Loss Aversion

A study of changes in loss aversion towards a

50/50 gamble

Financial Economics

Bachelor Thesis

Authors:

David Nilsson

Mauritz Smedensjö Myhre

Supervisor: Magnus Willesson

Examiner: Håkan Locking

Term: VT20

Subject: Financial economics

Level: Bachelor

Course code: 2FE32E

Abstract

Loss aversion is a theory which states that losses loom larger than gains.

Negative outcomes are weighted heavier than positive outcomes in decision

making but could this weight change when different prospects are evaluated?

This thesis focuses on how the loss aversion changes toward different

magnitudes of a loss for young individuals when they are faced with a 50/50

chance of winning or losing a gamble. The loss aversion is tested toward six

different magnitudes of a potential loss ranging from 100 kr to 4 000 kr. The

loss aversion toward these six different magnitudes is then compared to

examine how the loss aversion changes. This data was collected using a

survey experiment that was digitally distributed to economics students at

Linnaeus University in Växjö.The results from the subsequent analysis

showed that the loss aversion was not constant towards all six losses. The

loss aversion was different in ten out of fifteen pairwise comparisons.

Respondents became more loss averse when the loss increased but the loss

aversion did however seem to be less sensitive to increases in losses above

the 1 000 kr mark.

Keywords

Loss aversion, reference point, behavioural finance, losses and gains,

required win, risky prospects

Acknowledgements

We would first of all like to thank our examiner Håkan Locking and

supervisor Magnus Willesson who has been very helpful and given us advice

to help us move forward with this research. Further we would like to thank

My Gustafsson who has given a lot of good guidance and feedback during

this work even though she had no obligation to offer her help. A special

thanks is given to the 10 test subjects who have helped us with feedback on

interpretations on our survey. They helped us make sure that the survey was

interpreted the way it was supposed to, in order for us to gather reliable data.

We would of course also like to thank all 111 respondents of our survey who

have made it possible for us to gather the data for the analysis in this work

and our opponents for good constructive criticism and advice.

Table of contents

1.0 Inledning 1

1.1 Background 1

1.2 Problemdefinition 2

1.3 Purpose 5

1.4 Research questions 5

1.5 Limitations 5

2. Theoretical framework 7

2.1 Expected utility theory 7

2.2 Prospect theory 8

2.2.1 Evaluation is relative to a neutral reference point 9

2.2.2 Diminishing sensitivity 9

2.2.3 Loss aversion 10

2.2.4 Drawbacks 12

2.3 Perspectives on Loss aversion 12

2.3.1 Constant loss aversion 12

2.3.2 Adaptive loss aversion 13

2.3.3 Research on non-constant loss aversion 14

2.5 Endowment effect 15

2.6 Mental accounting 16

3. Method 18

3.1 Quantitative vs. qualitative method 18

3.2 Survey vs. structured interviews 18

3.3 Sample 20

3.4 Constructing a survey 21

3.4.1 Visual representation 21

3.4.2 Question order 21

3.4.3 How to ask questions 22

3.4.5 What is being measured 23

3.5 Test survey 24

3.6 The Survey 25

3.6.1 Distribution of the survey 27

3.7 Null hypothesis 27

3.7.1 Friedman Test 27

3.7.2 Post Hoc Test (Wilcoxon test) 27

3.8 Choice of analysis 28

4. Result 30

5. Discussion 35

6. Conclusion 40

7. Further research 41

8. Sources 42

8.1 Literature 42

8.2 Handbook/Survey instructions 42

8.3 Digital sources 43

8.4 Images 43

8.5 Articles 44

9. Appendix 49

9.1 First Draft of the Survey 49

9.2 Final Survey 51

9.3 Distributions 55

9.3.1 Gender 55

9.3.2 Age 55

9.3.3 Income 56

9.3.4 Total savings 56

9.3.5 Question A. 57

9.3.6 Question B. 57

9.3.7 Question C. 58

9.3.8 Question D. 58

9.3.9 Question E. 59

9.3.10 Question F. 59

9.4 Kolmoforov-Smirnov and Shapiro-Wilk Test for Normal Distribution 60

9.5 Friedman Test 63

9.6 Wilcoxon Signed Ranks Test 64

9.6.1 Wilcoxon signed rank test, comparing Q. A 64

9.6.2 Wilcoxon signed rank test, comparing Q. B 65

9.6.3 Wilcoxon signed rank test, comparing Q. C 66

9.6.4 Wilcoxon signed rank test, comparing Q. D 67

9.6.5 Wilcoxon signed rank test, comparing Q. E 67

9.7 Wilcoxon Signed Rank Test for the non significant difference between

distributions. 68

9.7.1 Wilcoxon Signed Rank Test between the distribution for Q. A & Q. B 68

9.7.2 Wilcoxon Signed Rank Test between the distribution for Q. C & Q. D 69

9.7.3 Wilcoxon Signed Rank Test between the distribution for Q. D & Q. E 70

9.7.4 Wilcoxon Signed Rank Test between the distribution for Q. D & Q. F 71

9.7.5 Wilcoxon Signed Rank Test between the distribution for Q. E & Q. F 72

1.0 Inledning

1.1 Background

Prospect theory is a theory that has been developed to explain the way in which people make

choices when there is risk involved (Häckler, Pfosser, Tränkler 2017). Test results show that

people do not make choices in the same way that the traditional utility theory predicts they

will. Within the traditional utility theory an individual will always experience the same utility

from having 100 000 kr no matter what their previous state was. The same utility will be

experienced for a person who previously had 110 000 kr, but now has 100 000 kr, as for

another individual which previously had 90 000 kr but now has 100 000 kr too (Tversky,

Kahneman, 1979). However, according to Tversky and Kahneman (1979) this is not what is

being observed in reality. Prospect theory says that individuals evaluate different types of

outcomes from the gains or loss perspective rather than the final state. This means that in the

previous example the individual who gained 10 000 kr to now have 100 000 kr will

experience a higher utility than the individual who lost 10 000 kr. Expressed in other words,

the value one experiences is dependent on the gain or loss rather than the final state

(Kahneman, Tversky, 1979).

As part of the prospect theory Tversky and Kahneman developed the theory of loss aversion

(Kahneman, 2013). Loss aversion is a theory which says that a change in wealth is evaluated

differently depending on if it is a gain or loss. If a gain and a loss is of an equal amount the

effect will be greater from the loss than the gain. The individual will feel a greater reduction

in value from the loss than he will feel an increase in value from the gain (Tversky,

Kahneman, 1991). According to Tversky and Kahneman (1979) the same behaviour is

observed within decision making. Given the same difference between two decisions, the

difference will be of a greater significance when the decision is between two losses than

when it is a decision between two gains (Tversky, Kahneman, 1979). These differences are

explained by the asymmetric relationship between gains and losses within individuals. This

asymmetric relationship is the reason that a greater weight is attached to losses than gains in

decision making (Tversky, Kahneman, 1991).

Does an individual always possess the same degree of loss aversion? The adaptive loss

aversion theory suggests that the degree of loss aversion an individual possesses fluctuate

when outcomes of decisions are different from what was anticipated. If a gain was bigger

than anticipated individuals become less loss averse and vice versa (Lindsay, 2019).

Furthermore, a study made by Wang et.al (2016) also showed that loss aversion could differ

depending on the magnitude of a potential loss.

Other research indicates that loss aversion is constant and independent from the reference

point. Shalev (2002) proposed a utility model which takes loss aversion into account. The

model assumes that loss aversion is a constant which lowers the utility compared to the

traditional utility theory (Shalev, 2002). Later Hans Peters (2011) strengthened this argument

by showing that the altering of the reference point1 does not affect the loss aversion (Peters,

2011).

1.2 Problem discussion

The expected utility theory (EUT) is normative in its nature, which means that it displays

how rational decisions should be made under risk in order to maximize one's expected utility

(Häckel, Pfosser, Tränkler, 2017).

“According to EUT, each action is ranked based on its expected utility, which

depends on both the consequences and the probabilities of each possible

scenario”

- Cappello, Zonta, Glišić, 2016

To exemplify this, we imagine a coin toss. If the coin toss lands on heads you win 10$ and if

it lands on tails u lose 5$. This scenario would yield an expected utility of:

1 “The earlier state relative to which gains, and losses are evaluated” – Kahneman, 2013

0,5 ∗ 10 + 0.5 ∗ (−5) = 2,5

Paul A. Samuelson was an American economist and the first American to win the Nobel prize

in economic science (Nobelprize, 2020), he has also been called “the father of modern

economics” (MIT, 2020). Samuelson once offered a colleague a wager in which they would

toss a coin, if the coin landed on heads the colleague would win 200$ but if the coin would

land on tails the colleague would lose 100$. This wager was turned down by the colleague,

but he would agree to the wager if they did it 100 times. Samuelson deemed this behaviour

irrational since if you agree to do a bet 100 times, the bet should not be turned down when it

is being played once. The colleague replied, “I won’t bet because I would feel the 100$ loss

more than the 200$ gain” (Thaler, Tversky, Kahneman, Schwartz, 1997). This behaviour

observed by Samuelson violates the EUT which is what Tversky and Kahneman (1979) later

investigated when proposing the prospect theory as an alternative theory to EUT (Tversky,

Kahneman, 1979).

In 1979 as part of the prospect theory Tversky and Kahneman proposed a value function for

losses and gains. The function is steeper for losses than for gains (Tversky, Kahneman,

1979).

Graph 1. An illustration of a Value function from Tversky and Kahneman (1979).

