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Review of "Religious Beliefs, Gambling Attitudes and Financial Market Outcomes"

Seminararbeit 2014 20 Seiten

BWL - Sonstiges



1 Introduction

2 First insights into gambling in financial markets
2.1 Cumulative prospect theory
2.2 Asset pricing

3 Religious beliefs and gambling propensities

4 Results
4.1 Empirical Analysis
4.2 Investors’ portfolio decisions
4.3 Employee stock option plans
4.4 IPO overpricing and lottery stocks

5 Conclusion

6 Discussion

7 References

1 Introduction

As religious faith plays a crucial role in people’s lives and largely influences their behavior as well as their decision making, the study of religiosity has a long tradition in many social science disciplines. Nevertheless, this relationship became only a topic of interest in modern economic studies since the last quarter of the twentieth century, when Ehrenberg and Azzi (1975) developed a utility-maximizing model taking into account both lifetime and afterlife utility (see, for example, Iannaccone, 1998; Jackson and Fleischer, 2007).

In 2012, around 91% of the US American population professed to ”believe in God or a universal spirit”1 (Lugo, 2012), suggesting that if religion does shape economic behavior, it should also affect aggregate market outcome. Hence, studies investigate both microand macroeconomic effects of religiosity2, while some recent papers specifically address the relationship between religion and financial decisions: risk aversion and speculative behavior in particular are believed to depend on religious adherence. Not only have studies linked religiosity with a higher level of pure risk aversion in corporate decision making (Hilary and Hui, 2009), but also suggests current research that religious beliefs spill over in investment decisions due to different notions of gambling. For instance, Kumar (2009) found Catholics to be more willing to take on speculative risk by investing more in risky stocks than Protestants do.

This paper aims to critically review Kumar, Page, and Spalt (2011) and structures as follows: firstly the theoretical framework of gambling in economics will be presented with a focus on cumulative prospect theory and its implications for asset pricing. Then follows a comprehensive overview of the theoretical background and empirical findings of the paper with focus on the influence of religion on investors’ portfolio decisions and on overpricing of initial public offerings. The subsequent section discusses the hypotheses of Kumar, Page, and Spalt (2011). Eventually, the last section concludes with a summary of the main findings in a broader context and with an outlook on future research.

2 First insights into gambling in financial markets

The question Kumar, Page, and Spalt (2011) investigate is whether heterogeneous gambling preferences affect outcomes in financial markets. A propensity to gambling imply that people choose uncertainty over certainty. However, under expected utility theory, agents are assumed to be risk-averse and thus always prefer a sure payoff over a gamble with the same expected value3. In other words, agents expect a compensating risk premium to accept uncertainty and take on additional risk. Although this model accounts for the purchase of insurances, its explanatory power is limited due to the strict assumption of diminishing marginal utility. For instance, the purchase of lottery tickets paying a small amount for the negligible possibility of hitting the jackpot - clearly belies this assumption. Utility functions elucidating the inclination towards gambling were first introduced by Markowitz (1952) and Friedman and Savage (1948), and later refined by Kahneman and Tversky (1979) and Tversky and Kahneman (1992).

The first subsection serves to outline the main features of these models, whereas the second presents a formalized application of Tversky and Kahneman’s (1992) model to asset pricing.

2.1 Cumulative prospect theory

It were Friedman and Savage (1948) and Markowitz (1952) who laid the theoretical framework to analyze preferences for gambling, i.e. choosing a lottery over a certain payoff due to some kind of convex utility function.

By implying a utility function with income-dependent curvature (see Figure 1) Friedman and Savage’s (1948) model was able to account for the purchase of both insurances and lottery tickets for the first time. The notion that marginal utility depends on different levels of wealth was based on empirical observations, for example that comparatively poor people are rather willing to invest in speculative stocks, whereas a large proportion of people with low income prefer to buy low-risk bonds and somewhat richer people receive a great share of their property income from dividends. Its interpretation as a representation of socioeconomic levels therefore predicts that an individual with an intermediate income - between A and B - will always participate in the symmetric gamble as depicted in Figure 1 due to increasing marginal utility. This is because the gamble, for example in the form of speculative stocks, offers the chance to climb the social ladder. A person with a slightly higher or lower income is willing to buy both lottery tickets and insurances, while a person with a significant higher or lower income experiences diminishing marginal utility and purchases the insurance.

