Received: 9 August 2019
Accepted: 17 October 2019
This study aims to question the assumptions of prospect theory using a sample of students enrolled in a master’s course on accounting and finance at a Portuguese polytechnic institution. Such theory has stood out among others developed in the field of Behavioural Finance due to the debate and investigation it has generated. To achieve this aim, we applied a questionnaire four consecutive years (2012–2015). The instrument included a set of alternative response questions that seek to unveil respondents’ preferences regarding the situations they were presented with. Bibliographic and descriptive research was carried out and the results were compared with those obtained by other authors but they were not always consistent. Thus, the isolation effect was confirmed; the reflection effect was almost always confirmed; and the certainty effect was not always confirmed. Regarding attitude toward risk, the assumptions of risk aversion, and importance given to changes in wealth (at the expense of wealth states), our results are in line with those obtained by said authors. Hence, this study contributes to support prospect theory with its results and the confirmation of the isolation effect.
Keywords: Traditional finance, modern finance, behavioural finance, prospect theory.
JEL Classification: D81, C52, G10.
El objetivo de este estudio es verificar los supuestos de la teoría de la perspectiva en una muestra compuesta por estudiantes que asistieron a un curso de maestría en contabilidad y finanzas en una institución politécnica en Portugal. Esta teoría se ha destacado entre otras desarrolladas en el campo de las finanzas conductuales por el debate y la investigación que ha generado. Para lograr el objetivo mencionado, adaptamos el cuestionario de los autores de la teoría de la perspectiva. El cuestionario se aplicó cuatro años consecutivos (de 2012 a 2015) e incluyó un conjunto de preguntas de respuesta alternativa que buscan conocer las preferencias de los encuestados frente a las situaciones que se exponen. También se realizó una investigación bibliográfica y descriptiva y se compararon los resultados con los obtenidos por otros autores. Los resultados no siempre fueron consistentes con los de dichos autores. Se verificó el efecto de aislamiento, el efecto de reflexión (casi siempre) y el efecto de certeza (no siempre). Adicionalmente, en cuanto a la actitud hacia el riesgo, los supuestos de aversión al riesgo y la importancia dada a los cambios en la riqueza (a expensas de estados de riqueza), nuestros resultados están en la misma línea que los de tales autores. Con estos últimos resultados y la confirmación del efecto de aislamiento, este estudio hace una contribución a la teoría de la perspectiva.
Palabras clave: finanzas tradicionales, finanzas modernas, finanzas conductuales, teoría de la perspectiva.
Clasificación JEL: D81, C52, G10.
The emergence of Traditional Finance seems to be prior to the middle of the 20th century. An early milestone in modern finance (or classical finance) was 1952, when Markowitz introduced the portfolio selection theory; later, Behavioural Finance was established in 1979 with Kahneman and Tversky’s prospect theory (
In
Thus, the aim of the present study is to verify the assumptions of prospect theory in a group of students enrolled in a master’s program in accounting and finance. For that purpose, bibliographical and descriptive research was conducted. We adopted
This paper is organized as follows. Section 2 describes the evolution of finance in relation to its main paradigms, highlighting the role of behavioural finance and, particularly, the importance and development of prospect theory. Section 3 details the methodology. Section 4 presents the results, which are discussed in Section 5. Finally, Section 6 outlines some conclusions, limitations of the study, and possible future research lines.
Evolution of finance
In the evolution of finance as a science, the literature refers to three major paradigms: Traditional Finance, Modern Finance (
The Modern Finance paradigm contradicted the traditional one in the sense that it recommended to investors not to seek to obtain returns higher than market returns, but equal to those returns or consistent with their risk profile (
A value function that is concave for gains, convex for losses and steeper to losses than to gains;
A nonlinear transformation of the probability scale that overweights small probabilities and underweights moderate and high probabilities (p. 297-298).