The shape of the function is derived from the fact that when the magnitude of a loss or gain

increases, the marginal value of a given change decreases. The change from 100 to 200 is

perceived as greater than a change between 1100 to 1200, hence the shape of the curve

(Tversky, Kahneman, 1979). The value function proposed by Tversky and Kahneman (1979)

shows the concept of loss aversion. The slope reflects the observed 2:1 relationship between

gains and losses (Kahneman, Knetsch, Thaler, 1991). This translates to a loss aversion

parameter of two with the definition given by Tversky and Kahneman (1992). They stated

that in a 50/50 gamble the loss aversion parameter could be calculated by the required win to

accept the bet divided by the given potential loss (Tversky, Kahneman, 1992). While Tversky

and Kahneman’s research shows that loss aversion is present in preferences and decision

making, one may wonder whether the loss aversion is constant for each individual or not?

Lindsay (2019) researched different scenarios with lottery tickets to test loss aversion. The

result from the different scenarios was that the adaptive loss aversion model best explained

the subject’s behaviour and the gap in their bid and ask spread. This research shows that loss

aversion tends to change based on if experiences exceeded or fell short of anticipated results

from the lottery (Lindsay, 2019).

Lindsay (2019) showed evidence of a change in loss aversion based on experience while

other research by Shalev (2002) and Peters (2011) have used a constant loss aversion factor

in their research. The constant loss aversion factor used by Shalev (2002) and Peters (2011)

was constant as long as the same relationship between wins and losses remained equal when

altering the reference point. Even though the constant loss aversion factor is based on certain

assumptions one could ask if loss aversion really is constant?

Wang et.al (2016) tested the impact that culture has on loss aversion. In the study they found

different loss aversion parameters for potential losses of 25$ and 100$ in a 50/50 gamble

(Wang et.al, 2016). Barsky et.al (1997) states that people's preference parameters could differ

due to sensitivity toward the size of the potential loss (Barsky et.al, 1997) which could

explain why the parameters differed. The results from Wang et.al (2016) showed that loss

aversion was significantly different (p < 0,001) between the two losses which is in line with

the notation by Barsky et.al (1997) that preference parameters could be sensitive to the size of

a potential loss (Wang et.al, 2016).

Tversky and Kahneman (1991) also presented the concept of diminishing sensitivity.

Diminishing sensitivity refers to the fact that a given change is of greater importance when it

is closer to the reference point (Tversky, Kahneman, 1991). To exemplify this, we imagine a

discount of 200 kr. If the discount is on an item worth 400 kr the discount will be perceived

as better than a 200 kr discount on an item worth 1 000 kr even though the discount itself is

the same (Sharma, Park, Nicolau, 2020). This raises a question of whether the case is the

same for losses. How do individuals behave when different magnitudes of potential losses are

evaluated?

1.3 Purpose

The purpose of this research is to examine how young individuals' loss aversion changes

towards different magnitudes of a potential loss when there is equal probability of winning or

losing a gamble.

1.4 Research questions

I. Do we see a change in the loss aversion within individuals for different magnitudes of

potential losses or does it remain constant?

II. Between which magnitudes of the potential loss are the loss aversion significantly

different?

III. Is an increase in the magnitude of a potential loss of less significance when losses are

further away from the reference point?

1.5 Limitations

In the research a few restrictions had to be implemented in order to achieve a result in the

given time period. The research is limited to Växjö in Sweden and the population we will

gather data from are students at the Linnaeus University in the major of economics. The

amount of money for potential losses will only be examined up to 4 000 kr since losses above

4 000 kr could be perceived as too large for students. This could then make our data

unreliable based on feedback from other students. Test subjects experienced that if the loss

were above 4 000 kr they would not be able to handle their finances that month. This research

is also a partial study to analyse the loss aversion strictly in the decision of a coin toss. It will

not consider further effects that the results could have on the utility function or other types of

decision making.

2. Theoretical framework

2.1 Expected utility theory

In Bernoulli's utility theory the state of wealth is all you need to know to determine its utility.

At the same amount of wealth, the same utility should be generated between two people no

matter their preferences. However, this is not always correct (Kahneman, 2013).

Kahneman (2013) gives an example that states:

“Today Jack and Jill each have a wealth of 5 million. Yesterday Jack had 1

million. Are they equally happy? (Do they have the same utility?)”

- Kahneman, 2013

According to Bernoulli's theory Jack and Jill should have the same utility and be equally

happy, but as Kahneman expresses it: “you don't need to have a degree in psychology to

know that today Jack is elated and Jill despondent” (Kahneman, 2013).

Moreover, Bernoulli stated that an item's value should be determined by the utility it provides

rather than the item's price. This is because the utility is dependent on a person's specific

circumstances while the price of an item is equal to everyone. For example, obtaining 1000$

is more significant for a poor person than a rich person even though both would obtain the

same amount. The poor person would have more use for the 1000$ and hence gain more

utility than the rich person. However, no matter how small or insignificant, any increase in

wealth will increase one’s utility (Bernoulli, 1954). Bernoulli (1954) summarizes this with a

quote:

“I believe that it results from the fact that, in their theory, mathematicians

evaluate money in proportion to its quantity while, in practice, people with

common sense evaluate money in proportion to the utility they can obtain from

it”

- Bernoulli, 1954

With this quote it becomes clear that a measurement of risk that does not take utility into

account becomes unreliable. However, an accurate generalization does not seem reasonable

to make because the utility of an item can change depending on its circumstances, an example

of this is “a rich prisoner who possesses two thousand ducats but needs two thousand ducats

more to repurchase his freedom, will place a higher value on a gain of two thousand ducats

than does another man who has less money than he” (Bernoulli 1954).

In EUT an individual faced with a decision will compare the decision’s anticipated utility by

multiplying the probabilities of each outcome with the utility value and then summarize them.

This will then provide an expected utility for the decision the individual is encountering and

the one with the highest expected utility will be chosen (Mongin, 1997).

Furthermore Häckel et.al (2017) states that the foundation of standard neoclassical theory is

built on the presumption that people act rationally and make their decisions to maximize their

expected utility. EUT is a normative theory that explores how decisions should be made

rationally while they are made under risk. They explain further that EUT can be split into

three main principles (Häckel et.al, 2017). To quote Häckel et.al (2017) the three main

principles are:

“(1) the overall expected utility of a choice is the expected utility of the

distribution of possible outcomes. (2) It exists a utility function u() that

represents the risk profile of an investor and can be used to value uncertain

future outcomes xi. (3) A choice is acceptable if it adds utility to the existing

assets.”

- Häckel et.al, 2017

2.2 Prospect theory

According to Tversky and Kahneman (1979) the prospect theory tries to describe how

decisions by individuals are made under risk (Tversky, Kahneman, 1979). Kahneman and

Tversky showed that people’s decision making do in fact violate EUT. When individuals are

faced with decisions about gains, they are risk averse but when the decision is about a loss

they are risk-seeking even when both are given the same value (Mishra, 2014). This

behaviour is called the reflection effect. Once outcomes turn negative individuals' preferences

shift from risk-aversion to risk seeking (Tversky, Kahneman, 1979). In contrast to Bernoulli’s

utility theory, prospect theory contains the aspect of the reference point which is according to

Kahneman “the earlier state relative to which gains and losses are evaluated” (Kahneman,

2013).

Kahneman (2013) explains that at the core of prospect theory there are three important factors

which are decisive when financial outcomes are evaluated (Kahneman 2013).

● “Evaluation is relative to a neutral reference point”

● “Diminishing sensitivity”

● “Loss aversion”

2.2.1 Evaluation is relative to a neutral reference point

The reference point is most often stated as the status quo. However, things such as

expectations or social comparison may also affect the reference point (Tversky, Kahneman,

1991). Kahneman and Tversky (1979) demonstrate this through an example; When touching

an object with a given temperature it can be perceived as either hot or cold. The reason why it

can be experienced differently is that individuals might have adapted to different

temperatures of the object. Transferring this over to a monetary example it means that a given

wealth might be experienced as poverty by one individual and being very wealthy for another

(Tversky, Kahneman, 1979).

2.2.2 Diminishing sensitivity

Diminishing sensitivity says that individuals are less sensitive to a given change when the

change is between two larger sums than between two smaller sums (Tversky, Kahneman,

1991). Stated in a different way, individuals put less weight into a change when it is distant

from the reference point (Klein, Deissenroth, 2017). To exemplify the diminishing sensitivity

concept, this gives an explanation to why people think of a 5$ discount as better when it is on

something that costs 15$ than something that costs 30$. The amount you save is the same in

both cases, but it is perceived as better in the first since it is closer to the reference point

(Sharma, Park, Nicolau, 2020).

2.2.3 Loss aversion

Loss aversion states that a loss of a given amount has a bigger impact than a gain of the same

amount (Tversky, Kahneman, 1991). Expressed in another way, individuals try harder to not

experience a loss than they try to reach gains (Riedl, Heuer, Strauss, 2015). Loss aversion is

an important part in explaining a gap that has been observed in trades between the

willingness to accept (WTA) and the willingness to pay (WTP) (Tversky, Kahneman, 1991).

Graph 2 is a visual representation of the loss aversion concept. The kink at the origin of the

function shows the fact that the observed difference between a smaller loss and a smaller gain

is a 2:1 relationship. In most cases two options at a given difference have more impact when

it is seen as two negative outcomes than when it has two positive outcomes which is why the

slope is steeper in the loss domain (Kahneman, Knetsch, Thaler, 1991).

Graph 2. Atypical value function by Kahneman, Knetsch and thaler (1991).

Furthermore the status quo bias is a concept very much related to loss aversion. Individuals

are unwilling to deviate from their status quo which is their current state. The reason behind

this is that potential negative outcomes of leaving it is given a higher decision weight than the

corresponding potential positive outcomes. However, the same effect can be observed when

remaining at the current state is not possible (Kahneman, Knetsch, Thaler, 1991).

