Before revision:  We show that this relative performance has three components: a term that can be interpreted as energy coming from the market fluctuations , a relative entropy term that measures "distance " between the portfolio holdings and the market capital distribution, and another entropy term that can be controlled by the trader by choosing a suitable strategy. The first aids growth in the portfolio value, and the second poses as relative risk of being too far from the market. We give several explicit controls of the third term that allows one to outperform a diverse volatile market in the long run . Named energy-entropy portfolios, these strategies work in both discrete and continuous time, and require essentially no probabilistic or structural assumptions.
After revision:  We show that this relative performance has three components: a term that can be interpreted as energy coming from the market fluctuations , a relative entropy term that measures "distance " between the portfolio holdings and the market capital distribution, and another entropy term that can be controlled by the investor by adopting a suitable rebalancing strategy. This framework leads to a class of portfolio strategies that allows one to outperform a diverse volatile market in the long run . Named energy-entropy portfolios, these strategies work in both discrete and continuous time, and require essentially no probabilistic or structural assumptions.