Assessing Levels of Risk When Solving a Decision Analysis Investment Problem

By Melody Flores Fall 2017

In Partial Fulfillment of Stat 4395 – Senior Project

Department of Mathematics and Statistics

Faculty Advisor:

Dr. Timothy Redl t

Committee Member:

Dr. Kendra Mhoon t

Committee Member:

Ms. Anna Simmons t

Department Chair:

Dr. Ryan Pepper t

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Table of Contents

Abstract ……………………………………………………………………………... 2

Acknowledgements …………………………………………………………………. 3

Table of Figures and Tables ………………………………………………………… 4

Motivation …………………………………………………………………………... 5

Purpose ……………………………………………………………………………… 6

Section 1: Introduction ……………………………………………………………… 7

1.1 Maximum Likelihood …………………………………………………… 8

1.2 Maximin Approach ……………………………………………………… 9

1.3 Bayes’ Decision Rule …………………………………………………... 10

1.4 Decision Tree …………………………………………………………... 11

Section 2: Investment Problem …………………………………………………….. 12

2.1 Description of Problem ………………………………………………… 12

2.2 Solution of Problem ……………………………………………………. 12

Section 3: Assessment of Respondents …………………………………………….. 15

3.1 Creation of Risk Assessment Survey …………………………………... 16

3.2 Administered Survey …………………………………………………… 18

3.3 Collection of Data ……………………………………………………… 18

3.4 Analysis of Data ………………………………………………………... 19

3.5 Observation …………………………………………………………….. 22

Section 4: Conclusion ……………………………………………………………… 27

Section 5: Extension/Future Work …………………………………………………. 28

Section 6: References ………………………………………………………………. 30

Appendix …………………………………………………………………………… 31

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Abstract

Decision making is used by everyone on a daily basis. It involves the process of thinking

rationally and making the best decision according to one’s circumstance. According to the book

Operations Research, there are three different categories in decision making: certainty, risk and

uncertainty (503). The way each individual makes decision is based on their personal way of

thinking and how they analyze situations.

In this paper, we will take a deep look into a decision under risk investment problem and

the decision analysis behind it. We will analyze different decision-making strategies such as

maximum likelihood, maximin approach, Bayes’ Decision Rule and create a decision tree for all

the possible outcomes. With the participation of fifty University of Houston-Downtown students

we will analyze their responses to the investment problem and collect a risk-taking questionnaire

from each individual.

The objective of this paper is to analyze the correlation between a person’s risk-taking

nature and the way they answer the investment problem. We will compare the results of the

participants’ answers to the problem and risk analysis survey to see if we can identify a

correlation between one’s risk and the way they make decisions.

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Acknowledgement

I will like to acknowledge and thank everyone who has supported and helped in the

completion of this project.

I will like to first acknowledge my senior project advisor Dr. Redl, who has shown support

through the course of this project. I am grateful for all the dedication, advice and commitment I

have received from him. Dr. Redl helped me choose my project and gave me the idea of combining

data analytics with a business base question to incorporate my mathematics major and business

minor. I highly appreciate him letting me borrow one of his books Operations Research, which

has provided me with the solid ground for this project. I am thankful for all the guidance and

encouragement he has provided me; this project would had not been possible without him.

Secondly, I will like to thank my two committee members Dr. Mhoon and Ms. Simmons,

for the support and contribution they have shown. Thank you for taking your time to assist me

during this semester. I have learned a lot and enjoyed being your student.

Thirdly, I want to acknowledge Dr. London for the support and commitment he has shown

not only to myself but my classmates in Stat 4395. Thank you for keep us on track and providing

us guidance with our oral presentations.

Lastly, I will like to acknowledge and thank every student who participated and helped

with my project. I appreciate the fifty individuals who took the time to complete the surveys. Thank

you for your commitment and honesty, this project could had not been completed without the help

of each one of you. I congratulate each student on their graduation achievements and wish them

the best of luck on their journeys.

