Globally evolutionarily stable portfolio rules,

Abstract The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to "survive," i.e. to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property-an analogue of the famous Kelly (1956) rule of "betting one's beliefs." A game theoretic interpretation of this result is given. JEL-Classification: G11, C61, C62

The Asset Market Game

This paper models asset markets as a game where assets pay according to an arbitrary payoff matrix,investors decide on fractions of wealth to allocate to each asset,and prices result from market clearing. The only pure-strategy Nash equilibrium is to split wealth proportionally to the assets´expected returns, which can be interpreted as investing according to the fundamentals. Further, the equilibrium is evolutionarily stable in the sense of Schaffer (1988). We also study the stability properties of the equilibrium in an evolutionary dynamics where wealth flows with higher probability into those strategies that obtain higher realized payoffs.

Evolutionary Finance for Multi-Asset Investors

Standard strategic asset allocation procedures usually neglect market interaction. However, returns are not generated in a vacuum but are the result of the market's price discovery mechanism which is driven by investors' investment strategies. Evolutionary finance accounts for this and endogenizes asset prices. This paper develops a multi-asset evolutionary finance model. Requiring little more than dividend and interest rate data, it facilitates an interesting glimpse into the inner workings of financial markets and provides a valuable guide to this class of models. While traditional mean/variance optimization is static and concerned with finding the optimal asset allocation, evolutionary portfolio theory is dynamic and its focus is on finding the optimal investment strategy. This paper shows that yield-based strategies generate asset allocations that outperform competing alternatives. Therefore, strategic asset allocation approaches that rely on such an economic foundation are evolutionarily advantageous for multi-asset investors

Random dynamics in financial markets

We study evolutionary models of financial markets. In particular, we study an evolutionary market model with short-lived assets and an evolutionary model with long-lived assets. In the long-lived asset market, investors are allowed to use general dynamic investment strategies. We find sufficient conditions for the Kelly portfolio rule to dominate the market exponentially fast. Moreover, when investors use simple strategies but have incorrect beliefs, we show that the strategy which is "closer" to the Kelly rule cannot be driven out of the market. This means that this strategy will either dominate or at least survive, i.e., the relative market share does not converge to zero. In the market with short-lived assets, we study the dynamics when the states of the world are not identically distributed. This marks the first attempt to study the dynamics of the market when the probability of success changes according to the relative shares of investors. In this problem, we first study a skew product of the random dynamical system associates with the market dynamics. In particular, we compute the Lyapunov exponents of the skew product. This enables us to produce a "surviving" investment strategy, i.e., the investor who follows this rule will dominate the market or at least survive. All the mathematical tools in the thesis lie within the framework of random dynamical systems

Evolutionary Finance: A model with endogenous asset payoffs

Evolutionary Finance (EF) explores financial markets as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some "survive" and some "become extinct". A central goal is to identify evolutionary stable (in one sense or another) investment strategies. The problem is analyzed in a framework combining stochastic dynamics and evolutionary game theory. Most of the models currently considered in EF assume that asset payo¤s are exogenous and depend only on the underlying stochastic process of states of the world. The present work develops a model where the payo¤s are endogenous: they depend on the share of total market wealth invested in the asset

An evolutionary explanation of the value premium puzzle

As early as 1934 Graham and Dodd conjectured that excess returns from value investment originate from a tendency of stock prices to converge towards a fundamental value. This paper confirms their insights within the evolutionary finance model of Evstigneev et al. (Econ Theory 27:449-468, (Evstigneev et al. 2006)). Our empirical results show the predictive power of the evolutionary benchmark valuation for the relative market capitalization and its dynamics in the sample of firms listed in the Dow Jones Industrial Average index in 1981-200

Conflict over non-partitioned resources may explain between-species differences in declines: the anthropogenic competition hypothesis

This is the final version of the article. Available from Springer Verlag via the DOI in this record.Human alterations of habitats are causing declines in many species worldwide. The extent of declines varies greatly among closely related species, for often unknown reasons that must be understood in order to maintain biodiversity. An overlooked factor is that seasonally breeding species compete for nest sites, which are increasingly limited in many anthropogenically degraded environments. I used evolutionary game theory to predict the outcome of competition between individuals that differ in their competitive ability and timing of nesting. A range of species following evolutionarily stable strategies can co-exist when there are sufficient nest sites, but my model predicts that a reduction in nest site availability has greater impacts on late-nesting species, especially the stronger competitors, whereas early-nesting, stronger species decline only slightly. These predictions are supported by data on 221 bird and 43 bumblebee species worldwide. Restoration and provision of nest sites should be an urgent priority in conservation efforts. More broadly, these results indicate a new ecological principle of potentially widespread importance: rapid reductions in the abundance of resources for which species’ preferences have not diversified will result in unprecedented conflicts that reduce the potential for species co-existence.This work was supported by the European Research Council (Advanced Grant 250209 to Alasdair Houston), a residential fellowship at the Wissenschaftskolleg zu Berlin and a NERC Independent Research Fellowship (NE/L011921/1)

Price and Wealth Dynamics in a Speculative Market with Generic Procedurally Rational Traders

An agent-based model of a simple financial market with arbitrary number of traders having relatively general behavioral specifications is analyzed. In a pure exchange economy with two assets, riskless and risky, trading takes place in discrete time under endogenous price formation setting. Traders' demands for the risky asset are expressed as fractions of their individual wealths, so that the dynamical system in terms of wealth and return is obtained. Agents' choices, i.e. investment fractions, are described by means of the generic smooth functions of an infinite information set. The choices can be consistent with (but not limited to) the solutions of the expected utility maximization problems. A complete characterization of equilibria is given. It is shown that irrespectively of the number of agents and of their behavior, all possible equilibria belong to a one-dimensional "Equilibrium Market Line". This geometric tool helps to illustrate possibility of different phenomena, like multiple equilibria, and also can be used for comparative static analysis. The stability conditions of equilibria are derived for general model specification and allow to discuss the relative performances of different strategies and the selection principle governing market dynamics.

Dynamic General Equilibrium and T-Period Fund Separation

In a dynamic general equilibrium model, we derive conditions for a mutual fund separation property by which the savings decision is separated from the asset allocation decision. With logarithmic utility functions, this separation holds for any heterogeneity in discount factors, while the generalization to constant relative risk aversion holds only for homogeneous discount factors but allows for any heterogeneity in endowments. The logarithmic case provides a general equilibrium foundation for the growth-optimal portfolio literature. Both cases yield equilibrium asset pricing formulas that allow for investor heterogeneity, in which the return process is endogenous and asset prices are determined by expected discounted relative dividends. Our results have simple asset pricing implications for the time series as well as the cross section of relative asset prices. It is found that on data from the Dow Jones Industrial Average, a risk aversion smaller than in the logarithmic case fits bes