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Portfolio theory (PT) has been widely used in finance as a tool to aid capital allocation and investment analysis, and to measure economic welfare. Recently, PT has been applied as a spectrum management tool for cognitive radio for QoS management in CR and the pricing of CR access rights. PT is characterized by the analysis of risk and return, concepts that feature widely in wireless communications due to the random nature of traffic and radio channels. Compared with traditional CR resource management techniques (e.g., game theory), where the aim has been the maximization of QoS or another utility measure, the key advantage of PTbased resource management stems from the focus on both the mean utility achieved by a communication system, as well as utility variance. Ignoring QoS (e.g., throughput) variance in communication system design may lead to systems that are unusable by some applications, even though mean QoS remains high. In applications such as pricing-based spectrum management, PT analysis incorporates the variance of investment returns, a key measure of economic welfare, into pricing and trading strategies. In this article we examine the key concepts behind PT, risk and return, as well as their importance in CR and wireless communications. As examples, we analyze the application of PT in solving CR spectrum management problems through QoS management and pricing of spectrum access rights.