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Table of Figures and Tables

Table 1: Newspaper Boy Example ………………………………………………….. 8

Table 2: Newspaper Boy Expected Values ………………………………….……... 10

Figure 1: Newspaper Boy Decision Tree …………………………………….…….. 11

Table 3: Investment Problem Percent Return ……………………………….……... 12

Table 4: Investment Problem ……………………………………………….……… 13

Table 5: Investment Problem Expected Value …………………………………….. 14

Figure 2: Investment Problem Decision Tree ……………………………………… 15

Figure 3: Investment Problem Results ……………………………………………... 19

Figure 4: Gender …………………………………………………………………… 19

Figure 5: Age ………………………………………………………………………. 20

Figure 6: Ethnicity …………………………………………………………………. 20

Figure 7: Investment Experience …………………………………………………... 21

Figure 8: Risk-taker ………………………………………………………………... 22

Table 6: Risk Score and Investment Chosen ………………………………………. 24

Table 7: Average Risk Score ………………………………………………………. 25

Table 8: Cumulative Average ……………………………………………………… 26

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Motivation

When I began to search for a project idea I did not know what exactly I wanted to do. I

knew I wanted to combine statistics with business. Even though I am an applied statistics major I

have always had a passion for business and since I am minoring in general business I wanted to

be able to incorporate both subjects into one project. As I met with Dr. Redl during the summer,

he suggested focusing on decision analysis. He then lend me a book called Operations Research,

which provided me with some ideas. As I scan through the book I became intrigue with decision

making. I never sat down and thought about how decision analysis worked and how it influence

the choices one makes and how they are made. Learning about maximum likelihood, maximin

approach and other decision making strategies became very interesting to my eyes. We use these

different approaches on a daily bases from minor to big decisions we make. In the book,

Operations Research there are problem sets offered after each section and there is where I found

my senior project. When I read the investment problem I knew that was what I wanted to focus

on. To be able to analyze my own collection of data and compare it with decision making

strategies excited me.

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Purpose

We will be looking at different decision making strategies. Step by step we will analysis

the three mutual funds investment problem and solve it by using the maximum likelihood,

maximin approach, Bayes’ Decision Rule and create a decision tree for all the outcomes. The

purpose of this project is to analyze the correlation between a person’s risk-taking nature and the

way they answer the investment problem. This project will focus on fifty college senior level

students from the University 0f Houston-Downtown in the ages between 20-25 pursuing a stem

degree. We will analyze their risk tolerance from a separate questionnaire and compare it to the

way they answered the investment question to see if individuals’ risk-taking nature plays a role

in the way they make decisions.

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Section 1

Introduction

Decision making is something that we all take part of on a daily basis; regardless of how

small or big a problem can be we are always having to make decisions. Without noticing every

time one makes a decision we are analyzing and choosing from one of the different decision

making approaches. According to University of Massachusetts-Dartmouth “decision making is

the process of making choices by identifying a decision, gathering information, and assessing

alternative resolutions,” but what influences us to make these types of decisions. There are many

factors that play a role on how a person thinks and why they make the decisions they make. The

factor that this paper will be focusing on is the levels of risk. Could it be that there is a

correlation between how risky one can be with the type of decisions they make? According to a

short film in MindTools “risk is made up of two parts: the probability of something going wrong,

and the negative consequences if it does.”

Weather if one is involved in the stock market we all know how risky it can sometimes

be to invest. The performance of the stock market is unknown regardless of the research and

probability there is always a chance it can go wrong. Many would say people who participate in

the stock market tend to be risk takers, but how true can that be. In this project we will take a

look at one investment problem and analyze how college senior students answered it. We will

also be comparing their answers with a risk assessment questionnaire that was given to them

before answering the investment question to see if we can find a correlation between the levels of

one’s risk and their investment decision.

