Limited profit in predictable stock markets

It has been assumed that arbitrage profits are not possible in efficient markets, because future prices are not predictable. Here, we show that predictability alone is not a sufficient measure of market efficiency because of the influence an order has on its dynamics. We instead propose to measure inefficiencies of markets in terms of the maximal profit an ideal trader who can perfectly predict the future behavior of the market can take out from a market. In a stock market model with an evolutionary selection of agents this method reveals that, the mean relative amount of realizable profits P is very limited and we find that it decays with the rising number of agents. Our results show that markets may self-organize their collective dynamics such that it becomes very sensitive to profit attacks, which demonstrates that a high degree of market efficiency can coexist with predictability.