However, this theory has been recently
questioned and, nowadays, there is a “general agreement that the expected
utility theory does not provide an adequate description of the individual
decision” (
The anomalies that were discovered tended to appear to be as often underreaction by investors as overreaction; and
The anomalies tended to disappear, either as time passed or as methodology of the studies improved. (p. 101).
Behavioural Finance has been defined by different authors. For example:
Sentiment: investor error. Errors originate at the level of the individual but can manifest themselves at the level of the market.
Behavioural preferences: “capture attitudes about risk and return which do not conform with the principles of expected utility theory … rational information traders exploit behavioural inconsistencies of irrational of noise traders, and in so doing lead prices to be efficient” (p. 11).
Limits to arbitrage: there are limits to arbitrage and, consequently, the prices need not be efficient.
Behavioural Finance examines what happens to prices when market participants do not share rational expectations (
The main features of behavioural preferences are, according to
Loss aversion: the reluctance of investors to obtain losses;
Regret aversion: stipulates that investors may want to avoid losses for which they can easily imagine having made a superior decision (ex-post);
Mental accounting: refers to how people categorize and evaluate financial results (Henderson & Peterson, 1992 );
Myopic loss aversion: combines time horizon framing-based and loss aversion. Investors are more averse to risk when their time horizon is short than when it is long (Haigh & List, 2005 );
Self-control: refers to the degree to which people can control their impulses (p. 11-12).
As stated by
To
Prospect Theory
In line with the relevance of prospect theory in the literature and the aim of the present study, it is important to mention the leading authors in this field.
In prospect theory,
According to
Reference dependence: the most basic idea in prospect theory.
Loss aversion: it plays a useful role in many applications.
Diminishing sensitivity: it seems to be much less important.
Probability weighting: it has drawn growing interest in recent years, attracting significantly more empirical support.
The same authors (
To
... expressed in terms of two scales, π and ν. The firs scale, π, associates with each probability p a decision weight π(p) which reflects the impact of p on the overall value of the prospect. However, π is not a probability measure and, … π (p) + π (1-p) is typically less than unity. The second scale v, assigns to each outcome x a number ν (x) which reflects the subjective value of that outcome. ... defined in relation to a reference point which serves as the zero-point value of scale. Hence, v measures the value of deviations from that reference point, i.e., gains and losses (Kahneman & Tversky, 1979, p. 14 ).
The value function is defined from that reference point, being concave for gains and convex for losses, but more inclined for losses than gains. This function, according to
In the evaluation phase, according to
testable hypothesis that people are risk averse when the probability of gain is large and positive, but risk seeking when the probability of gain is small and positive. The reverse is the case for losses. When the probability of losses is large the value function is convex and when the probability of loss is very small it becomes concave. This implies that investors are risk seeking when the losses are large and risk averse when the losses are small. Also the value function of losses is much steeper than the value function of gains. This shows that a loss creates a greater feeling of having low value (pain) compared to the feeling of having higher value (joy) created by an equivalent gain (Seth & Chowdary, 2017, p. 1139 ).
However, as suggested by
Thus, this theory is applicable to uncertain prospects and risk prospects regardless of the number of outcomes and allows different weight functions for gains and losses.
To stress the increasing importance of prospect theory,
Finance and insurance are two fields of economy where prospect theory has been further applied. Such theory became a model for decision making under conditions of risk; therefore, it may be more appropriate for situations in which risk attitudes play a crucial role. Lately, prospect theory has expanded its scope into several other areas, including consumer choice, industrial organization, and contract theory (
Based on the literature review above, one can deduce, as
Empirical studies
The following are some examples in a wide range of studies published in the field of Behavioural Finance, more specifically, prospect theory:
“were risk averse for gains and risk seeking for losses and their utility was concave for gains and (slightly) convex for losses. They were also averse to losses, but less so than commonly observed in laboratory studies and assumed in behavioral finance” (p. 411).