There is much decision making that goes in to choosing a mutual fund to invest in. When

looking at decision analysis we look at how decisions are made based on certainty, risk, and

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uncertainty. When someone makes a decision an action is taken and then a state of nature occurs.

There are many different types of approaches one can use to help them make a decision. In this

research project we will focus on three different approaches: maximum likelihood, maximin

approach, and Bayes’ Decision Rule.

Section 1.1 Maximum Likelihood

In maximum likelihood decisions are made based on the most likely state of nature. One

looks at the probability of each option in order to make their decision. Let’s look at an example.

A newsboy is trying to figure out how many copies of the newspaper should he order for the day.

From the table below, we can see four different demands of the newspaper when he orders 20-23

copies of the newspaper.

Table 1 Newspaper Boy Example

Demand

D=20 D=21 D=22 D=23 Y=20 $9.00 $9.00 $9.00 $9.00 Y=21 $8.30 $9.45 $9.45 $9.45 Y=22 $7.60 $8.75 $9.90 $9.90 Y=23 $6.90 $8.05 $9.20 $10.35 Probability 0.2 0.4 0.3 0.1

To make a maximum likelihood decision we look at the probability of each demand. From this

example the highest probability is 0.4. under the demand of 21 newspapers. Out of the four

different orders (Y) the profit is higher when the newsboy orders 21 newspapers ($9.45). In this

approach, the newsboy should make the decision to order 21 newspapers.

When making a decision under the maximum likelihood approach there is some

disadvantages. The first disadvantage is that this approach ignores a loth of other information

about the other possible choices. It is only focused on the probability of each. Another

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disadvantage is that sometimes the probability can be very small and the likelihood of the state of

nature can be cloudy.

Section 1.2 Maximin Approach

Another approach we will look at is the maximin approach. The maximin approach can

be classified as being the conservative approach to decision making. This approach takes a look

at the minimum payoff of each possible state of action. For each action, one finds the minimum

payoff over all possible states and chooses the maximum payoff from these values.

Let’s go back to our example before. Instead of looking at the probabilities, the newsboy will

have to compare the minimum payoff for each demand as illustrated below.

Demand

D=20 D=21 D=22 D=23 Minimum Payoff Y=20 $9.00 $9.00 $9.00 $9.00 $9.00 Y=21 $8.30 $9.45 $9.45 $9.45 $8.30 Y=22 $7.60 $8.75 $9.90 $9.90 $7.60 Y=23 $6.90 $8.05 $9.20 $10.35 $6.90 Probability 0.2 0.4 0.3 0.1

The minimum demand for the newspaper is 20 (D=20) and out of the four different order options

(Y) the newsboy need to choose the highest payoff. We can see that the highest payoff is $9.00

under Y=20. In this case the newsboy should make the decision to order 20 newspapers.

Even though the maximin approach is safe and has the best guaranteed payoff it does

provide some disadvantages. Some people might classify this approach as the pessimistic

approach. It looks at the worst outcomes blocking out any optimistic approach and their

probabilities. It can also be seen as too extreme because it is highly unlikely that the worse

outcome will occur.

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Section 1.3 Bayes’ Decision Rule

An approach that looks into all available data instead of just a portion of it is the Bayes’

Decision Rule. In this approach one chooses an action that maximizes the expected payoff. In

order to do so a specific formula must be used.

Maximize Expected Profit: E(Y)=∑D(P)

E(Y) – expected profit for each Y

D – demand outcome

P – probability

All we must do is for every Y we must multiply each demand outcome with its probability and

add them together. To further understand this approach let’s calculate the expected profit values

for our example.

Y=20 E(Y)= 9

Note: Y=20 does not need to be calculated because under every demand (D) the profits are the same.

