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A k a d e m i k A r a ç t i r m a l a r D e r g i s i 2 0 1 0 , S a y i 4 6 , S a y f a l a r 1 - 9

INDIVIDUALS' CHOICES: TRADITIONAL AND BEHAVIORAL FINANCE

I PERSPECTIVES Kadir Can YALÇIN'

INTRODUCTION

Traditional finance ignores the psychological and behavioral dimensions of individuals' choices. Because of this ignorance, behavioral finance has emerged in order to obtain a better explanation about how psychological factors affect individuals' behaviors and decisions.

Individuals' choices from the behavioral finance perspective differ from the traditional finance perspective. According to traditional finance, human behavior is rational during the decision making process described by the expected utility theory. That is, individuals always try to maximize their utilities by setting limits to their feelings and act only by using their minds as super- calculator, emotionless robots.

On the other hand, according to behavioral finance, this kind of rationality is hypothetical and, in reality, individuals suffer some cognitive limitations when they have to make decisions incorporating the prospect theory. Prospect theory is the descriptive explanation of how people behave and it has served as an anchor for behavioral finance supporters.

The aim of this paper is to examine the question "are individuals rational or not" during the decision making process by comparing the traditional and behavioral finance point of views and will begin with the expected utility theory. Next, the prospect theory and the mental accounting will be presented.

' EXPECTED UTILITY THEORY I

Uncertainty is present in almost all decisions concerning both social and business hfe, but financial decisions constitute a special case. Yet, one is expected to make healthy decisions when faced with uncertainty, because our decisions will designate how much pleasure and enjoyment will be attained in life. In economic terms, pleasure and enjoyment are defined as a utiliry. In other

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words, utility consists of pleasure and prevented pain'. However, it is quite difficult to measure utility in economical terms.

Daniel Bernoulli^ developed for the first time, an "Expected Utility Theory" in 1738; subsequently, it was formulated by John von Neumann and Oscar Morgenstern in 1944\ This model is widely accepted today as a formulated way of explaining rational human behavior under uncertainty by using a measurable utility function. The basic logic behind the expected utility theory is rationality. Kahneman and Smith" described the term rationality as follows "rationality means that deci.non-maker use available information in a logical and systematic way, so as to make optimal choices given the alternatives at hand and the objective to be reached"

The theory always expects rational behaviors from human beings no matter what the circumstances are. That is, economic actors are rational creatures who always try to maximize their expected utilities in three stages. In the first stage, they calculate the po.ssibility of the occurrence of the alternatives which they face. Then, they multiply these possibilities with the offered gains of the alternatives. In the last stage, they choose the maximum amount because they always try to maximize the gains and minimize the los.ses. Simply, they decide what to do by maximizing the probability-weighted average.

To illustrate this notion, consider the following example. Suppose there are two options that we have to choose from. In option A, with 30% probability we earn 500 $ and in option ß, with 35% probability we earn 450$. Under the rationality assumption of expected utility theory we have to choose option B. Because when we evaluate option A, we find a final value of 150 (0.30*500) where as option ß's final value is 157.5 (0.35*450) and 157.5 is bigger than 150. The same process applies to losses. For example when we face a choice between option C which offered 10% probability of losing 100$ and option D which offered 30% probability of losing 40$, we certainly have to choose option C. Because if we choose option C, the fmal amount that we lose will be 10$ whereas it will be 12$ in option D. If we are rational creatures as expected utility theory says, it is better to lo.se 10$ rather than 12$.

Thus, expected utility is defined as the final value which is found by the multiplication of the each possible utility resulting from a decision and events likely to happen. Here, it is assumed that there is a utility function («) which is the result of every individual's obtaining (x) from their decisions such that if one available action (a) results in probability (p) over the outcome {x), another available action (b) results in probability {qj over the same outcomes; simply iip*U(x) > q*U(x). then the individual must choose action {a) because its utility is greater than that of action (bf.

