Over the past decade there has been a surge of interest in “tail events,” or rare, high-impact events. In this article, I start by summarizing some recent progress in our understanding of the psychology of tail events. I suggest that much of this progress has centered on the concept of “probability weighting” and, in particular, on applications of this concept in various fields of economics. I then describe some major open questions in this area.

We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, there is enough predictability in returns to make investors allocate substantially more to stocks, the longer their horizon. Moreover, the weak statistical significance of the evidence for predictability makes it important to take estimation risk into account; a long‐horizon investor who ignores it may overallocate to stocks by a sizeable amount.

We study equilibrium firm‐level stock returns in two economies: one in which investors are loss averse over the fluctuations of their stock portfolio, and another in which they are loss averse over the fluctuations of individual stocks that they own. Both approaches can shed light on empirical phenomena, but we find the second approach to be more successful: In that economy, the typical individual stock return has a high mean and excess volatility, and there is a large value premium in the cross section which can, to some extent, be captured by a commonly used multifactor model.

A number of authors have suggested that investors derive utility from realizing gains and losses on assets that they own. We present a model of this “realization utility,” analyze its predictions, and show that it can shed light on a number of puzzling facts. These include the disposition effect, the poor trading performance of individual investors, the higher volume of trade in rising markets, the effect of historical highs on the propensity to sell, the individual investor preference for volatile stocks, the low average return of volatile stocks, and the heavy trading associated with highly valued assets.

Recent empirical research in finance has uncovered two families of pervasive regularities: underreaction of stock prices to news such as earnings announcements, and overreaction of stock prices to a series of good or bad news. In this paper, we present a parsimonious model of investor sentiment, or of how investors form beliefs, which is consistent with the empirical findings. The model is based on psychological evidence and produces both underreaction and overreaction for a wide range of parameter values.

ABSTRACT We investigate whether prospect theory preferences can predict a disposition effect. We consider two implementations of prospect theory: in one case, preferences are defined over annual gains and losses; in the other, they are defined over realized gains and losses. Surprisingly, the annual gain/loss model often fails to predict a disposition effect. The realized gain/loss model, however, predicts a disposition effect more reliably. Utility from realized gains and losses may therefore be a useful way of thinking about certain aspects of individual investor trading.

We argue that “narrow framing, ” whereby an agent who is offered a new gamble evaluates that gamble in isolation, may be a more important feature of decisionmaking than previously realized. Our starting point is the evidence that people are often averse to a small, independent gamble, even when the gamble is actuarially favorable. We find that a surprisingly wide range of utility functions, including many nonexpected utility specifications, have trouble explaining this evidence, but that this difficulty can be overcome by allowing for narrow framing. Our analysis makes predictions as to what kinds of preferences can most easily address the stock market participation puzzle. (JEL D81, G11) Economists, and financial economists in particular, have long been interested in how people evaluate risk. In this paper, we try to shed new light on this topic. Specifically, we argue that a feature known as “narrow framing ” may play a more important role in decision-making under

Survey evidence suggests that many investors form beliefs about future stock market returns by extrapolating past returns. Such beliefs are hard to reconcile with existing models of the aggregate stock market. We study a consumption-based asset pricing model in which some investors form beliefs about future price changes in the stock market by extrapolating past price changes, while other investors hold fully rational beliefs. We find that the model captures many features of actual prices and returns; importantly, however, it is also consistent with the survey evidence on investor expectations.

We argue that “narrow framing,” whereby an agent who is offered a new gamble evaluates that gamble in isolation, may be a more important feature of decision-making than previously realized. Our starting point is the evidence that people are often averse to a small, independent gamble, even when the gamble is actuarially favorable. We find that a surprisingly wide range of utility functions, including many nonexpected utility specifications, have trouble explaining this evidence, but that this difficulty can be overcome by allowing for narrow framing. Our analysis makes predictions as to what kinds of preferences can most easily address the stock market participation puzzle.

We test the hypothesis that, when thinking about allocating money to a stock, investors mentally represent the stock by the distribution of its past returns and then evaluate this distribution in the way described by prospect theory. In a simple model of asset prices in which some investors think in this way, a stock whose past return distribution has a high (low) prospect theory value earns a low (high) subsequent return, on average. We find empirical support for this prediction in the cross-section of stock returns in the U.S. market, and also in a majority of forty-six other national stock markets. ( JEL D03) Received November 19, 2014; accepted May 20, 2016, by Editor Stefan Nagel.