Kahneman and Tversky (1991) gives the following example:

“Imagine that as part of your professional training you were assigned to a part-

time job. The training is now ending and you must look for employment. You

consider two possibilities. They are like your training job in most respects except

for the amount of social contact and the convenience of commuting to and from

work. To compare the two jobs to each other and to present one you have made

up the following table:”

Job Contact with others Commute

Time

Present

job

isolated for long

stretches

10 min

job A limited contact with

others

20 min

job D moderately sociable 60 min

- Tversky, Kahneman, 1991

Both options are compared to the present job which is the reference point in this decision. In

both options, one condition with the job is better and the other is worse (Longer commuting

time and less social contact). The same option was also presented in the experiment where

job D had “much pleasant social interaction and 80 minutes daily commuting time” instead.

In the first example 70 percent of the experiment’s participants preferred job A but in the

second example only 33 percent preferred job A. This showed that individuals have a higher

sensitivity to the losing aspect of the option relative to their reference point (Kahneman,

Knetsch, Thaler, 1991).

2.2.4 Drawbacks

Prospect theory has some drawbacks brought up by Kahneman (2013). Firstly, prospect

theory is unable to handle that outcomes can be disappointing. When there is a very low

chance for a bad outcome the theory can not change its value to account for the

disappointment of the bad outcome. Second the theory will fail in the presence of regret.

When faced with two choices people might regret their decision. How the outcome is

perceived is largely dependent on the other option that could have been chosen (Kahneman,

2013).

2.3 Perspectives on Loss aversion

2.3.1 Constant loss aversion

When making a decision that contains risk, the preferences of the decision makers will be

based on the reference outcome. If the end product from the decision made does not reach the

reference outcome the result is regarded as a loss. Shalev (2002) proposed a model that was

both simple and elegant for this type of situation (Peters, 2011),

The utility of an outcome below the reference outcome is obtained from the basic

utility by subtracting a multiple of the loss in basic utility: this multiple, the loss

aversion coefficient, is constant across different reference outcomes. We provide

a preference foundation for this loss aversion model.

- Peters, 2011

Graph 3. An illustration of utility with constant loss aversion by Shalev (2002). In this graph the black line

represents a traditional utility function. The grey line represents a utility function which accounts for the

constant loss aversion (Peters, 2011).

Having a constant loss aversion factor is the reason behind the simplicity in Shalev’s model.

In the model, utilities that are below the reference outcome will be reduced by subtracting the

loss multiplied by the loss aversion coefficient. In this case the loss aversion coefficient is a

constant factor denoted as λ. There are two aspects one could take to the word “constant”

when measuring loss aversion this way. In the first aspect a specified reference outcome has

identical multiple λ of loss. This loss will then be subtracted from the regular utility in

different outcomes. In the second aspect, different reference outcomes will not affect the

multiple since it is constant (Peters, 2011).

Peters (2011) explains a scenario with two different lotteries that have the same reference

outcome. Both lotteries are constructed in a way that the total weights of negative outcomes

are identical. Now if the reference point were altered without altering the lotteries proportions

between the positive and negative outcome the preference between the lotteries would remain

equal. This would indicate that the loss aversion coefficient is not only constant but also

independent of the reference outcome (Peters, 2011).

2.3.2 Adaptive loss aversion

Adaptive loss aversion is a model that contains two aspects of trading behaviour in an

environment where payoffs can depend on your own actions, others actions and the state of

nature. The first aspect is about how people act when they do not know the joint distribution

of actions and states. The second aspect is about how people adapt their behaviour in

response to earlier experienced outcomes (Lindsay, 2019).

The adaptive loss aversion is a behavioural model that can be divided into three components.

The first component consists of people's expectations, this component is based on others

behaviour. The second component is that decisions are based on their predetermined utility.

The third and last component takes place after the trade is done and you have the result from

the trade. If the trade does not fulfil the anticipated utility, the rate of loss aversion will

change. If the trades utility is below the anticipated utility the individual's loss aversion will

increase and vice versa (Lindsay, 2019).

When a given strategy is played successfully it increases the probability for this strategy to be

played again. An individual has a degree of loss aversion that affects his or hers expected

gains from trades that involve risk, which in turn affects the individual's willingness to trade.

If the trades payoff is larger than anticipated, the individual will in all likelihood be less loss

averse and more open for future trades (Lindsay, 2019).

The third component that was just mentioned has also been researched by Novemsky and

Kahneman (2005), they explore the assumption that when goods are traded for the expected

price loss aversion does not exist. The reason behind this is because the traded good fulfils

the expected utility, with this argument Novemsky and Kahneman (2005) states that loss

aversion does not exist in routine transactions since the utility will always be equal to the

anticipated utility (Novemsky, Kahneman, 2005).

2.3.3 Research on non-constant loss aversion

Wang et.al (2016) tested the impact that culture has on loss aversion. The study found

different parameters for the loss aversion for potential losses of 25$ and 100$ in a 50/50

gamble. The results show that loss aversion is significantly different (p < 0,001) (Wang et.al,

2016). Barsky et. al (1997) also states that people's preference parameters could differ due to

sensitivity toward the size of the potential loss (Barsky et. al, 1997). Wang et.al (2016)

further found that culture could affect the degree of loss aversion an individual possesses

(Wang et.al, 2016).

Moreover, research by Rau (2014) shows that there is a difference between the male and

female gender when it comes to loss aversion, and that females behave less loss averse than

males (Rau, 2014). Schmidt and Traub (2002) also concluded that there were differences in

loss aversion between genders. Female subjects seemed to be more loss averse than male

subjects (Schmidt, Traub, 2002).

2.5 Endowment effect

The endowment effect theory states that a given good in your possession is deemed more

valuable than the same good if it has not yet been acquired. In other words, you would

require a higher price to sell the good than you would be prepared to pay for it (Thaler, 1980).

Thaler (1980) gives an example of the endowment effect:

“Mr. R bought a case of good wine in the late '50's for about $5 a bottle. A few

years later hxs wine merchant offered to buy the wine back for $100 a bottle. He

refused, although he has never paid more than $35 for a bottle of wine. “

- Thaler 1980

Chatterjee et.al (2013) argue that there are two major driving factors behind the endowment

effect which are loss aversion and ownership. The loss aversion part of the endowment effect

has the focus on the reference point. The reference point is whether you own the good or not.

Owning the good means that selling it is regarded as a loss and not owning it means that

buying the good is seen as a gain. Since losses weigh heavier than gains the selling price will

be higher than the price individuals are willing to purchase it for. The other major part of the

endowment effect is ownership (Chatterjee et.al, 2013). The authors give the following

reasons to why ownership is a part of the endowment effect:

“Two principles on which the ownership account of the endowment effect is built

are: (1) people get attached to what they own, that is, people’s possessions

become a part of themselves (Beggan 1992; Belk 1988; Dittmar 1992) and (2)

most people have a positive attitude toward themselves (Brown 1998; Steele

1988), and, thus, they are likely to see their possessions, which are associated

with the self, as attractive (see “the mere ownership effect”; Beggan 1992).”

- Chatterjee et.al, 2013

2.6 Mental accounting

Mental accounting (MA) is a part of behavioural economics where according to theory,

behaviour patterns in savings are analysed. Here saving indicates that an individual will

prioritize future spending to present spending (Shefrin, Thaler, 1988). MA is based on the

assumption that the value of money varies from individual to individual. One reason for this

is that the perception of money varies depending on how it is acquired and on what the

money is ment for (Thaler, 1990). For example, if you have worked hard to obtain a

paycheck, parting with that money will feel like a larger loss than money that you have been

given or acquired by chance (Thaler, 1985).

According to Yuntong et.al, MA can be divided into three divisions. The first one is how

something is funded, for example if it is funded by normal earnings or windfall. Windfall is

money that you have acquired “easier” than normal earnings and can be anything from

money that you have been given or that has been won by chance. The second division is

called consumer item which for example could be food expenditures, luxury expenditures or

entertainment expenditure. The third and last division of MA is saving patterns. Yuntong et.al

(2013) gives the following example to explain saving patterns (Yuntong et.al, 2013)

“people divide their wealth into fixed accounts and interim accounts on the basis

of their saving goals, and generally do not transfer money from the fixed account

in order to meet temporary consumption demands”

- Yutong et.al 2013

To summarize MA with an example we can take Tversky and Kahneman's experiment about

two similar scenarios, a jacket and a calculator.

“Example A. Imagine that you are about to purchase a jacket for $125 and a

calculator for $15. The calculator salesman informs you that the calculator you

wish to buy is on sale for $10 at the other branch of the store, located 20 minutes

drive away. Would you make the trip to the other store?

Example B. Imagine that you are about to purchase a jacket for $15 and a

calculator for $125. The calculator salesman informs you that the calculator you

wish to buy is on sale for $120 at the other branch of the store, located 20

minutes drive away. Would you make the trip to the other store?

Most people would make the travel in example A, but not in example B, indicating

that saving five dollars on a $15 purchase is perceived as more valuable than

saving five dollars on a $120 purchase.”

- Tversky, Kahneman, 1981

The evidence from research on the mental accounting topic have shown that a mental

categorization of expenses is present in a lot of different decisional situations. Entertainment

expenses for example are being tracked against previous expenses for the same purpose, i.e a

previous purchase of a sports game ticket makes another purchase of a ticket for sports or

another form of entertainment less desirable. This effect can be observed since these ticket

expenses are drawn from the same mental account (Hossain, 2018).

3. Method

3.1 Quantitative vs. qualitative method

When researching either a quantitative or a qualitative method can be applied. One of the

biggest differences between quantitative and qualitative research is that qualitative research

puts an emphasis on words while quantitative research has more focus on numbers. They

both also have a different relationship to theory. Quantitative method is deductive towards

theory and qualitative method is inductive (Bryman, Bell, 2005).

The method used in this research is quantitative. A hypothesis has been built from the theory

to test a certain phenomenon. The research that is going to be conducted is a testing of

existing theory which is a deductive way of handling theory. The approach taken in this

research to compare loss aversion for different magnitude of losses is a parametric approach.

