Globally Evolutionarily Stable Portfolio Rules
The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Asset 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 anlaogue of the famous Kelly (1956) rule of "betting one's beliefs".
NCCR FINRISK project, Evolution and Foundations of Financial Markets
Markets Do Not Select For a Liquidity Preference as Behavior Towards Risk
Tobin (1958) has argued that in the face of potential capital losses on bonds it is reasonable to hold cash as a means to transfer wealth over time. It is shown that this assertion cannot be sustained focusing on the evolution of wealth of cash holders versus non-cash holders. Cash holders will be driven out of the market in the long run by traders who only use a (risky) long-lived asset to transfer wealth. Similarly, in a model with a bond instead of cash, depending on the way consumption is modeled, bond holders do not survive in the presence of pure stock holders.
May 16, 2004
Survival of the Fittest on Wall Street
This paper studies an application of a Darwinian theory of portfolio selection to stocks listed in the Dow Jones Industrial Average (DJIA). We analyze numerically the long-run outcome of the competition of fix-mix portfolio rules in a stock market with actual DJIA dividends. In the model seemingly rational strategies can do very poorly against seemingly irrational strategies. Moreover, the interaction of strategies can lead to stochastic time series of asset prices that do not converge. The simulations also show that the evolutionary portfolio rule discovered in Hens and Schenk-Hoppé (2004) will eventually hold total market wealth in competition with fix-mix portfolio rules derived from mean-variance optimization, maximum growth theory and behavioral finance. According to this evolutionary rule, portfolio weights should be proportional to the expected relative dividends of the assets. As an implication asset prices converge to expected relative dividends.
February 2, 2004
Evolutionary Portfolio Selection with Liquidity Shocks
Insurance companies invest their wealth in financial markets. The wealth evolution strongly depends on the success of their investment strategies, but also on liquidity shocks which occur during unfavourable years, when indemnities to be paid to the clients exceed collected premia. An investment strategy that does not take liquidity
shocks into account, exposes insurance companies to the risk of bankruptcy, when liquidity shocks and low investment payoffs jointly appear. Therefore, regulatory authorities impose solvency restrictions to ensure that insurance companies are able to face their obligations with high probability. This paper analyses the behaviour of insurance companies in an evolutionary framework. We show that an insurance company that merely satisfies regulatory constraints will eventually vanish from the market. We give a more restrictive no bankruptcy condition for the investment strategies and we characterize trading strategies that are evolutionary stable, i.e. able to drive out any mutation.
Evolutionary Stable Stock Markets
This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded by portfolio rules that will gain market wealth and hence change the valuation. In the model the valuation of assets is given by the wealth average of the portfolio rules in the market. The wealth dynamics is modelled as a random dynamical system. Necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when (relative) dividend payoffs form a stationary Markov process. These local stability conditions lead to a unique evolutionary stable strategy according to which assets are evaluated by expected relative dividends.
October 27, 2003
Evolution of Portfolio Rules in Incomplete Markets
The paper considers the evolution of portfolio rules in markets with stationary returns and endogenous prices. The ultimate success of a portfolio rule is measured by the wealth share the rule is eventually able to conquer in competition with other portfolio rules. We give necessary and sufficient conditions for portfolio rules to be evolutionary stable. In the case of i.i.d. returns we identify a simple portfolio rule to be the unique evolutionary stable strategy. Moreover we demonstrate that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.
Market Selection and Survival of Investment Strategies
The paper analyzes the process of market selection of investment strategies in an incomplete asset market. The payoffs of the assets depend on random factors described in terms of a discrete-time Markov process. Market participants make dynamic investment decisions based on their observations and time. We show that a trader distributing wealth across available assets according to the relative expected returns eventually accumulates the entire market wealth. The result obtains under the assumption that the trader’s strategy is asymptotically distinct from the CAPM strategy (prescribing investment in the market portfolio). This assumption turns out to be essentially necessary for the conclusion.
Market Selection of Financial Trading Strategies: Global Stability
In this paper we analyze the long-run dynamics of the market selection process among simple trading strategies in an incomplete asset market with endogenous prices. We identify a unique surviving financial trading strategy. Investors following this strategy asymptotically gather total market wealth. This result generalizes findings by Blume and Easley (1992) to any complete or incomplete asset market.
July 11, 2001