Prospect theory and behavioral finance in investment decision-making

Integrated Case Analysis

Executive Summary
This paper covers a wide range of topics relating to behavioral finance. First, there is an examination of prospect theory, and how it relates to utility theory, and where it might fit in terms of overall discussion on behavioral finance. The second section is about bias identification, using a case study example. The third section uses another case study, of a client, to talk about the different types of utility functions and how they affect investments on an individual level. The next section looks at the current state of research on behavioral finance. The fifth and final section of this report makes four key recommendations for this firm going forward to leverage what we know about behavioral finance.

White Paper on Prospect Theory
Prospect theory is a form of behavioral finance/economics that posits that people make decisions based on expected gains, rather than expected losses. At the heart of behavioral finance is the idea that economic decision-making is not necessarily based on purely rational decisions. One of the baseline assumptions of finance is that actors have pure economic rationality. This idea is a baseline assumption that is made in order to help isolate other variables when studying financial decision-making, but it was never really intended to hold true in real life. In real life, emotions and biases enter into economic decision-making all the time, and behavioral finance or economics is the field in which such decision-making is studied.
Economic actors are broken into three categories, based on their decision-making heuristics. Some are viewed as being purely rational, but most fall into either the risk averse or the risk taking categories, based on their observed behavior. When prospect theory was first described, it is based on the idea that people make decisions based on perceived gains instead of perceived losses (Kahenmann & Tversky 1979). Their starting point for exploration was the finding that there are some decisions in which strict rationality in decision-making has not been observed, but rather irrational decision-making and the authors sought to expain this.
One example was a choice of either 1000 shekels or 0 shekels, with 50% probably of each, versus 450 shekels guaranteed. In this scenario the first option has an expected value of 500 shekels. The problem, of course, is that this is an average of many different runs of the simulation and that no one individual is faced with an option to take 500 shekels. The choices are between the default situation you are already in, and a shot at 1000 shekels. Thus, while the choice in the question implies that one is choosing between an expected value of 500 and certain value of 450, in fact it is a scenario in which is gambling with house money. If the subjects answering the question were starting with 450, they probably would make a different choice. So the idea that this example represents irrational decision-making is a bit loaded; it does not represent an equivalent scenario to other options where there is genuine loss involved. In fact, while Kahnemann and Tversky claim that the decision is being made under risk, there is literally no risk to the people answering the question because none of their own money is on the table.
Utility theory contrasts with prospect theory in that utility theory focuses on decision-making via perfectly rational evaluation. This means that an example of 1000 with a 50% odds has an expected utility of 500, versus the 450 that is certain. In other words, the utility of the first option is still higher. Where expected utility theory is based on the idea that “under uncertainty, the weighted average of all possible levels of utility will best represent the utility at any given time” (Kahnemann & Tversky, 1979).
Thus, for there to be a violation of expected utility theory, one would have to regularly choose an option that had higher upside, even if expected utility is the same. So a variation that works is if the certain outcome is 500, and the other option is a 50% chance at 1000 or a 50% chance at zero. Both have the expected value of 500, but the one with the 1000 upside is considered by more subjects that the option that has the certain 500 outcome. Again, this has to do with the structure of the question – when you are gambling on upside with house money, that’s different psychologically than a double-or-nothing wager. It is just that much easier to pursue the upside dollar values.
Tversky and Kahnemann (1992) followed up their original paper on prospect theory with a new version in 1992. This update to the theory “employs cumulative rather than separable decision weights” (p. 297). At the core of this work is the idea that in people’s decision making “overweights small probabilities and underweights medium to high probabilities” (p.298). Nonlinear preferences in particular are said in prospect theory to be in play. While Tversky and Kahnemann cite Allais (1953) who found that the difference in perceptions between .99 and 1.00 were different than 0.10 and 0.11, that example again is rooted in false equivalence – 1.00 is certainty of outcome while none of the others are, so of course it will be viewed differently – it is different.
Risk seeking is another key concept in prospect theory, one that leads to the overweighting of small odds with big outcomes. This is the land where lotteries live. A rational actor can calculate the expected value of a lottery ticket in some instances, and it is always much lower than the actual cost of the ticket. Hence the view that lotteries are a tax on the mathematically challenged. Those who purchase lottery tickets are overweighting the jackpot – or they are including the utility of daydreaming in their calculation. In either case, lotteries are an example where there is relatively low risk, unlikely but massive rewards, and therefore they are popular with a wide swath of the population and completely violate the principles of utility and rational decision-making.
The update to the theory specifies that framing matters – as noted above when discussing the obvious difference between playing with house money and playing with one’s own. The dollar values might be the same for outcomes, but it is not perceived that way because the money was never actually earned. In a way, this applies to lottery tickets, too. People see the cost of the lottery as meaningless in the scope of their monthly budgets, but the possible outcomes, however unrealistic, are life-changing. So framing most certainly matters in prospect theory.
Another element of the new model of prospect theory is the idea of cumulative prospect theory, which holds that the carriers of value are gains, and that the “value of each outcome is multiplied by a decision weight, not an additive probability” (Tversky & Kahnemann, 1992, p. 299). These elements of prospect theory seek to explain both why people behave irrationally and why prospect theory differs from utility theory.
The efficient market hypothesis is rooted in utility theory, and therefore does not take into account the behavior of actors who are using anything other than expected utility in their decision-making heuristic. It has long been known that investors are not rational actors, but the different types of irrational behavior manifest to some extent in the challenges in describing irrational investor behavior.
Prospect theory can be used, for example, to explain things like the dot-com bubble in 1999, where prices became disconnected from actual valuations. This was the function of people thinking that any random dot-com could become the next Amazon, without taking into account the particular and unique set of fundamental business attributes that made Amazon what it was. Such irrational behavior can also been seen in daily movements, where perhaps one company announces lower than expected earnings, and this affects other companies’ stocks, on the idea that the two are related. They might be, but they might not be, the sluggishness for the one firm could be firm-specific.