Therefore, researchers in the field of Behavioural Finance, in particular with regard to prospect theory, often seek to identify the reasons behind certain investment decisions in uncertain conditions, and they try to verify the assumptions of the theory.
Questionnaires are generally administered for data collection, but other instruments can also be used for different sample compositions; in addition, both laboratory and natural circumstances should be described.
In order to prove the assumptions in prospect theory, the present study adopted bibliographic and descriptive methods. We used primary sources, such as books and scientific papers, and primary data obtained from a questionnaire applied to students attending the first year of a master’s program in finance at a Portuguese Polytechnic Education Institution. The questionnaire, adopted from
The non-probabilistic sample included all the students in the class on the day that the topic of Behavioural Finance was taught in the context of a module on finance theory and research. Table 1 details the sample composition by sex and age group. Considering the characteristics of the study, we used (minimum and maximum) relative localization measures as statistics and a frequency table that summarises the information about the sample, where the values are distributed into intervals.
Total | Up to 25 years old | 26 to 30 years old | More than 30 years old | No answer | ||
2012 | ||||||
Male | 4 | 1 | 1 | 2 | - | |
Female | 11 | 1 | 5 | 5 | - | |
No answer | 1 | - | - | 1 | - | |
Total | 16 | 2 | 6 | 8 | ||
2013 | ||||||
Male | 12 | 4 | 5 | 3 | - | |
Female | 14 | 9 | 4 | 1 | - | |
No answer | - | - | - | - | - | |
Total | 26 | 13 | 9 | 4 | ||
2014 | ||||||
Male | 3 | 0 | 1 | 1 | 1 | |
Female | 12 | 5 | 2 | 5 | 0 | |
No answer | 1 | 0 | 0 | 0 | 1 | |
Total | 16 | 5 | 3 | 6 | 2 | |
2015 | ||||||
Male | 2 | 1 | 0 | 1 | - | |
Female | 8 | 3 | 3 | 2 | - | |
No answer | - | - | - | - | - | |
Total | 10 | 4 | 3 | 2 | - | |
Total | Male | 21 | 6 | 7 | 7 | 1 |
Female | 45 | 18 | 14 | 13 | 0 | |
No answer | 2 | 0 | 0 | 1 | 1 | |
Total | 68 | 24 | 21 | 21 | 2 |
In 2012 and 2014, the sample included exactly the same number of students; they were mostly females and over 30. In 2013, the sample involved a higher number of students, almost as many females as males and, above all, aged up to 25. Finally, in 2015, the sample gathered the lowest number of students, mostly female and, above all, under 25. There were 68 respondents in total; more than 66 % of them were females, more than 35 % were under 25, and the remaining participants were equally distributed into the other age groups under consideration.
As
This section presents
each question in the instrument followed by a table that details the results
obtained in this study and those in previous studies, namely,
Question 1 presents the choice between alternatives A and B:
A: 33 % chance to win €2500; and 66 % chance to win €2400 | B: 100 % chance to win €2400 |
Question 2 offers a choice between alternatives C and D as follows:
C: 33 % chance to win €2500 | D: 34 % chance to win €2400 |
Table 2 shows participants’ answers to both questions.
Question 1 | Question 2 | |||||
A | B | No answer | C | D | No answer | |
2012 | 31 % | 69 % | - | 31 % | 69 % | - |
2013 | 27 % | 69 % | 4 % | 54 % | 42 % | 4 % |
2014 | 44 % | 56 % | - | 25 % | 69 % | 6 % |
2015 | 30 % | 70 % | - | 30 % | 70 % | - |
Total | 32 % | 66 % | 2 % | 43 % | 54 % | 3 % |
Kahneman and Tversky (1979) | 18 % | 82 % | - | 83 % | 17 % | - |
Kimura et al., (2006) | 30 % | 70 % | - | 52 % | 48 % | - |
Seth and Chowdary (2017) | 17 % | 83 % | - | 50 % | 50 % | - |
The outcomes of Question 1 show that the majority of respondents chose B (a 100 % chance to win perspective) considered either annually or in total. However, that preference was less prominent among the students who attended the course in 2014. Regarding Question 2, except for 2013, respondents clearly indicated a preference for alternative D (a little higher chance to win a slightly lower amount), which was selected by most participants in total.