Y=21 8.30(0.2) + 9.45(0.4) + 9.45(0.3) + 9.45(0.1) = 9.22

Y=22 7.60(0.2) + 8.75(0.4) + 9.90(0.3) + 9.90(0.1) = 8.98

Y=23 6.90(0.2) + 8.05(0.4) + 9.20(0.3) + 10.35(0.1) = 8.40

Table 2 Newspaper Boy Expected Values

Demand

D=20 D=21 D=22 D=23 Expected Profit Y=20 $9.00 $9.00 $9.00 $9.00 $9.00 Y=21 $8.30 $9.45 $9.45 $9.45 $9.22 Y=22 $7.60 $8.75 $9.90 $9.90 $8.98 Y=23 $6.90 $8.05 $9.20 $10.35 $8.40 Probability 0.2 0.4 0.3 0.1

When using the Bayes’ Decision Rule we can conclude that the newsboy should order 21

newspapers. This approach is seen as an “educated guess” way of making a decision. For those

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who like to take consideration of all possible outcomes tend to lean toward this approach. When

making a decision under Bayes’ Rule it is important to keep in mind that the probability

estimates cannot always be trusted, sometimes they can be unsteady.

Section 1.4 Decision Tree

Lastly, we will look at a graphical tool used to analyze decisions under risk known as

decision trees. A decision tree evaluates all the possible outcomes and uses probability to

estimate the states of nature. It is called a decision tree because we can classify the decision as

the root that branches out to different nodes. Depending on the problem a decision tree can

branch out into several possible outcomes.

Using the same example as before we will create a decision tree to have a visual of the decisions

available for the newsboy.

With a decision tree we can visually see that the newsboy has four different choices he

can make and out of each choice there are four possible outcomes. Decision trees come in handy

Figure 1 Newspaper Boy Decision Tree

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whenever one is uncertain or cannot seem to lean to a certain approach. It identifies all possible

actions and payoffs each decision has.

Section 2 Investment Problem

Now that we have looked into the different decision making approaches we can take a

look into the investment problem we will be analyzing.

Section 2.1 Description of Problem

You have the chance to invest in one of three mutual funds: utility, aggressive growth,

and global. The value of your investment will change depending on the market conditions. There

is a 10% chance the market will go down, 50% chance it will remain moderate, and 40% chance

it will perform well. The following table provides the percentage change in the investment value

under the three conditions:

Table 3 Investment Problem Percent Return

Percent return on investment

Alternative Down Market (%) Moderate Market (%) Up Market (%) Utility +5 +7 +8 Aggressive Growth -10 +5 +30 Global +2 +7 +20

Note: (+) refers to profit and (-) refers to lose

Which mutual fund should you select?

Section 2.2 Solution of Problem

Let’s solve the problem by first looking at the maximum likelihood.

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Maximum Likelihood:

For this strategy we will first look at the mist likely state of nature (probability of each

market). It is given in the problem that there is a 10% chance the market will go down, 50%

chance it will remain moderate, and 40% chance it will perform well.

The probabilities are: Down Market = 0.1 Moderate Market= 0.5 Up Market= 0.4 which are

illustrated in the table below for better understanding.

Table 4 Investment Problem

Alternative Down Market (10%) Moderate Market (50%) Up Market (40%) Utility +5 +7 +8 Aggressive Growth -10 +5 +30 Global +2 +7 +20 Probability .1 .5 .4

As we can see the highest probability from the three is moderate market with 50% chance

the market will remain moderate. Now we look at the three mutual funds return profit under

moderate market and choose the highest one.

In this case we run into a problem, Utility and Global have the same return profit (+7).

When this occurs we must take a look at the second highest state of nature, up market with 40%.

This time we will only look at utility and global return profits as illustrated below.

Alternative Down Market (10%) Moderate Market (50%) Up Market (40%) Utility +5 +7 +8 Aggressive Growth -10 +5 +30 Global +2 +7 +20 Probability .1 .5 .4

We can see that Global has a higher return profit than Utility. Using the Maximum Likelihood

approach, we conclude that the best mutual fund to invest in is Global.