The focus is on what the required win is for taking the risk of losing a certain amount of

money. Since the focus is on the amount itself and not the reasoning behind why that amount

is required, the quantitative method is more suitable in this case. A qualitative approach could

perhaps be more suitable if the purpose was to research why a certain individual would

require a certain amount to bear the risk of losing.

3.2 Survey vs. structured interviews

The process of gathering data is mainly split into structured interviews and surveys (Bryman,

Bell, 2017). In this thesis the data will be gathered from a digital survey. The choice of a

survey instead of structured interviews was made because of the time restriction in this thesis

since a survey would be the most effective way to obtain a larger sample. The initial idea was

to make both a digital and physical survey, but due to the Covid-19 physical surveys were no

longer an option.

There are both advantages and disadvantages with a survey method compared to structured

interviews. One disadvantage is that while answering a survey, subjects won't be able to ask

questions if they deem something unclear. Therefore, the survey needs to be comprehensible

with questions that are easy to answer. This minimizes the room for misinterpretation and

omitted answers. Short predetermined answers i.e. multiple choice are preferable to open

answers since it reduces the risk of subjects to tire and answer all questions or in the worst

case scenario they do not answer the survey at all (Bryman, Bell, 2017).

Another advantage that a survey has is that it is cheaper and less time-consuming to conduct

than interviews, but the response time to gather the data can be longer. A further advantage

with surveys is that the so-called “interviewing effect” is not present. The interviewing effect

is that the interviewers ethnic background, gender, social background and emphasizing on

key words can affect the answers of the subjects (Bryman, Bell, 2017).

There is a larger risk of respondents giving dishonest and incomplete answers in a survey

than in interviews (Bryman, Bell, 2017). One additional advantage that a survey has which is

extra beneficial during the existing pandemic is that it is easier to adapt a survey to the

subjects' needs since they can answer the survey where and whenever they want. Having a

survey for gathering the data also has some disadvantages. Since surveys try to avoid open

answers, follow-up questions become a lot harder (Bryman, Bell, 2017).

Another disadvantage is that in a survey all the questions are available at once, this makes a

specific order that the subject has to answer impossible to regulate. This leads to the

questions no longer being independent from each other. Other things that are important are

anonymity as well as clear instructions and an attractive layout, to increase the chance of

more truthful answers and increase the response rate. Surveys also generally have worse

response rates than interviews. Response rate can be increased by distinct questions phrasing.

It can also be increased by short and easy answers in a language that respondents are fluent in

(Bryman, Bell, 2017).

3.3 Sample

The population targeted in this research are economics students at Linnaeus University in

Växjö Sweden. This population is chosen mainly because of accessibility to the subjects.

Since we are studying at Linnaeus University, we would have easier access to acquire data

from economics students at our university than in other locations. This due to our connections

with teachers that can help us to distribute the survey and connections to other fellow

students. Another reason that economics students at Linnaeus university are chosen as the

population from which we draw our sample is that they have similar previous education, age

and monthly income. In addition to this, some earlier studies in behavioural finance by for

example Tversky and Kahneman (1979) and Kahneman, Tahler and Knetsch (1990) have

also used students at universities in their research.

Bryman & Bell (2005) describe two different types of sampling techniques, probability

sampling and non-probability sampling (Bryman, Bell, 2005). In this research non-

probability sampling will be used due to time and budget constraints.

There are three main non-probability sampling techniques, convenience sampling, snowball

sampling and quota sampling. First there are a few things that are important to keep in mind

when using a non-probability sample. The fact that the whole population does not have the

same probability of being chosen in the sample has implications when we will interpret the

answers from the research. Especially concerning convenience sampling and snowball

sampling the results can not be generalized since the population it reflects can not be

identified. This does not mean that this type of sampling is inherently bad or useless. We can

not generalize results across a whole population, but it works well as a preliminary research

which can be further developed (Bryman, Bell, 2005).

The sampling technique we are applying is mainly convenience sampling and snowball

sampling. However, the choice of doing a probability sample would give us the ability to do a

generalization of the results across all economics students at Linnaeus university in Växjö.

Unfortunately, we do not have access to all the students which makes it very hard and time-

consuming for us to take a sample from all economics students. This is why the use of

convenience sampling and snowball sampling is applied in our study. Therefore, there will be

mainly MBA students in the sample because it is the most accessible and most populated

group at the university. This will as mentioned earlier make it impossible for us to generalize

the results from our study across the population, but our result can still be useful for future

research on the topic.

3.4 Constructing a survey

3.4.1 Visual representation

There are a few factors to keep in mind concerning the layout of the survey in order to get a

better response rate. According to Bryman & Bell (2005) a survey should not be too long, it

should be kept as short as possible so respondents do not get deterred by the size of the

survey. At the same time, a well worked and professional layout is important too. A survey

that is too dense in order for it to be short may deter the respondent because it looks like the

survey is hard to answer when the text is small and the lines are squeezed too tight together

(Bryman, Bell, 2005).

With this in mind a large focus has been put into constructing a short and concise survey. The

total amount of questions mounts up to ten, four control questions for age, gender, income

and savings and then six questions for the measurement of loss aversion. The relatively low

amount of questions enables us to have a survey that does not have to be dense in order to not

look too massive.

Further the authors explain that having a certain font for each different kind of text in the

survey is important, i.e. one font for headlines, one for the questions, one for the headings

and so on. The use of the same font between different kinds of text may even confuse the

respondent (Bryman, Bell, 2005). There are relatively few instructions and headlines in the

survey but in order for respondents to not miss the instructions for the loss aversion questions

they have been set to a different font to highlight its importance.

3.4.2 Question order

Dean Lacy (2001) states that the order of questions in a survey can affect the responses. Each

question has a certain effect on the subject. Different questions activate a specific thought

process and certain stored information, which then affect answers in the following questions

(Lacy, 2001). This is certainly an important part that has been considered in the construction

of the survey. The question order in the survey is the lowest potential loss to the highest.

Considerations of having the potential losses in random order have been made but feedback

received from test-subjects have led to the conclusion that there was too big of a risk for

confusion with a random question order.

Other important factors to think of concerning question order is that the survey should start

off with the easier questions to answer, questions that may be sensitive to answer for

respondents (i.e. income) should be asked close to the end of the survey (Harrison, 2007).

Harrison says that questions about income should preferably be asked later in the survey.

However, deviations from this recommendation have been made in the survey construction in

order to avoid confusion and misinterpretation. Feedback in the test-surveys indicated that

subjects in this case would prefer this type of question in the beginning of the survey.

3.4.3 How to ask questions

When writing survey questions, it is important that every respondent can understand the

question and that all respondents understand it in the same way (Dolnicar, 2013) & (Harrison,

2007). To accomplish this Dolnicar (2013) and Harrison (2007) says that things such as

technical terms and acronyms, the use of long or complex sentences and nonspecific

questions should be avoided (Dolnicar, 2013) & (Harrison, 2007). Furthermore Harrison

(2007) also mentions that strong words should be avoided. With strong words he refers to

words that are leading, emotionally loaded or evocative (Harrison, 2007).

Moving on to response options there are two main options that can be chosen for survey

experiments, open-ended or closed-ended questions. The main advantage of an open-ended

question is that it allows for more variety in the answers of the questions and no influence

from different given response options is placed on the respondent. When using closed-ended

questions the response options must include all possible answers, so respondents do not have

to choose an answer which is not their preferred answer (Dolnicar, 2013). Harrison (2007)

further explains that the use of good closed-ended questions lessens the risk of different

interpretations of the survey questions (Harrison, 2007).

Bryman & Bell (2005) further explains that for closed-ended questions the answers can be

presented vertically or horizontally. Having vertical answers is in most cases the preferred

choice. It distinguishes the different answers from each other in a more distinct way whilst it

at the same time makes coding of the answers easier (Bryman, Bell, 2005).

3.4.5 What is being measured

Most researchers agree that the definition of what is being measured has to be clear in order

to develop good survey questions. However, guidelines on how this should be done have

been hard to come by. Dolcinar (2013) highlights three elements specified by Rossiter (2011)

that are key in the definition of what is being measured (Dolcinar 2013):

“1. the rater (the person being asked),

2. the object (the object under study), and

3. the attribute (what exactly about the object will be studied).”

- Dolcinar 2013

If either the object, the attribute or both contains more than one component or if there are

some kind of ambiguity two more elements need to be specified according to Rossiter (2011)

(Dolcinar, 2013):

“1. the rater

2. the object

3. the components of the object

4. the attribute

5. the components of the attribute”

- Dolcinar 2013

The survey used in this research has the respondents as the rater, loss aversion is the object

under study and changes in loss aversion for different magnitudes of a potential loss is the

attribute.

3.5 Test survey

To make sure that the data obtained from the survey would be possible to analyse and that

the subject interpreted the questions as they were intended, the survey was tested on two

different occasions.

The first test survey was sent out to ten test subjects to see how they interpreted our questions

and to give us feedback. From the first test survey a lot of feedback was acquired. The

subjects deemed the surveys title as confusing and they felt a decrease in their interest. The

test subject also thought that it was unnecessary to have the survey in English since all of the

subjects are fluent in Swedish, they thought that a Swedish survey would leave less room for

misinterpretation. Another issue was that questions were experienced as too similar, this led

to a “pattern” in how they answered. Test subjects felt that after the first two questions they

had decided what to do after a positive or a negative change in their wealth. The phrasing of

the questions and the survey in general had too much room for interpretation. The subjects

also felt that a fixed reference point like in question 1 (appendix 9.1) would help them to

understand the question better.

The most consistent feedback was that we should have multiple choice questions instead of

open answers since it is more compelling and easier to answer. To quote one of the subjects

“It felt more like I was taking a test than answering a survey, and therefore my initial feeling

was that I didn't want to finish it”.