On the other hand, there are some attempts to present alternative views against expected utility and its "rationality". Nobel laureate Herbert Simon'.s* economic man (homo economicus), which he also referred to as an

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administrative man. needs to be revised, because economic man refers to an individual who always tries to maximize his utility by .setting limits to his feelings and acts only by using his logic and rationahty. This definition of economic man is hypothetic; and in reality, when he makes decisions, an individual suffers .some cognitive limitations because of limited computational skills and memory capacities. Moreover, individuals do not always try to reach the best alternative (maximize the utility), and often find the "good enough" satisfying. Simon labeled the departures from rational behavior as intendedly rational and approximate rationality^ These notions are known as bounded rationality.

Maurice Allai.s* and Daniel Ellsberg^ are two who presented counter evidences against expected utility. Consider this paradox. Why do individuals prefer a certain 3.000$ (100% probability) gain instead of 4.000$ gain with 80% probability? It is clear that according to the expected utility theory the second option's utility (4000*0.80=3200) is greater than the first one (3000*1=3000); however, 80% of the participants chose the first one; on the other hand, they behave as rational creatures consistent with the expected utility by choosing 4.000$ with 20% probability (65% of them chose this option) than 3.000$ with 25% probability (4.000*0.20=800 > 750= 3.000*0.25). Kahneman and Tversky'" called this tendency to choose certain gains as certainty effect.

Allais, Simon, EUsberg and other academicians' researches gave rise to views agaiast the notion of "unlimited rationality" and "maximization of utilities under every circumstance". However, despite the great criticism against expected utility theory, they did not offer a new substitute model that can describe human behavior satisfactorily until Kahneman and Tversky".

PROSPECT THEORY AND MENTAL ACCOUNTING

Standard (traditional) finance theory is based on expected utility theory and, while it was widely accepted among academicians, in 1979 famous American psychologi.sts Daniel Kahneman and Amos Tversky pre.sented a critique of expected utility theory and developed an alternative model in order to explain human behavior under uncertainty. It has since seemed as an anchor for behavioral finance supporters. Kahneman and Tversky'' demonstrated some evidences that individuals do not always choose the alternative that will maximize their utilities. In fact, the pre.sentation of the decision problem could lead to a deviation from rational behavior. Consider these typical examples".

In addition to whatever you own, you have been given 1,000$. You are now asked to choose between;

A: 50% chance to win 1000$

B: 100% chance to win 500$

As a matter of fact both option's overall utility are equal to each other (50%* 1000 = 100%*500). However only 16% of the participants cho.se option A and 84% of them cho.se option B. The respondents chose the sure gain and

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Individuals' Choices: Traditional and Behavioral Finance Perspectives

avoided the risk of winning nothing in spite of the equal possibility of winning the maximum amount. On the other hand, risk-averse behavior tends to continue even if the questioti format is changed. To test this, a further question is asked.

In addition to whatever you own, you have been given 2,000$. Now choose between:

C: 50% chance to lose 1000$

D: 100% chance to lose 500$

If the same risk-averse behavior continues, the participants ought to choose option D. However, only 31% of them chose option D, whereas 69% chose option C. By evaluating the responses to these questions, it is concluded that individuals are risk-averse with respect to gains which is consistent with expected utility theory; however, they are risk-seeker with respect to los.ses which is against the invariance feature of the expected utility theory; i.e. the decisions should not be affected by the presentation of the alternatives. The violation of this feature is also exhibited in a non-monetary question by Tversky and Kahneman''' as follows;

It is estimated that 600 people will die because of the disease in Asia. Choose one of the two alternative programs proposed to combat the disease.

Program A: 200 people will be saved for sure.

Program B: There is 1/3 probabilit}' that 600 people will be saved, and 2/3 probability that no one will be saved.

72% of 152 of undergraduate students of Stanford and British Colombia Universities chose program A, while 28% chose program B. Same question is asked and program A and program ß is given in another way.

Program C: 400 people will die for sure.

Program D: There is 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.

This time, only 22 % of the participants selected program C which is identical to program A: 200 people to be saved out of 600 means that 400 people will die for sure. Same shift is seen in program D. Even though it is exactly the same as program B, this time 78% of the participants selected prog- ram D.