Bias Identification
There are a number of biases that can influence economic decision making. One of these is risk aversion, or loss aversion. This is basically the opposite of prospect theory, wherein the investor makes decisions based on minimizing their risk of catastrophic loss. Coval and Shumway (2005) examined the influence of cognitive biases on the market, noting that risk-averse traders may unwind positions in the afternoon, to hedge against negative news after hours that would lead to significant losses. Other studies have noted a relationship between cognitive abilities and risk preference, the latter of which risk aversion is a subset of (Oechssler, Roider & Schmitz, 2009). Bernartzi and Thaler (2007) find that cognitive biases also influence retirement plan investing, especially the fear of downside risk, as this influences the risk preferences of the participants of defined contribution plans.
What these and other studies illustrate is that investors are not rational actors, and that there are different causes for economically irrational behavior in market participants. Risk aversion is often related to somebody who sees downside risk as catastrophic in nature, as is the case with retirement plan participants. A sophisticated investor may be perfectly rational under the assumption that any money lost can be recouped later – that investments will balance each other out. Someone saving for retirement might have a different view, especially the closer to retirement they get. Risk aversion is going to lead my colleague to make more conservative decisions in investing. She might prefer fixed income securities, stocks that pay high dividend rates, or simply stick to index funds, rather than attempt to build a portfolio with a higher risk profile. Such an approach may work just fine, but it is an example of how risk aversion can change one’s behavior versus what they should be doing with their investments.

