This study introduces a research path to obtain alternative trading rules by using nonlinear dynamical analysis of stock returns. We examine the daily return data of Istanbul Stock Exchange index and Shenzhen Index B-Shares. Both stock returns series are shown to exhibit chaotic behavior and associated maximal Lyapunov exponents (LE) are computed. A new prediction method which bases on the properties of detected chaotic behavior is proposed to perform one-week out-of-sample prediction of the stock returns. Finally we develop a nonlinear model of active trading, in which traders rely only on their heterogeneous forecasts of future periods' maximum and minimum returns. The model motivates active trading under chaotic behavior. (C) 2015 Elsevier Inc. All rights reserved.