The presentation of the alternatives is the reason for these dramatic shifts from one program to another despite being the same. That is, the participants chose program A because they evaluate "living" as a positive term or gain and they behave as a risk averse. On the other hand, they chose program D because they evaluate "dying" as negative term or loss and select the risk-

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acceptance behavior. Kahneman and Tversky" called this shift a reflection effect.

The utility function in the expected utility theory transformed to the value function (figure 1) in the prospect theory.

LOSSES -

Figure 1-Value Function'*

As seen in figure 1, "value" is used instead of "utility". The zero-point IS called reference point, that is, in order to assess the outcomes, people use the deviation trom it rather than u.se net as.set levels. This reference point often is the beginning of the wealth, but sometimes it can be an ultimate point that the decision maker wants to reach. Gains and losses are evaluated with respect to this reference point. The area above the reference point through gains is concave and it is convex for los.ses. It tells us that people tend be to risk-averse when facing alternatives containing gains and they have a tendency to accept the risk (risk-seeker) when losses are concerned''. Furthermore, it has a kink at zero, being steeper for small losses compared to small gains. The function u in expected utility theory, by contrast, is usually taken to be smooth and concave everywhere . Moreover, people feel doubled pain when they lose compared to feeling pleasure when they win. Thus they become loss averse". Loss aversion leads people to segregate each investment in terms of gains and Ios.ses causing mental accounting.

Mental accounting is the set of cognitive operations used by individuals to organize, evaluate, and keep track of financial activities which can be balanced daily, weekly, monthly, and can influences the choices'" Tversky and Kahneman" used the term psychological account, that is, many times 1$ is not equal to another 1$ in their minds. Consider this typical example ;

"Imagine that you have decided to see a play where admission is 10$ per ticket. As you enter the theater you discover that you have tost a 10$ bill Would you pay 10$ for a ticket for the play? "

88% of the 183 participants said they would still pay 10$ for a ticket for the play. After this result, Tversky and Kahneman"' changed the format of the question.

"Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theater you discover that you have lost

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the ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $10 for another ticket? " , |

This time, the 46% of the 200 participants said "yes". In both ca.ses, the total cost for seeing the play is 20$. Under expected utility theory, 20$ must be equal another 20$ no matter what the circumstances are. So, why do people accept to pay another 10$ when they lose a bill, but do not accept it when they lose the ticket? Because, people segregate different costs into different mental accounts and they weigh these different accounts by looking at the effects of the costs. As seen from the example, the psychological impact (pain) of losing the ticket is higher than that of losing same amount of money because people do not relate the "lost money" with the "play" whereas the lost ticket is directly related with the "play". Simply, in participants' minds the "lost money" and the ticket are not substitutable even though the total costs are .same.

According to Kahneman and Tversky'". prospect theory consists of two phases. First one is the editing phase which involves initial analysis of the problem. Second one is the evaluation phase. The more important and dangerous pha.se is the editing phase, because it involves several mental operations such as coding, combination, segregation, cancellation, simplification and detection in order to organize and reformulate the options for the simplification of the choice problem. Consequently, with the help of these mental operations, evaluation task become easy. However, many anomalies of choices ari.se in the editing phase" ' " .

According to the prospect theory, in the evaluation phase, the following equation is used under uncertainty"^

7r(p). V(Aw)

where n: denotes the decision weights, Vdenotes to the value function and Aw denotes the final changes in wealth which is the deviation from the reference point.

A probability (p) in the expected utility theory is replaced by decision weight l7c (p)] in the prospect theory.

,!(•.:, , • • • • I ' , ' . ,

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STATED PROBABILITY: p

29 Figure 2- A hypothetical weighting function

The decision weight function is monotonically increasing, with discontinuities at 0 and 1, such that it systematically overweighs small probabilities and underweighs large probabilities. This can explain the Allais paradox""'. In other words, individuals clump intermediate probabilities in their minds, making the difference between 45 and 55 percent much less noticeable than that between zero and two percent or 98 and 100 percent". The dotted line in the figure 2 represents the objective probabilities in the expected utility theory and the concave line exhibits how people transform the objective probabilities while deciding'^.