After reconstructing the survey with regards to the feedback received on the first draft of the

survey, another reworked draft of the survey was sent out. The second draft was sent out to

the same ten test subjects to give feedback on their interpretation of the questions. This led to

some minor adjustments in the phrasing of the questions. After these minor adjustments the

questions in the survey are interpreted as intended.

3.6 The Survey

The questions in this survey have been constructed on the basis of two sources, “The impact

of culture on loss aversion” by Wang et.al (2016) and “Advances in Prospect Theory:

Cumulative Representation of Uncertainty” by Tversky and Kahneman (1992). Tversky and

Kahneman specified that a parameter of loss aversion could be estimated by dividing the

required win with the potential loss in a 50/50 gamble, i.e. a coin toss. If the potential loss is

100$ and the required win for a certain individual in order to accept the bet is 250$, the loss

aversion parameter is:

This approach was applied in the study by Wang et.al. In their research individuals were

asked how much the win would have to be in order to accept a bet with a 50 percent chance

to lose 25$ and 100$ respectively.

“Y should be at least $____ to make the lottery acceptable.”

Figure 4 Illustration of survey question from the study by Wang et.al (2016)

The required win would then be divided by the loss to obtain the loss aversion parameter for

each individual. In their questions, open answers were used where respondents would state

their required win in order for them to see the bet as acceptable (Wang et.al, 2016).

The questions used in this survey research are somewhat different. Instead of open answers,

predetermined multiple choice answers that respondents can choose between is used. This

change has been made largely due to feedback received from test subjects, but it is also a

recommendation by Bryman & Bell (2005) to use multiple choice answers over open

answers. The respondents are faced with six different situations stated as the question below:

D. För en sannolikhet på 50% att förlora 1.000 kr kräver du en vinst på lägst:

❒ 0 - 1.000 kr

❒ 1.000 - 1.500 kr

❒ 1.500 - 2.000 kr

❒ 2.000 - 2.500 kr

❒ 2.500 - 3.000 kr

❒ 3.000 +

Respondents have a 50 percent chance to lose 1000 kr in a coin toss. Instead of open answers,

required wins are stated in intervals. The respondents select the interval which contains their

required win in order to accept the bet. One immediate drawback with this compared to the

study by Wang et.al (2016) is that we can not get a precise parameter of loss aversion since

the answers are within certain intervals. If the answer for a given individual in the question

above is 2000 - 2500 the loss aversion parameter is between 2 - 2,5 but knowing if it is 2,1 or

2,4 is impossible. If the analysis shows that there are differences in the distribution of

answers over different magnitudes of the potential loss it will be interpreted as a difference in

loss aversion parameter, but the exact difference will not be possible to determine.

Another potential problem that could be discussed is the intervals chosen in the answers.

What are the appropriate intervals? The reason for this survey’s intervals is fairly simple.

Kahneman, Knetsch, Thaler (1991) proposed a 2:1 relationship between gains and losses.

This would indicate a loss aversion parameter of 2. The answers in this survey have three

alternatives lower than the 2:1 relationship and three answers higher than the 2:1 relationship.

To conclude the answers are constructed in order for the proposed loss aversion parameter of

2 to be in the middle of the possible answer alternatives.

Concerning the question itself the word probability has been chosen over the words chance

and risk which could otherwise have been used. These two words were omitted because they

are suggestive to people and can have different meaning to respondents. The word risk could

be negatively associated, and chance can be positively associated. Probability is a more

neutral word which lowers the risk of influencing respondents’ answers. The probability of

50 percent to lose and to win have been applied partly because it was used in the study by

Wang et.al (2016) and because the 50/50-coin toss is a relatively easy hypothetical situation

to relate to.

3.6.1 Distribution of the survey

This survey will be distributed through Linnaeus Universities webpage Mymoodle to the

MBA programs year one and two on their course forums. Year one and two on the MBA

program were selected due to their larger number of students compared to other classes in the

department of economics. The distribution has also been made through two separate MBA

program groups on the social media platform Facebook, where only second and third years

MBA students are members. The reason behind using social media and Mymoodle was to

gather as much data as possible during the current circumstances of the pandemic.

3.7 Null hypothesis

3.7.1 Friedman Test

H0: There are no significant difference between the distributions (D)

(D1=D2=D3=D4=D5=D6)

H1: At least one of the distributions (Di) are different from another (Dj) (Di ≠ Dj)

3.7.2 Post Hoc Test (Wilcoxon test)

H0: There are no significant difference between the distributions (D) (Di=Dj)

H1: At least one of the distributions (Di) are different from another (Di ≠ Dj)

3.8 Choice of analysis

This research produces dependent samples since the six different distributions of interest are

drawn from the same subjects. Since the distributions are dependent, the choice of statistical

test is narrowed down. The distributions will first be tested for normality to see if they are

normally distributed. The tests for normality that will be used are the Kolmogorov-Smirnov

test and the Shapiro-Wilk test. The test used in order to test the null hypothesis is a Friedman

test. The Friedman test does not assume a normal distribution nor homogeneity in the data. It

is used to analyse multiple related samples, data that are drawn from the same subject on

multiple occasions and it is typically used to analyse ordinal data (Sheldon, Fillyaw,

Thompson, 1996).

Other research on the subject such as Wang et.al (2016) and Rau (2014) have used ANOVA

and Mann-Whitney tests respectively. This research has more than two distributions to

compare which excludes the Mann-Whitney U test but leaves us with the possibility of

performing a repeated measures ANOVA test (Anderson et.al, 2017). The problem is that

ANOVA assumes a normal distribution and the distributions in this data are not normally

distributed (Ruthford, 2000). This leaves us with the option of doing a Kruskal-Wallis test or

a Friedman test. The Kruskal-Wallis test is not suitable because it assumes independent

samples (Anderson et.al, 2017). This concludes that the Friedman test is the test that suits the

data since it can handle both non normal distributions and dependent samples. A disclaimer

should be made about the chi square test too. The reason for not using a chi square test is that

this research does not seek to compare the results to any hypothetical value (Rana, Singhal,

2015). It is strictly aimed at looking for differences in loss aversion between different

potential losses.

The data collected in the survey are multiple choice answers within certain intervals. We can

not know the exact answer that has been given, only which interval it lies within. Therefore,

the answers are ordinal and in the analysis each answer corresponds to a number on the

ordinal scale of one to six, with one being the lowest interval and six the highest.

1. ❒ 0 - 1.000 kr

2. ❒ 1.000 - 1.500 kr

3. ❒ 1.500 - 2.000 kr

4. ❒ 2.000 - 2.500 kr

5. ❒ 2.500 - 3.000 kr

6. ❒ 3.000 +

There are also six distributions to be compared which makes us unable to use a regular

Wilcoxon test without significantly lowering the statistical power of the analysis (Wild,

1997), all these tests will be performed in SPSS. What the Friedman test does is that it allows

us to test for differences between all six distributions in order to see if any of the distributions

are significantly different from any of the other.

When the Friedman test has been performed a post hoc test is run to see where the differences

are between the distributions. This post hoc test is a Wilcoxon test where all distributions are

compared pairwise in order to determine which of them significantly differs from each other.

The pairwise tests p-value are then compared to the α=0,05 with a Bonferroni correction.

The Bonferroni correction can be used when conducting many dependent or independent

statistical tests simultaneously. The correction takes the number of tests into account and

lowers the α in order to reduce the risk of type 1 errors (Goldman, 2008). For example, in this

research the α was 0,05 and 15 tests were made. With the Bonferroni correction α(0,05)/n(15)

the p-value would need to be less than 0,003 to reject the null hypothesis. Two disadvantages

to keep in mind while performing the Bonferroni correction is that the method can be

considered unnecessarily conservative and the adjusted α will in most cases be smaller than

necessary. This leads to a reduction in type I errors but the risk of making a type II error

increases (Lee, Lee, 2018).

4. Result

Loss aversion is a part of the prospect theory suggested by Tversky and Kahneman (1979).

They observed that losses had more impact on decisions than gains. People have a reference

point which is most often the status quo to which different prospects are evaluated (Tversky,

Kahneman, 1991). A 2:1 weighting relationship between losses and gains have been observed

in experiments with smaller gains and losses (Kahneman, Knetsch, Thaler, 1991).

However, Wang et.al (2016) did a study of the impact of culture on loss aversion. This study

showed that there was a statistically significant difference between the loss aversion

parameter when potential losses were set to 25$ and 100$ respectively (Wang et.al, 2016).

Barsky et. al (1997) also states that people's preference parameters could differ due to

sensitivity toward the size of the potential loss (Barsky et. al, 1997). This was indeed also

noted in the research of Wang et.al (2016) because a difference in loss aversion was detected.

This indicates that loss aversion is not a constant but that it changes depending on the

magnitude of the potential loss.

This research will examine how young individuals' loss aversion changes over different

magnitudes of potential losses ranging from 100 kr - 4 000 kr when there is equal probability

of winning or losing a gamble.

After removing the uncompleted survey answers we had a total of 111 survey responses (N),

and the test had 6 questions which gave us a degree of freedom of 5 (n-k). First a test for

normality was carried out on all six distributions to test if they are normally distributed or

not.

Since all p<0,001 < α=0,05 we can reject the null hypothesis that the distributions are

normally distributed at a five percent significance level. At a five percent significance level,

we can say that none of the distributions are normally distributed.

The null hypothesis was tested on a five percent significance level by a Friedman test to see if

the distributions of the required wins differed between the magnitude of potential loss.

The observed p-value is smaller than alpha, p<0,001 < α=0,05, therefore we reject the null

hypothesis at a five percent significance level. According to the Friedman test we can say that

at a five percent significance level, at least one of the distributions is different from another

(Di ≠ Dj) i.e. different loss aversion.

When the Friedman test showed statistical significance on differences between at least two

distributions we performed a post hoc test. The post hoc test is performed in order to identify

which distributions are significantly different from each other. The post hoc test that has been

performed is a Wilcoxon test with a Bonferroni correction.