Behavioral Finance and Investments
Siosan has demonstrated behaviors that are consistent with a convex utility function. She spends money on luxuries, so does not exhibit strong risk aversion behavior, but she also spends within the means of her salary and a part of her sizable bonus. She has committed to saving the other portion of her bonus, so therefore is not spending in a risky manner. She could certainly have a bit more fiscal discipline, but Siosan seems to fall within the convex utility curve.
The convex utility curve for Siosan highlights some deviations from the traditional utility function in finance theory. That traditional function, as elaborated in expected utility theory, holds that people are predominantly rational in the economic sense, and will make decisions based on expected utility. Hey and Orme (1994) were unable to conclude that there are significant differences among subjects in their study with respect to expected utility theory – that this theory fit just as well with responses as any other theory might have.
Rabin (1999) found that “a person has lower marginal utility for additional wealth when she is wealthy than when she is poor” (p.1), in the sense that any concave utility function over small stakes is irrational. Siosan does not demonstrate a concave utility function, and therefore her behavior is more consistent with what might be expected, even if it does step outside the realm of pure economic rationality. For her, there are some activities that provide a certain utility in her current day-to-day life that justify spending the money she spends, but she maintains some discipline and balance in her spending.
Siosan’s behavior reflects a slight bias towards risk-taking in the sense that she is not investing all of her money. Her present spending is probably more than a person would undertake given a purely rational decision-making process. Siosan, however, derives utility from this spending, in particular as this spending is on herself and within her means. This is the nature of the convex utility function – it incorporates some risk taking, or at least a lack of risk aversion. She is still making investments with some of her bonus money, but a more rational approach would not be to assume a bonus every year.
A more traditionally rational individual would behave differently. Such an individual would seek to maximize economic utility. At her age and stage of career, this would mean that she should be investing more, and spending less. She should be less indulgent in that sense. Furthermore, she should do something more like invest her entire bonus, and finance her lifestyle from her salary, or even save some of her salary as well. So her behavior is not quite as conservative as might be expected under traditional economic rationality.
Siosan’s portfolio allocation should be a little more realistic. I feel that she is not investing enough into the portfolio, and that might be what is leading her to take on some of the riskier behaviors. Buying out-of-money options on stocks is usually something that should be a part of an overall strategic plan for the portfolio, but Siosan appears to be basically gambling with these, treating her retirement savings a bit too much like a casino. This is the same thing as with the earthquake insurance. Her entire approach to investing at this points seem to be to gamble to make up for underinvesting.
Siosan is still at a good stage of her career, with twenty-odd working years in front of her, and those should be her prime earning years. As such, the gambles she has made to this point will not necessarily have a negative impact, depending on where her earning ceiling is. Not all lawyers are rich, after all. But Siosan has put herself at a disadvantage by spending too much of her income at the expense of saving, and taking advantage of the benefits of compounding. She should curtail her spending somewhat and invest more, in order to compound over the course of the next twenty-odd years until retirement. This might mean putting all of her bonus into savings, instead of spending half of it. It should also mean putting some of her salary into savings as well, if she can be that disciplined.
Siosan should also adopt more sound investing strategies. Options trading, especially the out of market stuff to try to score big, is more gambling than investing, and she probably is not earning good returns on this. She is demonstrating the risk-taking aspect of the convex utility function, the prospect theory part. The retirement account needs to be built, but on a sound foundation of equity investments, not options, and with more money flowing into it. Siosan cannot continue to count on either big options wins, or her future salary. At her present age, the future is now and she has to start investing like it – she should have done that several years ago.