Question 3 offers a choice between alternatives A and B, as follows:
A: 80 % chance to win €4000 | B: 100 % chance to win €3000 |
Question presents the choice between alternatives C and D:
C: 20 % chance to win €4000 | D: 25 % chance to win €3000 |
Table 3 presents the responses to Questions 3 and 4.
Question 3 | Question 4 | |||
A | B | C | D | |
2012 | - | 100 % | 25 % | 75 % |
2013 | 35 % | 65 % | 27 % | 73 % |
2014 | 19 % | 81 % | 31 % | 69 % |
2015 | 30 % | 70 % | 40 % | 60 % |
Total sample | 22 % | 78 % | 29 % | 71 % |
Kahneman and Tversky (1979) | 20 % | 80 % | 65 % | 35 % |
Kimura et al., (2006) | 29 % | 71 % | 57 % | 43 % |
Seth and Chowdary (2017) | 18 % | 82 % | 48 % | 52 % |
The preference for alternative B (a 100 % chance to win perspective) is notorious in Question 3, considered both annually and in total; in turn, the answers to the fourth question are mostly D (a little higher chance to win a slightly lower amount), also considered both annually and in total.
Question 5 offers a choice between two alternatives, A and B, as follows:
A: 50 % chance to win a three-week trip to England, France and Italy. | B: 100 % chance to win a one-week trip to England. |
Question 6 presents a choice between alternatives C and D, as follows:
C: 5 % chance to win a three-week trip to England, France and Italy. | D: 10 % chance to win a one-week trip to England. |
Table 4 presents the responses to Questions 5 and 6.
Question 5 | Question 6 | ||||
A | B | No answer | C | D | |
2012 | 25 % | 75 % | - | 38 % | 62 % |
2013 | 12 % | 85 % | 3 % | 31 % | 69 % |
2014 | 31 % | 63 % | 6 % | 38 % | 62 % |
2015 | 30 % | 70 % | - | 40 % | 60 % |
Total sample | 22 % | 75 % | 3 % | 35 % | 65 % |
Kahneman and Tversky (1979) | 22 % | 78 % | - | 67 % | 33 % |
Kimura et al., (2006) | 20 % | 80 % | - | 49 % | 51 % |
Most answers to the fifth question were alternative B (a 100 % chance to win perspective), annually and in the entire sample. However, regarding Question 6, there is a preference for alternative D (a double % chance to win the lowest prize).
Question 7 offers a choice between alternatives A and B, as follows:
A: 45 % chance to win €6000 | B: 90 % chance to win €3000 |
Question 8 presents a choice between alternatives A and B as follows:
C: 0.1 % chance to win €6000 | D: 0.2 % chance to win €3000 |
Table 5 shows the responses to Questions 7 and 8.
Question 7 | Question 8 | ||||
A | B | No answer | C | D | |
2012 | 13 % | 87 % | - | 56 % | 44 % |
2013 | 19 % | 81 % | - | 62 % | 38 % |
2014 | 7 % | 87 % | 6 % | 37 % | 63 % |
2015 | - | 100 % | - | 50 % | 50 % |
Total sample | 12 % | 87 % | 1 % | 53 % | 47 % |
Kahneman and Tversky (1979) | 14 % | 86 % | - | 73 % | 27 % |
Kimura et al., (2006) | 23 % | 77 % | - | 72 % | 28 % |
Seth and Chowdary (2017) | 21 % | 79 % | - | 52 % | 48 % |
In question 7, alternative B (a double % chance to win half the prize) was consistently selected by the majority. However, in Question 8, respondents expressed dissimilar views. In some years, they preferred alternative C (2012, 2013); in 2014, it was alternative D; and, in 2015, they were equally divided. This situation may occur because the chances to win in both alternatives are very low. Nevertheless, considering the total number of respondents, option C (perspective to win the best prize) was selected by most.