CONCLUSION

Expected utility theory and prospect theory actually deal with the same thing: decision making by individuals. Expected utility theory was developed from a set of logical axioms and tries to describe what rational behavior has to be; on the other hand, prospect theory is developed from the empirical ob.servations and tries to describe what the actual behaviors are. Although there is still some common ground, two theories' suggestions are different and it seems like the former (normative) explanations are less powerful than the latter (descriptive) ones.

Humans have a desire to be rational and believe that they actually behave rationally. However, it is clear that individuals do not always choose the alternative that will maximize their utilities and the presentation of the decision problem could lead a deviation from the rational behavior. There are mainly two reasons for irrational behaviors. First, individuals are not emotionle.ss creatures. They have emotions and the.se emotions are the barriers in front of rational behaviors. Their choices under uncertainty, especially for the future pro.spects, can be affected by their emotions. Second, even if we accept individuals can control their emotion for a while, they again behave irrationally because they can not use their minds as super-calculator robots. Individuals have limited computational skills and they have to use some shortcuts

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Individuals' Choices: Traditional and Behavioral Finance Perspectives

(heuristics) in order to reduce the mental efforts for simplifying the complex tasks and make the decision process easier. These shortcuts many times lead people to some irrational behaviors.

Traditional finance incorporating with expected utility theory says what individuals should do and define all the behaviors out of these "ideal" behaviors as irrational behaviors. However, according to behavioral finance incorporating with prospect theory there is no ideal behaviors, and all the behaviors can be accepted as normal. Simply, people are "rational" in traditional finance; they are "normal" in behavioral finance".

" Ögr. Gör. Dr., Fatih Ünivcrsite.si, Istanbul Me.slck YUk.sekokuki, Bankacilik vc Sigortacilik Bölümü, [email protected]

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^ Bernoulli, D. "Exposition of A New Theory on The Mea.suremeiit of Ri.sk", Econoinetrica, Vol. 22, No. 1, 1954, pp. 23-36 (Translated by Louise Sommer, the original article is "Specimen Theoriae Novae de Men.sura Sortis")

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Kahneman, D - V. Smith. "Foundations of Behavioral and Experimental Economics" The Royal Swedi.sh Academy of Sciences Advanced Information on the Prize in Economic Sciences 2002, pp.11, (http://nobelprize.org/nobel_prizes/eeonomics/laureate.s/2002/ecoadv02.pdt) (Mareh 20"', 2010)

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" Kahneman, D. - A. Tversky. "Prospect Theory..." pp. 277-279 ' "* Kahneman, D. - V. Smith. "Foundations of..." pp. 17-18 ' '"̂ Tversky, A. - D. Kahneman. "Advances in prospect theory; Cumulative repre.sentation under uncertainty" Journal of Risk and Uncertainty, Vol.5, No. 4, 1992, pp. 297-323

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BlREYLERiN SECÍMLERÍ: GELENEKSEL VE DAVRANI§SAL FiNANS PERSPEKTiELERi

Özet I Gelenek.sel finans beklenen fayda teorisini baz alarak bireylerin seçimle-

rinde her durum, her çartta faydalanni maksimi/e etmeye çaliijtiklarini varsayar. Ote taraftan bireylerin seçimlerinde psikolojik boyutun ihmal edilmemesi gerek- tigini savunan davraniçsal finans ise baz aldigi beklenti teorsi ile çeçitli biliçsel sinirliliklardan etkilenen bireylerin .seçimlerinde her zaman rasyonel davran- madigini ortaya koyar. Davrani§sal finansa göre bireylerin seçimlerinde kazanç .söz konusu oldugunda bireylerin riskten kaçinirken, kayip söz konusu oldugun- da riski kabul eder (.sever) bir davraniç .sergiledigini ortaya koyar. Bunun diçin- da davraniçsal finans, zihinsel muhasebe kavrami Ile karar alma probleminin sonuçlan ayni kalarak sadece sunumun degiçmesiyle bile bireylerin seçimlerinin degiçtigini savunur. Geleneksel finansa göre bireyler "rasyonel" iken, davraniç- sal finansa göre "normar'dirler.

Anahtar kelimeler; Rasyonellik, beklenen fayda teorisi, beklenti teorisi, zihinsel muhasebe I

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