Beating the market? A mathematical puzzle for market efficiency

Abstract The efficient market hypothesis is highly discussed in economic literature. In its strongest form, it states that there are no price trends. When weakening the non-trending assumption to arbitrary short, small, and fully unknown trends, we mathematically prove for a specific class of control-based trading strategies positive expected gains. These model free, i.e., trader neither has think about predictable patterns nor estimate parameters such as trend’s sign like momentum traders have do. That means, since does not know any trend, even trends too small find enough beat market. Adjustments risk comparisons with buy-and-hold do satisfactorily solve problem. detail, generalize results from literature on settings without assumptions, but time-varying discrete continuous time. We give closed-form formulae gain well gain’s variance rules setting where older information counts less. addition, perform an exemplary backtesting study taking transaction costs bid-ask spreads into account still observe—on average—positive