After years of relative neglect in academic circles, portfolio choice problems are again at the forefront of financial research. The economic theory underlying an investor’s optimal portfolio choice, pioneered by Markowitz (1952), Merton (1969,1971), Samuelson (1969), and Fama (1970), is by now well understood. The renewed interest in portfolio choice problems follows the relatively recent empirical evidence of time-varying return distributions (e.g., predictability and conditional heteroskedasticity) and is fueled by realistic issues including model and parameter uncertainty, learning, background risks, and frictions. The general focus of the current academic research is to identify key aspects of real-world portfolio choice problems and to understand qualitatively as well as quantitatively their role in the optimal investment decisions of individuals and institutions.
Whether for academic researchers studying the portfolio choice implications of return predictability, for example, or for practitioners whose livelihood depends on the outcome of their investment decisions, a critical step in solving realistic portfolio choice problems is to relate the theoretical formulation of the problem and its solution to the data. There are a number of ways to accomplish this task, ranging from calibration with only vague regard for the data to decision theoretic approaches which explicitly incorporate the specification of the return model and the associated statistical inferences in the investor’s decision process. Surprisingly, given the practical importance of portfolio choice problems, no single econometric approach has emerged yet as clear favorite. Since each approach has its advantages and disadvantages, an approach favored in one context is often less attractive in another.
This chapter is devoted to the econometric treatment of portfolio choice problems. The goal is to describe, discuss, and illustrate through examples the different econometric approaches proposed in the literature for relating the theoretical formulation and solution of a portfolio choice problem to the data. The chapter is intended for academic researchers who seek an introduction to the empirical implementation of portfolio choice problems as well as for practitioners as a review of the academic literature on the topic.
The chapter is divided into three parts. Section 2 reviews the theory of portfolio choice in discrete and continuous time. It also discusses a number of modeling issues and extensions that arise in formulating the problem. Section 3 presents the two traditional econometric approaches to portfolio choice problems: plug-in estimation and Bayesian decision theory. In Section 4, I then describe a more recently developed econometric approach for drawing inferences about optimal portfolio weights without modeling return distributions.
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Portfolio Choice Problems