Behavioral Corporate Finance

To: CFO
From: Me

Re: Recent literature on behavioral corporate finance
At your request, I am providing you with this brief overview of the recent literature on behavioral corporate finance. The field of behavioral corporate finance is a newly-emerging one, aimed at building frameworks by which the biases that influence decision-making find their way into corporate behavior. The rationale is much the same as for behavioral finance in general – markets assume rational behavior and yet irrational behavior can be observed.
One study on this topic, by Malmendier and Tate (2015) looks at overconfidence in senior executives – CEOs in particular – as a form of bias that can negatively affect corporate finance decisions. C-suite executives are often richly rewarded for work that leads to stock appreciation, but are seldom punished in any meaningful way when their company struggles. They might lose their jobs, but often have golden parachutes in their contracts, so the downside risk is lower than the upside risk. Plus, these are typically individuals with high levels of confidence. In their work, the authors are seeking to develop a framework to estimate overconfidence and apply that definition to studies that measure the influence of this bias on corporate decision-making. Garcia-Meca et al (2015) studied whether having institutional investors on boards affects the behavior of firms, finding mainly that there are different types of institutional investors and behaviors, and therefore they cannot be taken as a singular body, but broken up into categories for further study.
Hrnjic, Reeb and Yeung (2019) are among the authors that have studied behavioral corporate finance in the context of international markets. For companies that trade in the US, Sarbanes-Oxley creates specific risks for CFOs and CEOs, but the same governance structures do not exist in foreign countries. By applying behavioral corporate finance theories to foreign companies, it is possible not only to learn how cultural differences can influence behavior, but also to generate hypotheses as to the influence of different governance structures. Xu, Jin and Xin (2018) have also contributed to emerging market behavioral finance, by studying the differences between executive behavior in state-controlled firms in China, versus private ones.
The research is typical of a new field, with a lot of threads of research starting to emerge. These studies reflect that academics are investigating the topic from a number of angles, changing different variables in order to better understand behavioral corporate finance. There are no clear models for study, either, but there is some work being done to develop out such models. It is important to stay abreast of the latest research in this field, for when breakthoughs do occur.

Your Future and Behavioral Finance
There are several issues relating to behavioral finance that the firm can and should focus on going forward. The first is that the field of behavioral finance is still a work in progress. Aspects of it have been around for a while, but we should be aware that there is more that we do not know than what we do know. This has certain implications for our company. First, it means that we must continue to pay attention to the research on this subject. A lot of our competitors might wait until whatever pop book comes out to explain these concepts in lay-speak. That means we can get first mover advantage in applying a lot of these concepts to our business, if we follow the journals, where the research is first published. We’ll need to be able to parse the complexity of some of the work – the high end mathematics, and the detailed application of behavioral studies. But at the end of the day, insights are emerging regularly, as researchers test different variables and hypotheses and models. From a tactical perspective, I recommend that we task somebody with monitoring developments in this field, and reporting those back to the executive team to provide regular insight that might allow us to gain advantage over competitors who are unwilling or unable to do this sort of work.
The second issue going forward is that, as a company, we should be aware that biases will almost always exist, and therefore there are opportunities to identify and exploit these biases. The research I have done indicates that even sophisticated investors, and those with ample experience, are still subject to biases. They might be subject to biases less often, and those biases might have less impact on their decision-making, but the biases are still there and influential. The same goes for studies showing biases are stronger with people who have lower cognitive ability. But that does not mean that the highly intelligent are immune from biases. Companies like ours can benefit from seeking out and exploiting biased decision-making. If we can identify patterns in biased decision making, such as investors falling in love with a certain stock for reasons that might not be rational, then we can make investment decisions that take advantage of that. As we learn more about biases in emerging markets, or how biases are built into automated trading algorithms, we have the opportunity to stay ahead of the markets by identifying these trends ahead of our competition.
The third issue for the company to be aware of going forward is that investors are likely to be more risk averse going forward. A lot of money is held by the baby boomer generation, and just as many of them have been entering their retirement, or just about to do so, the markets have seen a sharp decline. A lot of people who might have previously been examples of prospect theory – holding onto optimism that has them thinking about the big gains that they can win with certain stocks, or their real estate holdings, have been burned. For older investors, this is going to have a long-run cooling effect. Boomers who still held a lot of their retirement funds in equity might have sold, but they also are unlikely to get back into the markets. They might have been in a position where they actually should have sold earlier, but did not want to sell in a rising market, only to be burned. The rational investor will see that the decline in the market is an example of probably an overly emotional reaction to the recession and start to buy stocks at a discount. But a lot of people are unlikely to do that, especially those who do not have a lot of money to invest. That is going to impact on how much money is in mutual funds, for example. In the long run, this might make people want to plow money into the markets during boom periods, to try to make as much possible in the hopes of timing their exit, but it might just make a lot of people, especially anybody over 40, more risk averse, having seen what can happen to people in relatively precious positions when markets go south.
The fourth consideration for the future is that there is a role in this company for understanding how human behavior impacts on financial decision making. Most of us, when we are taught finance, learn about the efficient market hypothesis, and rational investors. A lot of the theories that we are taught are rooted in the assumption of rational investors. In a lot of instances, this assumption is merely a pragmatic one on the part of a researcher, allowing them to isolate some other variable that they wish to study. But we have ample evidence that investors are not rational. They are subject to biases, and those biases affect their decision-making. What this means for the company is that if we are making most of investment decisions based on the assumption of rational markets, we are missing opportunities. If we truly believe in the efficient market hypothesis, we would only invest in the index. We might believe in some weaker form of EMH, and think we can beat the markets by knowing more than other investors. The reality is that if markets are efficient, it is definitely in a weak form, as there is considerable evidence showing multiple types of biases in financial decision making.
For the company, this means that we should have a specialist who can untangle the web of behavioral finance. Given the relatively nascent stage of the field, this role should be something more as an advisor – not someone to make specific investment decisions but someone who can contribute to investment decision making by lending advice based on this alternative perspective. There are clear opportunities to exploit biased thinking in the stock markets. There are opportunities to help our clients learn more about their own biases, and guide them towards better decisions. If we have a specialist who can both advise our senior people, and contribute to the production of white papers or other content that helps our clients’ portfolios perform better, we can advance our position in the market. I therefore recommend that we create a role if not a unit dedicated to behavioral finance, to continue the firm’s ability to learn about this field, and apply its insights into our everyday decision-making. By fostering this expertise, we can put ourselves in a position of having competitive advantage, and use that to win share in a market that is becoming increasingly competitive, with firms struggling to find any form of differentiation. Behavioral finance expertise is an edge we can scarcely afford to overlook.





