Preference Models in Portfolio Construction and Evaluation

This chapter begins by setting up the typical portfolio problem, providing relevant definitions and notations. Next, the chapter introduces the main types of preference frameworks used in the portfolio literature and, to a lesser extent, in the practice of applied wealth management, often borrowing from microeconomic theory. Because various researchers have proposed that Taylor approximations applied to the functional representation of standard preferences may replace more complex mathematical constructs, the chapter includes an in-depth discussion of the advantages and disadvantages of using Taylor approximations, which emphasize the role played by statistical moments (mean, variance, skewness, and kurtosis) of either terminal wealth or portfolio returns. Some discussion is then devoted to new and exciting developments that have recently occurred at the intersection between decision theory and portfolio management in the form of frameworks that emphasize the concepts of robust decisions and ambiguity aversion. We provide an illustrative example that aims at investigating some aspects of the interaction between preferences and statistical models of investment opportunities is undertaken. In particular, optimal portfolio decisions are computed under regime-switching models that capture various features of time-varying investment opportunities.