Investment funds typically vary with regard to the emphasis that the managers place on acceptable risk and expected returns on investment. This chapter highlight a nonlinear analytic strategy, orbital decomposition (ORBDE) for identifying and extracting patterns of categorical events from time series data. The contributing constructs from symbolic dynamics, chaos, and entropy are described in conjunction with the central ORBDE algorithm. A study in task switching, which can alleviate or induce cognitive fatigue, is used an illustrative example of the basic mode of analysis. The aggregate more of ORBDE allows category codes from multiple variables to be assigned to each event in a time series. An illustrative example of the aggregate mode is presented for risk profile analysis in financial decisions. The results open up many possibilities for studying sequences of decisions made by fund managers and individual investors to determine profiles of risk acceptance, expected returns, and other features of portfolio management.