The following questions, as the previous ones, offer a choice between two alternatives, but they introduce chances of loss in order to show the reflection effect (risk aversion in the case of gain and propensity to risk in the case of loss).
Question 3 presents a choice between two alternatives, A and B:
A: 80 % chance of losing €4000 | 100 % chance of losing €3000 |
Question 4 also offers a choice between A and B:
A: 20 % chance of losing €4000 | B: 25 % chance of losing €3000 |
Table 6 presents the responses Questions 3 and 4.
Question 3 | Question 4 | |||||
A | B | No answer | A | B | No answer | |
2012 | 69 % | 31 % | - | 63 % | 37 % | - |
2013 | 81 % | 15 % | 4 % | 65 % | 35 % | - |
2014 | 63 % | 31 % | 6 % | 44 % | 50 % | 6 % |
2015 | 80 % | 20 % | - | 50 % | 50 % | - |
Total sample | 74 % | 24 % | 2 % | 57 % | 41 % | 2 % |
Kahneman and Tversky (1979) | 92 % | 8 % | - | 42 % | 58 % | - |
Kimura, et al., (2006) | 82 % | 18 % | - | 37 % | 63 % | - |
Seth and Chowdary (2017) | 80 % | 20 % | - | 47 % | 53 % | - |
With a very high preference, alternative A, an 80 % chance of losing €4000 (vs a 100 % chance of losing €3000), was the most popular answer to Question 3. In turn, a disparity of choices may be observed regarding Question 4. During the first two years, alternative A was clearly preferred, but in the last two that trend became blurry. However, in total terms, the majority selected alternative A, a 20 % chance of losing €4000 (vs a 25 % chance of losing €3000).
Question 7 offers a choice between alternatives A and B:
A: 45 % chance of losing €6000 | B: 90 % chance of losing €3000 |
And Question 8 presents a choice between alternatives A and B:
A: 0.1 % chance of losing €6000 | B: 0.2 % chance of losing €3000 |
Table 7 presents the responses to Questions 7 and 8.
Question 7 | Question 8 | |||
A | B | A | B | |
2012 | 62 % | 38 % | 56 % | 44 % |
2013 | 73 % | 27 % | 42 % | 58 % |
2014 | 56 % | 44 % | 44 % | 56 % |
2015 | 70 % | 30 % | 20 % | 80 % |
Total sample | 66 % | 34 % | 43 % | 57 % |
Kahneman and Tversky (1979) | 92 % | 8 % | 30 % | 70 % |
Kimura et al., (2006) | 75 % | 25 % | 50 % | 50 % |
Seth and Chowdary (2017) | 61 % | 39 % | 41 % | 59 % |
The responses to Question 7 indicate that most participants selected alternative A (half % of losing double the amount), both every year and in the total sample. Such preference was more prominent in 2013 and less so in 2014. In turn, the answers to Question 8 show, except in 2012, that the preference for alternative B (double the chance of losing half the amount) was more prominent in 2015 and less so in 2014.
Question 9 offers a choice between alternatives A and B:
Consider a game with two stages. In the first stage, there is a 75 % probability that the game ends without winning anything and a 25 % probability that you pass to the second stage. Reaching the second stage, one can choose between the following alternatives. Note that the choice must be made before starting the game. | |
A: 80 % chance to win €4000 | B: 100 % chance to win €3000 |
Question 10 offers a choice between alternatives A and B:
Consider that, in addition to the resources you own, you have received €1000 more. Now, you must choose between the following alternatives. | |
A: 50 % chance to win €1000. | B: 100 % chance to win €500. |
Finally, Question 11 represents a choice between alternatives C and D, as follows:
Consider that, in addition to the resources you own, you have received €2000 more. Now, you must choose between the following alternatives. | |
C: 50 % chance of losing €1000 | D: 100 % chance of losing €500 |
Table 8 presents the responses to Questions 9, 10, and 11.
