We investigate a simple model based on the idea of the minority game to predict the movement of individual stocks, where we restrict ourselves to predict whether the stock moves up or down in the next time step. We evaluate the performance of all possible strategies with a memory length of M = 1, 2, …, 10. A strategy consists of the prediction for each of the 2^M possible histories and strategies differ in these predictions. Every time a strategy makes a correct prediction, its score is increased by one and every time it makes a wrong prediction its score is reduced by one. The best strategy is the strategy that has the highest score. In each time period we select the strategy which performed best in the past and once other strategies outperform our chosen strategy we change the strategy accordingly. This model allows us to constantly review the strategy we do follow and change our behaviour in reaction to past events. This is in contrast to most models where over time only a single “optimal” strategy is followed, making our model much more flexible.

Using daily data over the past 15 years of 375 stocks continuously traded in the S&P500 during that time, we empirically evaluate the performance of our algorithm. Overall we find that the algorithm works best with a memory of 2 trading days, providing the correct prediction of the movement of the stock in 50.58%, a marginal improvement on a random forecast which would yield 50%. Despite this small improvement on the forecast, we find in nearly three quarter of stocks that the correct prediction is more often given than not. This result provides some evidence for the relative efficiency of the market for these commonly traded stocks. We furthermore find that only a very small fraction of the available strategies are actually chosen and those chosen are frequently changing.

Following a simple trading strategy in which one share is bought when prices are predicted to fall (buy low) and sold when prices are predicted to rise (sell high) yields widely varying performances, on average underperforming a buy-and-hold strategy. On the other hand, the risk of this strategy is significantly lower than that of the buy-and-hold strategy providing significant advantages in portfolio selection by producing a superior portfolio than is possible with a buy-and-hold strategy.

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1. A Comparison of Market Structures with Near-Zero-Intelligence Traders