References

Bernartzi, S. & Thaler, R. (2007) Heuristics and biases in retirement savings behavior. Journal of Economic Perspectives. Vol. 21 (3) 81-104.

Coval, J. & Shumway, T. (2005) Do behavioral biases affect prices? Journal of Finance. Vol. 60 (1) 1-34.

Garcia-Meca, E., Lopez-Iturriaga, F., Tejerina-Gaite, F. (2015) Institutional investors on boards: Does their behavior influence corporate finance? Journal of Business Ethics. Vol. 146 (2) 365-382.

Hey, J. & Orme, C. (1994) Investigating generalizations of expected utility theory using experimental data. Econometrica. Vol. 62 (6) 1291-326.

Hrnjic, E., Reeb, D. & Yeung, B. (2019) Financial decisions, behavioral biases, and governance in emerging markets. The Oxford Handbook of Management in Emerging Markets. Chapter 7.

Kahnemann, D. & Tversky, A. (1979) Prospect theory: An analysis of decision making under risk. Econometrica. Vol. 47 (2) 263-292.

Malmendier, U. & Tate, G. (2015) Behavioral CEOs: The role of managerial overconfidence. Journal of Economic Perspectives. Vol. 29 (4) 37-60.

Oechssler, J., Roider, A. & Schmitz, P. (2009) Cognitive abilities and behavioral biases. Retrieved April 22, 2019 from https://www.ssoar.info/ssoar/bitstream/handle/document/29366/ssoar-jebo-2009-1-oechssler_et_al-cognitive_abilities_and_behavioral_biases.pdf?sequence=1&isAllowed=y&lnkname=ssoar-jebo-2009-1-oechssler_et_al-cognitive_abilities_and_behavioral_biases.pdf

Rabin, M. (1999) Risk aversion and expected utility theory: A calibration theorem. University of California – Berkeley. Retrieved April 22, 2019 from https://cloudfront.escholarship.org/dist/prd/content/qt731230f8/qt731230f8.pdf

Tversky, A. & Kahnemann, D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty. Vol. 5 (1992) 297-323.

Xu, L., Jin, X. & Xin, Y. (2018) Equity-based compensation in China. Routledge Companion to Accounting in China. Chapter 9.