Question 9 | Question 10 | Question 11 | |||||||
A | B | No answer | A | B | No answer | C | D | No answer | |
2012 | 25 % | 75 % | - | 38 % | 62 % | - | 44 % | 56 % | - |
2013 | 19 % | 77 % | 4 % | 39 % | 57 % | 4 % | 65 % | 31 % | 4 % |
2014 | 38 % | 62 % | - | 19 % | 81 % | - | 44 % | 56 % | - |
2015 | 10 % | 90 % | - | 20 % | 80 % | - | 50 % | 50 % | - |
Total sample | 24 % | 75 % | 1 % | 32 % | 67 % | 1 % | 53 % | 46 % | 1 % |
Kahneman and Tversky (1979) | 22 % | 78 % | - | 16 % | 84 % | - | 69 % | 31 % | - |
Kimura et al., (2006) | 22 % | 78 % | - | 38 % | 70 % | - | 65 % | 35 % | - |
Seth and Chowdary (2017) | 30 % | 70 % | - | - | - | - | 44 % | 56 % | - |
The answers to Questions 9 and 10 were clearly focused on alternative B (a 100 % chance to win perspective). Finally, the answers to Question 11 express different opinions. In 2013, respondents preferred alternative C; in 2012 and 2014, most selected alternative D; and, in 2015, they were divided equally. However, considering the total sample, option C (a 100 % chance of losing half the amount perspective) was preferred.
As suggested by prospect theory and shown in Table 2, the answers to Question 1 confirm the certainty effect. This happened because respondents preferred certain results over probabilistic ones. These results are consistent with studies by
The answers to Question 3 (Table 3), once again (as
The answers to Question 5 (Table 4) clearly show the presence of the certainty effect as the preference was for the 100% certain scenario, which is consistent with
As expected (
The responses to Question 3 (Table 6), are in line with those obtained by the above mentioned authors, focused mostly on the smaller probability of loss. In turn, in the answers to Question 3, respondents chose the certain gain. An analysis of the responses to those two Questions, 3 and 3, confirms the reflection effect. However, such effect was not proven by the answers to Question 4 (Table 6), unlike
When faced with very low probabilities of losing, respondents chose the lesser amount (Question 8, Table 7), as proposed in prospect theory and confirmed by
Therefore, some theory assumptions were empirically confirmed in general and others, in all the cases. In the first group were the certainty and the reflection effects; and, in the second, the isolation effect and crucial aspects of the theory, such as risk aversion in the field of earnings, reference dependence, and the relevance given to changes in wealth (at the expense of wealth states). Regardless, further research should be conducted in the field of Behavioural Finance and, in particular, prospect theory.
Behavioural Finance reflects an evolution in the field of Finance because it extends the knowledge included in Traditional and Modern Finance through the incorporation of psychological aspects, thus acknowledging their role in investment decisions. Although multiple theories make up this area of knowledge, prospect theory, by
This study adopted bibliographic and descriptive methods, using
The answers to the questions confirmed the isolation effect, the reflection effect (almost always), and the certainty effect (not always). These results were not always consistent with the outcomes of previous studies (
This study is justified because it presents a theoretical framework based on relevant references and contributes to the deepening of the study of the effects defended by prospect theory. However, it has some limitations that derive, for example, from the size of the sample. As a result, one-year analyses had little meaning and the study had to cover several years. Furthermore, the outcomes are only valid in the context of the selected sample.
Further studies could apply the questionnaire to students enrolled in other undergraduate courses at the same institution in the same or different areas. Subsequently, the results could be compared in order to understand the possible effect of financial knowledge on investment decisions and confirm (or reject) the assumptions of prospect theory.