Foundations for Learning How to Invest when Returns are Uncertain

Most asset returns are uncertain, not merely risky: investors do not know the probabilities of different possible future returns. A large body of evidence suggests that investors are averse to uncertainty, as well as to risk. This paper builds up an axiomatic foundation for the dynamic portfolio and consumption choices of an uncertainty-averse (as well as risk-averse) investor who tries to learn from historical data. The theory developed, model-based multiplepriors, generalizes existing theories of dynamic choice under uncertainty aversion by relaxing the assumption of consequentialism. Examples are given to show that consequentialism, the property that counterfactuals are ignored, can be problematic when combined with uncertainty aversion. An analog of de Finetti’s statistical representation theorem is proven under model-based multiple-priors, but consequentialism combines with multiple priors to rule out prior-by-prior exchangeability. A simple dynamic portfolio choice problem illustrates the contrast between a model-based multiple-priors investor and a consequentialist multiple-priors investor. ∗This paper is a revision of the first chapter of my doctoral thesis; I am indebted to Gary Chamberlain and John Campbell for guidance and encouragement throughout the writing of my thesis. I am also grateful for the insights of Brian Hall, Lars Hansen, Parag Pathak, Jacob Sagi, Tom Sargent, Jeremy Stein, and James Stock, and for the helpful comments of seminar participants at the University of California, Berkeley, the University of Chicago Graduate School of Business, the Fuqua School of Business at Duke University, Harvard Business School, Harvard University, the Kellogg School of Management at Northwestern University, New York University Stern School of Business, Princeton University, and the Wharton School of the University of Pennsylvania. I benefitted from detailed suggestions made by Larry Epstein and Martin Schneider. I am solely responsible for the remaining shortcomings of this paper.