The idea of this project is to apply evolutionary dynamics (mutation and selection) to study the evolution of trading strategies and the evolution of financial innovations.
Evolution as a Paradigm for Finance
We believe that thinking in evolutionary terms like strategies, market selection and mutation is an appropriate framework for finance. In this view, for example, a stock market is understood as a heterogeneous population of frequently interacting portfolio strategies in competition for market capital. Market selection is perhaps most severe in these markets and innovations, respectively mutations, occur frequently. The aim of our project is to build a Darwinian theory of portfolio selection.
Our Evolutionary Market Model
The building blocks of the model are strategies and not individual investors, i.e. for each strategy all wealth being managed by that strategy is added up. This is analogous to Darwin 's view according to which the species but not the individual animal counts for evolution. One then realizes that strategies but not individual investors have an impact on market prices. The strategies considered in our project are for example the mean-variance rule, the growth-optimal rule, the CAPM rule, na´ve diversification, prospect theory based rules and fundamental rules like relative-dividends rule. In our evolutionary market model the impact of any such rule on market prices is proportional to the amount of wealth managed by the rule. This gives a very simple and robust asset pricing equation. In a Darwinian model two forces are at work: one reducing the variety of species and one increasing it. In our model the first such force is the endogenous return process acting as a market selection mechanism that determines the evolution of wealth managed by the portfolio rules. That is to say, if some rule has gained wealth because it has managed to buy low and to sell high then other rules must have lost an equal amount of wealth. Secondly, any system of portfolio rules that is selected by the market selection process is checked for its evolutionary stability, i.e. it is checked whether the innovation of a new portfolio rule with very little initial wealth can grow against the incumbent rule.
Relevance of our model
The Darwinian theory of asset markets seems to describe very well a modern asset market in which most of the available capital is invested by delegated management. Indeed investors typically choose funds by the portfolio rules, also called "styles", according to which the money is invested. Style consistency appears nowadays to be one of the most important features in monitoring fund managers. Hedge funds are a sector of the financial market that can perfectly be described by our model. Moreover, using functions that describe the flow of wealth between hedge fund strategies our model can also be used to give good predictions of asset returns for sectors quite different to the hedge fund business.