Prospect theory, first described in a 1979 paper by Daniel Kahneman and Amos Tversky, is widely viewed as the best available description of how people evaluate risk in experimental settings. While the theory contains many remarkable insights, it has proven challenging to apply these insights in economic settings, and it is only recently that there has been real progress in doing so. In this paper, after first reviewing prospect theory and the difficulties inherent in applying it, I discuss some of this recent work. It is too early to declare this research effort an unqualified success. But the rapid progress of the last decade makes me optimistic that at least some of the insights of prospect theory will eventually find a permanent and significant place in mainstream economic analysis.

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Thirty Years of Prospect Theory in Economics: A Review and Assessment

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We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases when the reference point is the risk-free return and when it is not (while the utility function is piece-wise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1676549_code1346556.pdf?abstractid=1479580&mirid=5&type=2

Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

A large body of evidence has documented that risk preferences depend nonlinearly on outcome probabilities. We discuss the foundations and economic consequences of probability-dependent risk preferences and offer a practitioner's guide to understanding and modeling probability dependence. We argue that probability dependence provides a unifying framework for explaining many real-world phenomena, such as the equity premium puzzle, the long-shot bias in betting markets, and households' underdiversification and their willingness to buy small-scale insurance at exorbitant prices. Recent findings indicate that probability dependence is not just a feature of laboratory data, but is indeed manifest in financial, insurance, and betting markets. The neglect of probability dependence may prevent researchers from understanding and predicting important phenomena.

https://www.annualreviews.org/doi/suppl/10.1146/annurev-economics-080511-110950/suppl_file/EC-04-FehrDuda-SupApp.pdf

Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences

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.

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The Psychology of Tail Events: Progress and Challenges

This paper shows that the framework proposed by Barberis and Huang (2009) to incorporate narrow framing and loss aversion into dynamic models of portfolio choice and asset pricing can be extended to also account for probability weighting and for a value function that is convex on losses and concave on gains. We show that the addition of probability weighting and a convex-concave value function reinforces previous applications of narrow framing and cumulative prospect theory to understanding the stock market non-participation puzzle and the equity premium puzzle. Moreover, we show that a convex-concave value function generates new wealth eff ects that are consistent with empirical observations on stock market participation.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=1413087

Dynamic Portfolio Choice and Asset Pricing with Narrow Framing and Probability Weighting

Dynamic portfolio choice and asset pricing with narrow framing and probability weighting

This paper extends the model with narrow framing suggested by Barberis and Huang (2009) to also account for probability weighting and a convex-concave value function in the specification of cumulative prospect theory preferences on narrowly framed assets We show that probability weighting is needed in order that investors reduce their holding of narrowly framed risky assets in the presence of negative skewness and high Sharpe ratios, which are typical characteristics of stock index returns The model with framing and probability weighting can thus explain the stock participation puzzle under realistic assumptions on stock market returns We also show that a convex-concave value function generates wealth effects that are consistent with empirical observations on stock market participation Finally, we address the asset pricing implications of probability weighting in the model with narrow framing and show that in the case of negative skewness the equity premium of narrowly framed assets is much higher than when probability weighting is not taken into account

Shane Legg

Papers

Dynamic Portfolio Choice and Asset Pricing with Narrow Framing and Probability Weighting

Dynamic portfolio choice and asset pricing with narrow framing and probability weighting

Portfolio Selection with Narrow Framing: Probability Weighting Matters