A numerical study on the evolution of portfolio rules

In this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of distribution of wealth in a financial market where some traders invest as prescribed by CAPM and others behave according to different portfolio rules. Our study is motivated by recent analytical results that show that, whenever a logarithmic utility maximiser enters the market, CAPM traders vanish in the long run. Our analysis provides further insights and extends these results. We simulate a sequence of trades in a financial market and: first, we address the issue of how long is the long run in different parametric settings; second, we study the effect of heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM is particularly “unfit” for highly risky environments

Adaptive Trading for Anti-correlated Pairs of Stocks

The effect of anti-correlation between stocks in real stock market can be exploited for profit if one can also properly set the criterion for trading that takes into account the volatility of the stock pair. This complex problem of resource allocation for portfolio management of stocks is here simplified to a problem of adaptive trading with an investment criterion that evolves along with the time series of the stock data. The trend of the stock is modeled with standard stochastic dynamics, from which the volatility of the stock provides a criterion for investment on a two stock portfolio that consists of the anti-correlated pair using mean variance analysis that optimizes the return. The action of buy and sell of the two-stock portfolio will be based on the fractional return of the pair: when the fractional return of the pair is greater than an upper threshold of 1.01, the action “buy” is taken; and when this fractional return is less than a lower threshold of 0.99, the action “sell” is taken. Since both the volatility criterion for investment and the fractional return of the two-stock portfolio are time dependent, the entire trading scheme is adaptive. Comparison of this evolving strategy of investment with time-average performance of the respective stocks indicates a consistent superiority