All the post hoc tests can be seen in appendix 4, ten of the fifteen tests showed significant

difference between the distributions. For the purpose of not making this part too long the five

tests that did not show statistical significance will be presented.

Test for differences between distributions of the potential loss of 2000 and 4000

The observed p-value is larger than alpha, p = 0,207 > α/n = 0,003, therefore we do not reject

the null hypothesis at a five percent significance level. According to the Wilcoxon test we can

not say that there is a significant difference in loss aversion between the potential losses of 2

000 and 4 000 at a five percent significance level.

Test for differences between distributions of the potential loss of 1000 and 4000

The observed p-value is larger than alpha, p = 0,016 > α/n = 0,003, therefore we do not reject

the null hypothesis at a five percent significance level. According to the Wilcoxon test we can

not say that there is a significant difference in loss aversion between the potential losses of 1

000 and 4 000 at a five percent significance level.

Test for differences between distributions of the potential loss of 1000 and 2000

The observed p-value is larger than alpha, p = 0,056 > α/n = 0,003, therefore we do not reject

the null hypothesis at a five percent significance level. According to the Wilcoxon test we can

not say that there is a significant difference in loss aversion between the potential losses of 1

000 and 2 000 at a five percent significance level.

Test for differences between distributions of the potential loss of 500 and 1000

The observed p-value is larger than alpha, p = 0,008 > α/n = 0,003, therefore we do not reject

the null hypothesis at a five percent significance level. According to the Wilcoxon test we can

not say that there is a significant difference in loss aversion between the potential losses of

500 and 1000 at a five percent significance level.

Test for differences between distributions of the potential loss of 100 and 250

The observed p-value is larger than alpha, p = 0,135 > α/n = 0,003, therefore we do not reject

the null hypothesis at a five percent significance level. According to the Wilcoxon test we can

not say that there is a significant difference in loss aversion between the potential losses of

100 and 250 at a five percent significance level.

In total fifteen pairwise post hoc tests were carried out and ten of these pairs showed

differences in loss aversion that was statistically significant at a five percent significance

level.

5. Discussion

One of the questions of interest in this research is if loss aversion is constant for different

magnitudes of potential losses. Shalev (2002) proposed a model for utility using a constant

loss aversion factor which was the same across different reference outcomes. Our result

indicates that the loss aversion is not constant across different magnitudes of potential losses.

This is more in line with the research by Wang et.al (2016) that found different loss aversion

parameters for potential losses of 25$ and 100$ respectively. The difference between these

two potential losses are also detected in this research. The post hoc test conducted shows that

there are significant differences in the loss aversion parameter between 250 kr and 1000 kr

which is roughly the same amounts as 25$ and 100$.

Just like Kahneman and Tversky (1979) we observe that the answers to our questions are not

in line with what the EUT predicts. A choice is acceptable if it adds utility to the existing

asset (Häckel, Pfosser, Tränkler, 2017). According to the EUT a win of 500-750 kr with a

corresponding loss of 500 kr yields a positive expected utility for every possible win in the

interval except 500 kr. However, this is not what is being observed in the data gathered from

the survey. If subjects were to answer in accordance with the EUT the larger part of the

answers given would be in the second interval (see Appendix 9.3). That answers are not in

line with the EUT was to be expected since losses and gains are weighted differently in

prospect theory. The increase in loss aversion when potential losses increase could indicate

that the weight put on losses increases with the magnitude of the loss. This would be

rationalized by the notation from Barsky et.al (1997) where they stated that preference

parameters of individuals could be sensitive to the magnitude of the money at risk. However

it is important to clarify that this is not an invalidation of EUT. EUT is a very useful and

important part of economic theory but it does not seem to work as a predictor of decision

making under risk.

Furthermore, the main question of interest in this research is how young individuals' loss

aversion changes towards different magnitudes of a potential loss when there is equal

probability of winning or losing a gamble.

A statistically significant difference was found in the loss aversion towards the losses in pair

C (see table 1) but no significant differences in loss aversion towards the losses in pair D, E

and F respectively could be detected. This could be explained from a perspective of

diminishing sensitivity. Kahneman and Tversky (1991) defines the concept of diminishing

sensitivity by stating that individuals are less sensitive to a given change when the change

occurs further away from the reference point. The increase in potential loss is smaller in pair

C (750) than the increase in potential loss in pair D (1 000), E (3 000), and F (2 000) but there

is no statistically significant difference in loss aversion for the losses in the three latter pairs.

Since the difference between the two losses are larger in the three latter examples,

diminishing sensitivity could explain why no significant difference is found in loss aversion

between the larger losses. It could also be explained from a mental accounting perspective.

Kahneman and Tversky (1981) gave an easy to understand example of the mental accounting

effect by illustrating how a 5$ discount is perceived as more valuable on a 15$ item than on a

125$ discount. This could be a possible explanation for the observed behaviour. The

difference between the losses in pair C is perceived as more significant to the subject than the

difference between the losses in pair F. However, the change itself in absolute monetary

terms is smaller (750<2 000). The relative change in pair C is larger than the relative change

in pair F (750/250>2 000/2 000). A view from this perspective might suggest that part of the

evaluation of risky prospects is based on relative differences rather than absolute differences.

However, we have to be cautious when making this kind of interpretation since no significant

difference was found in loss aversion towards a potential loss of 100 kr and 250 kr (pair A,

table 1). The relative difference between the losses in pair A is bigger than it is in pair F

(150/100>2 000/2 000) but both are non-significant in terms of differences in the loss

aversion parameter. Further a significant difference in loss aversion towards the losses in pair

B were found. The relative difference between the losses is the same in pair B and pair F

(250/250=2 000/2 000) and smaller than in pair A (250/250<150/100) but yet differences in

loss aversion were found. This can be seen from three perspectives. Firstly, it could be

regarded as an anomaly in the data and a larger sample would reveal a clearer pattern.

Secondly it could also mean that this explanation for the observed behaviour is not feasible

and it is not possible to find a clear and suitable explanation from the theoretical framework

in this research. Thirdly it could indicate that they have paid poor attention to the question

and answered without giving it a real thought.

The results could be further discussed by looking for a certain breaking point in which the

increase in loss aversion flattens out. We observe statistical differences in loss aversion

towards the losses in pair C (Table 1) but not in pair E even though the relative size

difference in the potential loss is the same (1 000/250=4 000/1 000). This could maybe

indicate that there is a breaking point somewhere in the neighbourhood of 1 000 kr for our

subjects where the increase in the loss aversion parameter slows down considerably. This

argument is strengthened by the fact that there was a significant difference between a loss of

500 and 2 000 (2 000/500=4 000/1 000) but the breaking point itself would most probably

differ based on economic situation when the theoretical framework is considered. However,

this can not be concluded without further research. An important thing to acknowledge is that

the post hoc test used to detect where these differences has been performed with a Bonferroni

correction which increases the risk of making a type II error (Lee, Lee, 2018). With this in

mind, there could be a difference in loss aversion towards the losses in pair F that is

overlooked due to the conservatism of the Bonferroni correction.

Moreover, the observed increase in loss aversion between smaller and larger potential losses

could be related to the status quo bias. The status quo bias according to Kahneman, Knetsch

and Thaler (1991) is a concept very much related to loss aversion. Individuals are unwilling

to deviate from their status quo which is their current state. The reason behind this is that

negative outcomes of leaving it is given a higher decision weight than the corresponding

positive outcomes. Since a larger loss also entails a larger deviation from the status quo

individuals are more reluctant to accept the risk of losing and deviate from the status quo by

requiring a higher compensation. The higher decision weight given to losses is reflected in

the higher loss aversion observed when bigger potential losses are considered.

While considering possible interpretations to the results from this study it is important to keep

in mind that these results can not be generalized. They are only applicable to the subjects in

this study due to the sampling not being random but since a lot of the results are in line with

what the theoretical framework suggests it strengthens the reliability of the results.

Concerning the gathered data, this research was performed during the covid-19 pandemic

which could have influenced individuals answers in the survey. How the data has been

influenced by the pandemic is something that is not possible to determine. It is possible that

the pandemic has influenced the risk preferences of the subjects which we can not control for.

Preferences might have been influenced so that greater loss aversion is seen towards potential

losses due to uncertainty. The opposite effect can not be excluded either. There is a

possibility that some people may be less loss averse and differences that could otherwise be

observed are not observed in this research. To conclude there are a lot of possible effects of

the pandemic that could have affected the results in this study, but the determination of these

effects is a question for future research.

Another aspect that should not be ignored when discussing the survey responses is mental

accounting. Since all of the subjects in this research are students, the probability that some of

the subjects have gone directly from studying at the senior high school to starting their

university education is rather high. This would mean that unless they are working part time

on weekends, evenings or during the summer their money could be seen as being acquired

easier than through regular hard work. The majority of most students' income comes from

student grants and loans with very favourable terms. Students that haven't obtained a

paycheck could be less loss averse since they might experience less of a loss when parting

from money. This due to the fact that their money has been acquired easier than from a

regular paycheck, and spending that money is deemed as easier. This reasoning is based on a

study by Thaler (1990) where he states that the perception of money varies depending on how

it is acquired and on what the money is ment for. Thaler (1985) exemplifies this with the

following statement: if you have worked hard to obtain a paycheck, parting with that money

will feel like a larger loss than money that you have been given or acquired by chance.

Another thing to keep in mind while reading these results is that this research is based on

hypothetical situations while the theory is trying to describe real-life decision-making

behaviour. In a hypothetical situation the subject's answer does not entail any consequences.

This could lead to answers being different from what would be observed in real life

investments. Another aspect is that this survey could be seen as a game by respondents of it

and therefore not enough thought to their answer is given, which would hide their true

preferences. A third possibility is that the subject has answered the survey truthfully and

revealed their true preferences. The subjects do not have any real incentives to give dishonest

answers. All of these views could be true and should be considered as possible reasons to

why these answers have been given.