Later Markowitz (1952) claimed those implications unlikely to be reliable since both poor and rich gamble, whereas middle class people would not participate in a large symmetric bet as illustrated in Figure 1. To support his hypothesis, he conducted a survey investigating in which kind of gamble people were willing to engage. In accordance with his findings, he introduced a utility function with a specific reference point, i.e. present wealth, and with a slope depending on whether the payoffs are positive or negative (see Figure 2). These adaptations reflect risk avoidance when faced with the chance of a large gain (small loss) and risk tolerance when faced with the chance of a large loss (small gain) relative to present wealth. In effect, he dropped the assumption of absolute measurement of wealth while retaining the traditional assumption of objectively weighted utilities.

Taking into account these observations, Kahneman and Tversky (1979) found that people’s choices involving uncertainty could still not be predicted reliably. In their experiments, they presented to agents various binary decision problems in order to formalize their model accordingly. For instance, people were asked to choose between

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Figure 1: The Friedman-Savage (1948) utility function

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Figure 2: Utility function according to Markowitz (1952)

They observed that first, people tend to overvalue certainty (the certainty effect)4. On the other hand, when the chance of winning was negligible, people chose the lottery offering a higher gain because of an overvaluation of probabilities close to zero (the possibility effect). Thus risk averse behavior with gains as well as risk seeking behavior with losses should be more pronounced than Markowitz suggested, resulting in a steeper curve in the proximity of the reference point (see Figure 3). Under cumulative prospect theory (CPT) (Tversky and Kahneman, 1992), the utility of a prospect builds on a probability weighting function and reflects both the overweighing of small and the underweighing of moderate possibilities (see Figure 3). The model captures preferences for lotteries, for example for stock return distributions with a positive skew. Thus, an agent decides as if the density for large outcomes was higher and is willing to participate in the gamble.

Formally, the assigned value of a prospect with payoffs x−m, . . . , x0, x1, . . . , xn where xi > xj for i > j and x0 = 0, and corresponding probabilities p−m,...,p0,p1,...,pn is

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Stated Probability: p

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(a) Utility function

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(b) Probability weighting function

Figure 3: Kahneman and Tversky (1979) utility and probability weighting function respectively5. In accordance with their survey results, Tversky and Kahneman (1992) offered explicit functions which will not be discussed for the sake of brevity.

2.2 Asset pricing

Building on Tversky and Kahneman’s (1992) model, Barberis and Huang (2008) developed an asset pricing model where financial market participants behave according to CPT and share gambling preferences. Specifically, they focused on the implications of the weighting function, which states inter alia that agents overvalue very small probabilities and consequently overweigh them in the decision making process.

When CPT holds and returns of all available assets are normally distributed, the capital asset pricing model’s (CAPM) predictions do not alter, i.e. all investors invest in the same portfolio on the efficiency frontier and the expected return of a risky asset is composed of the risk-free interest rate and the risky asset’s beta times the market risk premium. This is because the decision parameters only depend on expected return and volatility and because CPT complies with first order stochastic dominance; in other words, for any two assets with identical volatility, all investors prefer the one with the higher expected yield.


1 This number has only slightly decreased since the first poll in 1944 with 96% believing in God.

2 At the macroeconomic level cross-country studies showed inter alia that religious belief fosters growth whereas church attendance dampens it (Barro and McCleary, 2003), influences institutional structure as well as economic attitudes (Guiso, Sapienza, and Zingales, 2003, 2006) and social ethics Arrunada (2010). Furthermore, microeconomics studies do indeed indicate that religion exerts influence on behavior in many ways (for a detailed review, see Iannaccone, 1998)

3 Agents maximize E (U ) = piu (xi) with i = 1 . . . n, where agents receive the outcome xi with the i=1 objective probability pi and u is a concave function.

4 Referring to the example a significant proportion of subjects preferred B over A. This can be rewritten as u (2, 400) > 0.33u (2, 500) + 0.66u (2, 400) or, more simple, 0.34u (2, 400) > 0.33u (2, 500). However, when asked to decide between a 33% chance of winning 2,500 and a 34% chance of winning 2,400, people chose the former, contradicting expected utility theory.

5 This presentation follows Barberis and Huang (2008).


ISBN (eBook)
ISBN (Buch)
764 KB
Institution / Hochschule
Universität Heidelberg Alfred-Weber-Institut für Wirtschaftswissenschaften
Gambling Stock market Religion Behavioral Economics Kahneman Kumar




Titel: Review of "Religious Beliefs, Gambling Attitudes and Financial Market Outcomes"