optimal leverage from non-ergodicity

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of ergodicit

Whither Capitalism? Financial externalities and crisis

As with global warming, so with financial crises – externalities have a lot to answer for. We look at three of them. First the financial accelerator due to ‘fire sales’ of collateral assets -- a form of pecuniary externality that leads to liquidity being undervalued. Second the ‘risk- shifting’ behaviour of highly-levered financial institutions who keep the upside of risky investment while passing the downside to others thanks to limited liability. Finally, the network externality where the structure of the financial industry helps propagate shocks around the system unless this is checked by some form of circuit breaker, or ‘ring-fence’. The contrast between crisis-induced Great Recession and its aftermath of slow growth in the West and the rapid - and (so far) sustained - growth in the East suggests that successful economic progress may depend on how well these externalities are managed