The gender effect could also be discussed since 60% of the subjects were males. According to

Rau (2014) men generally have a lower loss aversion. Rau (2014) did not research how the

change between male and female subjects' loss aversion changed with the magnitude of

potential loss. Since we have no clear indications of whether this inequality in responses

between genders could affect the results of the study the possibility that it has some kind of

effect on the results can not be discarded.

Since we have discussed that gender could affect the loss aversion, we will discuss the

potential effect that income and current state of wealth could have. For an individual with an

income of more than 20 000 kr per month the risk of losing 1000 kr might not have as big of

an impact on the individual’s economic situation as for an individual with a lower income.

The same thing can be said for an individual's total savings. A loss of 1 000 kr might not have

the same economic impact for an individual with total savings of more than 250 000

compared to an individual with total savings of less than 100 000. There is a possibility that

individuals with significantly different economic situations have similar preferences towards

smaller losses but differ towards larger losses or that preferences could differ towards all

losses, since different states of wealth entails different reference points according to Tversky

and Kahneman (1991).

6. Conclusion

This research was aimed to examine how young individuals' loss aversion changes over

different magnitudes of a potential loss when there is equal probability of winning or losing a

gamble based on a survey experiment. Based on the survey experiment and the statistical

analysis performed, loss aversion changes when potential losses increase in a coin toss

scenario. A difference in loss aversion is detected between the smaller and the larger losses

which indicates that loss aversion is not constant. This result is in line with previous research

that has shown differences in loss aversion toward different magnitudes of a loss.

Moreover, the analysis showed that an individual's loss aversion is less sensitive to increases

in potential losses when losses are further away from the reference point. Differences are

observed in loss aversion between the smaller and larger potential losses examined. When

only the larger potential losses are considered on the other hand (1 000, 2 000 and 4 000 kr),

this research could not determine a significant difference in loss aversion. This could indicate

a possible breaking point around the 1 000 kr mark for students in the same economic

situation as our subjects.

Overall these results are in line with what theory predicts. However, the theoretical

framework is not conclusive concerning a potential breaking point in loss aversion, but this

area has to be further researched to make a decisive conclusion about any breaking point. It is

important to keep in mind that these results can not be generalized due to the sampling

technique. However, the results seem plausible since they from most aspects are in line with

what the theoretical framework suggests.

7. Further research

Further research that can be done with this thesis is to conduct qualitative research or

quantitative research with structured interviews instead of surveys. If the data obtained would

be the exact amount of money required to bear a 50 percent risk of losing any given amount

the results could be more detailed. A loss aversion parameter could then be calculated since

the uncertainty of where in the interval the answers of each individual lies would be

eliminated. This would also make it easier to do comparisons to previous works in a more

conclusive way.

One of the more obvious ways this research could be extended is to do the research on a

broader population with a random sample. This research is aimed at economics students at

Linnaeus University, but the sampling method narrows it down even more and takes away the

generalizability. A random and larger sample would provide a smaller margin of error while

at the same time making it more generalizable thus give the conclusion even more reliability.

Further research could also be extended to a comparison of loss aversion, or if loss aversion

changes differently in two different populations. This could be a way to see if the results

found in this research can be generalized to a broader population. This comparison could be

between students and middle-aged workers, young and old people, high- and low-income

workers etc.

Another extension of this research could be for future research to study how the Covid-19

pandemic affected the loss aversion since we can not be certain if it has affected the results or

not. Future research could compare their results to this study to research how a pandemic

crisis could affect individual’s loss aversion.

8. Sources

8.1 Literature

Kahneman, Daniel (2011). Thinking, Fast and Slow. United States of America: Farrar, Straus

and Giroux. 978-0-374-53355-7

Pp. 260-268

Bryman, Alan & Bell, Emma (2019). Företagsekonomiska forskningsmetoder. Edition 3.

Stockholm: Liber AB. 978-91-47-11207-4

Pp. 238-246

Bryman, Alan & Bell, Emma (2005). Företagsekonomiska forskningsmetoder. Edition 1:1.

Malmö: Liber AB. 91-47-07510-4

Pp. 109-131, 161-170

Rutherford, Andrew (2000), Introducing Anova and Ancova : A GLM Approach, Edition 1.

SAGE Publications, London. ISBN 9780761951605

Pp. 125-126

Anderson, D.R., 2017. Statistics for business and economics: Edition 4. Andover: Cengage

Learning. 978-1-4737-2665-7

Pp. 554-577

8.2 Handbook/Survey instructions

Mongin, P. (1997). Expected Utility Theory. In J. Davis, W. Hands, & U. Maki, Handbook of

Economic Methodology. Pp. 342-350. London: Edward Elgar.

[2020-04-21]

Harrison, C. (2007). TIP SHEET ON QUESTION WORDING. Harvard University -

Program on Survey Research. Pp. 1-4

https://psr.iq.harvard.edu/files/psr/files/PSRQuestionnaireTipSheet_0.pdf

[2020-04-24]

8.3 Digital sources

Nobelprize (2020), Biographical – Paul A. Samuelson

https://www.nobelprize.org/prizes/economic-sciences/1970/samuelson/biographical/

[2020-04-09]

MIT, Father of Modern Economics

https://betterworld.mit.edu/father-modern-economics/

[2020-04-09]

Goldman, M. (2008). Statistics for Bioinformatics. Pp 1-5.

https://www.stat.berkeley.edu/~mgoldman/Section0402.pdf

[20-05-23]

Wild, C. (1997) The Wilcoxon Rank-Sum Test. Pp1-10.

https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf

[20-05-14]

8.4 Images

Hans Peters, 31 march 2011, Fig 1 from A preference foundation for constant loss aversion,

Graph, viewed 5 May 2020, < https://doi.org/10.1016/j.jmateco.2011.11.003>.

Daniel Kahneman, Jack L. Knetsch, Richard H., Winter 1991, Figure 2 - A typical value

function from Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias,

Graph, viewed 21 April 2020, <https://www.aeaweb.org/articles?id=10.1257/jep.5.1.193,

DOI: 10.1257/jep.5.1.193>

Daniel Kahneman, Amos Tversky, 1 March 1979, Figure 3 - A hypothetical value function

from Prospect Theory: An Analysis of Decision Under Risk, Graph, viewed 30 March 2020,

<https://www-jstor-

org.proxy.lnu.se/stable/1914185?sid=primo&origin=crossref&seq=1#metadata_info_tab_con

tents, ISSN: 0012-9682>

8.5 Articles

Barsky, B. R., Juster, T. F., Kimball, S. M., Shapiro, D. M. (1997). Preference Parameters

and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement

Study. Pp. 537-579 Vol. 112(2)

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Bernoulli, D. (1954). Exposition of a New Theory on the Measurement of Risk. Pp. 23-26

Vol.22

ISSN: 0012-9682

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Cappello, C., Zonta, D., Glišić, B. (2016). Expected Utility Theory for Monitoring-Based

Decision-Making. Pp. 1647-1661 Vol.104(8)

DOI: 10.1109/JPROC.2015.2511540

[2020-04-06]

Dolnicar, S. (2013). Asking Good Survey Questions. Pp. 551-574 Vol. 52(5)

DOI: 10.1177/0047287513479842

[2020-05-03]

Hossain, M., T. (2018). How Cognitive Style Influences the Mental Accounting System: Role

of Analytic versus Holistic Thinking. Pp. 615(18) Vol. 45(3)

DOI: https://doi-org.proxy.lnu.se/10.1093/jcr/ucy020

[2020-05-08]

Häckel, B., Pfosser, S., Tränkler, T. (2017) Explaining the energy efficiency gap – Expected

Utility Theory versus Cumulative Prospect Theory. Pp. 414-426 Vol.111

DOI: 10.1016/j.enpol.2017.09.026

[2020-04-07]

Kahneman, D., Tversky, A. (1979). Prospect Theory: An Analysis of Decision Under Risk.

Pp. 263 Vol.47(2)

ISSN: 0012-9682

[2020-03-30]

Kahneman, D., Knetsch J., L., Thaler, R., H. (1991). Anomalies: The Endowment Effect, Loss

Aversion, and Status Quo Bias. Pp. 193-206 Vol.5

DOI: 10.1257/jep.5.1.193

[2020-04-21]

Klen, M., Deissenroth, M. (2017). When do households invest in solar photovoltaics? An

application of prospect theory. Pp. 270-278 Vol.109

DOI: https://doi-org.proxy.lnu.se/10.1016/j.enpol.2017.06.067

[2020-04-20]

Lacy, D. (2001). A Theory of Nonseparable Preferences in Survey Responses. Pp. 239-258

Vol. 45(2)

DOI: 10.2307/2669339

[2020-05-03]

Lee, S., Lee D., K. (2018). What is the proper way to apply the multiple comparison test?.

Pp. 353-360 Vol. 71(5)

DOI: 10.4097/kja.d.18.00242

[2020-05-13]

Lindsay, L. (2019). Adaptive loss aversion and market experience. Pp. 43-61 Vol.168

DOI: 10.1016/j.jebo.2019.09.023

[2020-03-29]

Malmendier, U., Nagel, S. (2011). Depression Babies: Do Macroeconomic Experiences

Affect Risk Taking? Pp. 373-416 Vol.126(1)

ISSN: 00335533

E-ISSN: 15314650

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Mishra, S. (2014). Decision-Making Under Risk: Integrating Perspectives From Biology,

Economics, and Psychology. Pp. 208-307 Vol.18(3)

DOI: https://doi.org/10.1177/1088868314530517

[2020-04-17]

Novemsky, N., Kahneman, D. (2005). The Boundaries of Loss Aversion. Pp. 119-128.

Vol.42(2)

DOI: https://doi.org/10.1509/jmkr.42.2.119.62292

[2020-04-03]

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DOI: https://doi.org/10.1016/j.jmateco.2011.11.003

[2020-05-05]

Rana, R., Singhal, R. (2015). Chi-square test and its application in hypothesis testing.

