by Dr Mehrshad Motahari, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance
The Nobel Prize–winning Cumulative Prospect Theory of Tversky and Kahneman (1992) has revolutionised our understanding of how humans make economic decisions in the face of uncertainty. This theory takes all possible future outcomes and their probabilities into account and returns a value that shows how attractive a particular economic choice is for an individual. This is very similar to the function of expected utility but the two are fundamentally different. One particular area in which Cumulative Prospect Theory differs from the expected utility frameworks is the assignment of probabilities to uncertain outcomes. Unlike the expected utility framework which uses objective probabilities, Cumulative Prospect Theory transforms probabilities by assigning a weight to them. The outcome of this transformation is overweighting of low probabilities and underweighting of high probabilities.
Probability weighting under Cumulative Prospect Theory may seem bizarre at first, but it can explain a number of longstanding puzzles in finance and economics. One particularly interesting one is gambling. Almost everyone knows in advance that the likely outcome of gambling is loss, so why do people gamble then? Cumulative Prospect Theory says that, even if the likely outcome is loss, probability weighting may increase the very small probability of winning sufficiently so that the individual is convinced that it is worthwhile to enter the gamble. In other words, the small probability of winning a large prize is so lucrative for the gambler that he is willing to bear the risk of losing most of the time.
Gambling behaviour is not limited to betting in casinos and has widespread implications in financial markets. An asset with features akin to those of a gamble can be equally lucrative and can trigger the same kind of gambling behaviour by investors. Gamble- or lottery-like features in financial assets are often translated to positively skewed return distributions, suggesting that the asset has the potential to generate very high returns, albeit with small probabilities. Investors who are attracted to such features are therefore formally known as those who have a preference for skewness and are shown to be the same type of individuals who exhibit a strong propensity to gamble in nonfinancial settings (Kumar, 2009).
Gambling or preference for skewness is so robust and widespread that it can shape aggregate market outcomes and help our understanding of asset prices and their movements. Barberis and Huang (2008) demonstrate that investor preference for holding positively skewed assets under Cumulative Prospect Theory results in overvaluation of securities that are likely to generate positively skewed payoffs. This can explain many asset pricing puzzles we have struggled with over the years. One major example is the financial distress anomaly. In contrast to theoretical expectations, stocks with very high distress risk levels are highly overvalued compared to those with low distress risk levels. Conrad et al. (2014) provide an explanation for this by showing that distressed stocks are highly positively skewed. Essentially, they can be thought of as a lottery ticket, considering that they have a very high probability of failure (i.e. bankruptcy) and a small chance of surviving the troubled times and surprising the market.
In the article “Skewness Preference and Market Anomalies”, CERF/CCFin Research Associate Mehrshad Motahari, and co-authors Alok Kumar (University of Miami) and Richard Taffler (University of Warwick), build on previous studies and show that preference for skewness has wider implications in generating mispricing in the market. This study looks at a range of market anomalies, defined as variables that can predict which stocks will outperform or underperform in the future. A large part of this predictability has been shown to be due to mispricing (Stambaugh et al., 2012) and the subset of stocks responsible for generating anomalies are often highly skewed in the cross section. The authors demonstrate that the common mispricing-related patterns shared among market anomalies are largely driven by investors exhibiting a preference for skewness.
The authors look at a range of sources to provide proof for the link between market anomalies and preference for skewness. First, the portfolio holdings data of a sample of retail investors obtained from a large US discount brokerage house indicate that investors with a history of investing in positively skewed stocks are more likely to invest in stocks that market anomalies predict will underperform. Moreover, the mispriced stocks that generate market anomalies are likely to be headquartered in regions with high ratios of Catholics over Protestants. According to Kumar et al. (2011), counties having relatively more Catholic than Protestant residents exhibit stronger gambling propensities, which is also reflected in the prices of local stocks.
The main takeaway is that gambling behaviour plays too strong a role in financial markets to be neglected. Not only do we need more research in order to identify all areas where this behaviour is consequential but we also have to find a way to integrate it into our asset pricing frameworks. Barberis (2013) provides a broader discussion of the research in this area and the challenges ahead and is recommended for further reading.
References
Barberis, N. (2013) “The psychology of tail events: progress and challenges.” American Economic Review, 103: 611-616
Barberis, N. and Huang, M. (2008) “Stocks as lotteries: the implications of probability weighting for security prices.” American Economic Review, 98: 2066-2100
Conrad, J., Kapadia, N. and Xing, Y. (2014) “Death and jackpot: why do individual investors hold overpriced stocks?” Journal of Financial Economics, 113: 455-475
Kumar, A. (2009) “Who gambles in the stock market?” Journal of Finance, 64: 1889-1933
Kumar, A., Page, J.K. and Spalt, O.G. (2011) “Religious beliefs, gambling attitudes, and financial market outcomes.” Journal of Financial Economics, 102: 671-708
Stambaugh, R.F., Yu, J. and Yuan, Y. (2012) “The short of it: investor sentiment and anomalies.” Journal of Financial Economics, 104: 288-302
Tversky, A. and Kahneman, D. (1992) “Advances in prospect theory: cumulative representation of uncertainty.” Journal of Risk and Uncertainty, 5: 297-323