Pp. 69-71 Vol. 1(1)

ISSN: 2395-5414

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Rau, A., H. (2014). The Disposition Effect and Loss Aversion: Do Gender Differences

Matter? Pp. 1-20

DOI: http://dx.doi.org/10.2139/ssrn.2327813

[2020-05-19]

Riedl, D., Heuer, A., Strauss, B. Why the Three-Point Rule Failed to Sufficiently Reduce the

Number of Draws in Soccer: An Application of Prospect Theory. Pp. 316-326 Vol.37(3)

DOI: https://doi-org.proxy.lnu.se/10.1123/jsep.2015-0018

[2020-04-20]

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25(3)

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Shalev, J. (2002). Loss aversion equilibrium. Pp. 269-287 Vol. 29(2)

DOI: 10.1007/s001820000038

[2020-05-05]

Sharma, A., Park, S., Nicolau, J. (2020) Testing loss aversion and diminishing sensitivity in

review sentiment. Pp. 1-8 Vol.77

DOI: 10.1016/j.tourman.2019.104020

DOI: https://doi-org.proxy.lnu.se/10.1016/j.tourman.2019.104020

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Vol.26(4)

ISSN 0095-2583

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Sheldon, R., M., Fillyaw, J., M., Thompson, D., W. (1996). The usa and interpretation of the

Friedman test in the analysis of ordinal-scale data in repeated measures designs. Pp 221-228

Vol. 1(4).

DOI: https://doi.org/10.1002/pri.66

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Economic Perspectives. Pp. 193-205 Vol.4(1)

DOI: 10.1257/jep.4.1.193

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Loss Aversion on Risk Taking: An Experimental Test. Pp. 647-661 Vol.112(2)

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[2020-04-21]

9. Appendix

9.1 First Draft of the Survey

The change in your wealth during the last month was -50%. You are now facing a coin toss,

how much would the win need to be in order for you to accept the bet?

50% chance to lose 5 000 kr

50% chance to win:

The change in your wealth during the last month was +10%. You are now facing a coin toss,

how much would the win need to be in order for you to accept the bet?

50% chance to lose 5 000 kr

50% chance to win:

The change in your wealth during the last month was +50%. You are now facing a coin toss,

how much would the win need to be in order for you to accept the bet?

50% chance to lose 5 000 kr

50% chance to win:

The change in your wealth during the last month was -30%. You are now facing a coin toss,

how much would the win need to be in order for you to accept the bet?

50% chance to lose 5 000 kr

50% chance to win:

The change in your wealth during the last month was -10%. You are now facing a coin toss,

how much does the win need to be in order for you to accept the bet?

50% chance to lose 5 000 kr

50% chance to win:

The change in your wealth during the last month was +30%. You are now facing a coin toss,

how much does the win need to be in order for you to accept the bet?

50% chance to lose 1 000 kr

50% chance to win:

9.2 Final Survey

Enkätundersökning del 1

Vi är två studenter på Linnéuniversitetet som skriver vår kandidatuppsats. Enkäten kommer

att vara helt anonym och är baserad på ett singla slant scenario. Vi skulle uppskatta om ni

kunde ta er några minuter och svara på dessa frågor.

Kön

❒ Man

❒ Kvinna

❒ Annat

Ålder

❒ 18 - 21

❒ 22 - 25

❒ 26 - 29

❒ 30 +

Månadsinkomst

❒ 0 - 5.000 kr

❒ 5.000 - 10.000 kr

❒ 10.000 - 15.000 kr

❒ 15.000 - 20.000 kr

❒ 20.000 kr +

Totalt sparkapital

❒ 0 - 100.000 kr

❒ 100.000 - 250.000 kr

❒ 250.000 - 500.000 kr

❒ 500.000 kr +

Enkätundersökning del 2

I den här delen av enkäten står du inför en slantsingling där sannolikheten för

vinst är 50% och sannolikheten för förlust är 50%, krona = vinst och klave =

förlust. Ange den lägsta vinst för vilket du skulle vara villig att delta i

slantsinglingen utifrån din nuvarande ekonomiska situation.

A. För en sannolikhet på 50% att förlora 100 kr kräver du en vinst på lägst (OBS! Se

instruktioner ovan):

❒ 0 - 100 kr

❒ 100 - 150 kr

❒ 150 - 200 kr

❒ 200 - 250 kr

❒ 250 - 300 kr

❒ 300 - 350 kr

❒ 350 kr +

B. För en sannolikhet på 50% att förlora 250 kr kräver du en vinst på lägst:

❒ 0 - 250 kr

❒ 250 - 375 kr

❒ 375 - 500 kr

❒ 500 - 625 kr

❒ 625 - 750 kr

❒ 750 - 875 kr

❒ 875 kr +

C. För en sannolikhet på 50% att förlora 500 kr kräver du en vinst på lägst:

❒ 0 - 500 kr

❒ 500 - 750 kr

❒ 750 - 1.000 kr

❒ 1.000 - 1.250 kr

❒ 1.250 - 1.500 kr

❒ 1.500 kr - 1.750 kr

❒ 1.750 kr +

D. För en sannolikhet på 50% att förlora 1.000 kr kräver du en vinst på lägst:

❒ 0 - 1.000 kr

❒ 1.000 - 1.500 kr

❒ 1.500 - 2.000 kr

❒ 2.000 - 2.500 kr

❒ 2.500 - 3.000 kr

❒ 3.000 - 3.500 kr +

E. För en sannolikhet på 50% att förlora 2.000 kr kräver du en vinst på lägst:

❒ 0 - 2.000 kr

❒ 2.000 - 3.000 kr

❒ 3.000 - 4.000 kr

❒ 4.000 - 5.000 kr

❒ 5.000 - 6.000 kr

❒ 6.000 - 7.000 kr

❒ 7.000 kr +

F. För en sannolikhet på 50% att förlora 4.000 kr kräver du en vinst på lägst:

❒ 0 - 4.000 kr

❒ 4.000 - 6.000 kr

❒ 6.000 - 8.000 kr

❒ 8.000 - 10.000 kr

❒ 10.000 - 12.000 kr

❒ 12.000 - 14.000 kr

❒ 14.000 kr +

9.3 Distributions

9.3.1 Gender

9.3.2 Age

40%

60%

Gender

Kvinna

Man

16%

69%

13%

2%

Age

18 - 21

22 - 25

26 - 29

30 +

9.3.3 Income

9.3.4 Total savings

16%

26%

45%

7%6%

Income

0 - 5.000 kr

5.000 - 10.000 kr

10.000 - 15.000 kr

15.000 - 20.000 kr

20.000 kr +

36%

34%

24%

6%

Total savings

0 - 100.000 kr

100.000 - 250.000 kr

250.000 - 500.000 kr

500.000 kr +

9.3.5 Question A.

9.3.6 Question B.

0

5

10

15

20

25

30

35

0 - 100 kr 100 - 150 kr 150 - 200 kr 200 - 250 kr 250 - 300 kr 300 kr +

A. För en sannolikhet på 50% att förlora 100 kr

kräver du en vinst på lägst (OBS! Se instruktioner

ovan):

0

5

10

15

20

25

30

35

0 - 250 kr 250 - 375 kr 375 - 500 kr 500 - 625 kr 625 - 750 kr 750 kr +

B. För en sannolikhet på 50% att förlora 250 kr

kräver du en vinst på lägst:

9.3.7 Question C.

9.3.8 Question D.

0

5

10

15

20

25

30

35

40

0 - 500 kr 500 - 750 kr 750 - 1.000 kr 1.000 - 1.250

kr

1.250 - 1.500

kr

1.500 kr +

C. För en sannolikhet på 50% att förlora 500 kr

kräver du en vinst på lägst:

0

5

10

15

20

25

30

35

40

0 - 1.000 kr 1.000 - 1.500

kr

1.500 - 2.000

kr

2.000 - 2.500

kr

2.500 - 3.000

kr

3.000 kr +

D. För en sannolikhet på 50% att förlora 1.000 kr

kräver du en vinst på lägst:

9.3.9 Question E.

9.3.10 Question F.

0

10

20

30

40

50

60

0 - 2.000 kr 2.000 - 3.000

kr

3.000 - 4.000

kr

4.000 - 5.000

kr

5.000 - 6.000

kr

6.000 kr +

E. För en sannolikhet på 50% att förlora 2.000 kr

kräver du en vinst på lägst:

0

10

20

30

40

50

60

0 - 4.000 kr 4.000 - 6.000

kr

6.000 - 8.000

kr

8.000 - 10.000

kr

10.000 -

12.000 kr

12.000 kr +

F. För en sannolikhet på 50% att förlora 4.000 kr

kräver du en vinst på lägst:

9.4 Kolmoforov-Smirnov and Shapiro-Wilk Test for Normal Distribution

9.5 Friedman Test

9.6 Wilcoxon Signed Ranks Test

9.6.1 Wilcoxon signed rank test, comparing Q. A

9.6.2 Wilcoxon signed rank test, comparing Q. B

9.6.3 Wilcoxon signed rank test, comparing Q. C

9.6.4 Wilcoxon signed rank test, comparing Q. D

9.6.5 Wilcoxon signed rank test, comparing Q. E

9.7 Wilcoxon Signed Rank Test for the non significant difference between

distributions.

9.7.1 Wilcoxon Signed Rank Test between the distribution for Q. A & Q. B

9.7.2 Wilcoxon Signed Rank Test between the distribution for Q. C & Q. D

9.7.3 Wilcoxon Signed Rank Test between the distribution for Q. D & Q. E

9.7.4 Wilcoxon Signed Rank Test between the distribution for Q. D & Q. F

9.7.5 Wilcoxon Signed Rank Test between the distribution for Q. E & Q. F