MaxiMin Approach:

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With this approach we will be looking at the maximum payoff over the minimum payoffs. The

minimum payoff can be found under the down market. From looking at the down market we

must choose the highest return profit from the three mutual funds.

Alternative Down Market (10%) Moderate Market (50%) Up Market (40%) Utility +5 +7 +8 Aggressive Growth -10 +5 +30 Global +2 +7 +20

From the maximin approach the best mutual fund to invest in would be Utility

Bayes’ Decision Rule:

With Bayes’ Decision Rule we will focus on the expected payoff by using the formula:

Maximize Expected Profit: E(Y)=∑D(P)

We calculate the expected value for each fund as illustrated below

5(.1)+7(.5)+8(.4)=7.2

-10(.1)+5(.5)+30(.4)=13.5

2(.1)+7(.5)+20(.4)=11.7

Table 5 Investment Problem Expected Value

Alternative Down Market (10%)

Moderate Market (50%)

Up Market (40%)

Expected Value

Utility +5 +7 +8 7.2 Aggressive Growth

-10 +5 +30 13.5

Global +2 +7 +20 11.7 Probability .1 .5 .4

According to the expected values it seems that using the Bayes’ Decision Rule the best mutual

fund to invest in is aggressive growth.

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Now that we have solved this problem using three different decision-making approaches,

we will construct a decision tree for better understanding.

Decision Tree:

Figure 2 Investment Problem Decision Tree

With the decision tree we have a visual picture of the outcomes of each decision one can make.

To incorporate the different decision approaches the expected values are present in the tree as

they branch out to its corresponding fund. Each outcome is represented with its probability () and

the outcome profit.

Section 3: Assessment of Respondents

The investment problem has been solved in different approaches. We have looked at

three different ways which can be classified as risky (Bayes’ Decision Rule), moderate

(Maximum Likelihood) and non-risky (Maximin Approach). According to the decision-making

approaches depending on which level of risk one falls into should determine their decision. For

example, when we looked at the maximin we are thinking in a conservative mindset and the

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wright choice under this approach would be to choose utility. If we used maximum (the moderate

approach) the decision to choose is global and for Bayes’ Decision Rule (the risky approach) the

decision to choose is aggressive growth.

After looking at the problem and the decision-making approaches the question if there is a

correlation between one’s risk and the fund that was chosen by the individual arises. It is easy to

state that depending on one’s risk assessment will determine what fund they would choose, but

how true can this be.

Section 3.1 Creation of Risk Assessment Survey

In order to compare if someone’s risk assessment correlates with the way they answered

the investment problem a risk-taking questionnaire was created. After looking online at different

risk questionnaires’, I came up with ten statement questions that would help identify the risk

levels of the individuals and each question contained three answer choices: mostly true,

somewhat true/false and mostly false. Before answering the questions three different statements

are given to the individual and they must choose which statement best describes their investment

experience as illustrated below.

Which one of the following statements best describes your investment experience? A) I have a fair investment in shares and I check the prices regularly. B) I have a small investment in shares or unit trusts and I hardly ever check what it’s worth. C) I have never invested in shares or unit trusts

Each statement question was designed to correlate with the three different decision

approaches without making it obvious for the respondents. For example, let’s look at two of the

questions from the questionnaire. “Before making a business decision, I fully research all

possible outcomes and likelihood to determine what is the right path to take.” If one was to

answer true for this question we can say that they used the Bayes’ Decision Rule approach

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because they take a look at all the outcomes instead of just a specific one. Or let’s look at this

question “When I make a risky decision, I plan for the worst-case scenario.” If one were to

answer true for this question we could classify them as conservative or non-risk takers under the

maximin approach.

The reason only ten statement questions were given was to not overbear the respondents

with questions and to keep the calculations from becoming too confusing. It helped to keep the

questionnaire simple and to the point.

Also, what one can notice in the questionnaire is that each question is arranged in a

pattern. The pattern goes from the first statement question being true for the non-risk takers, then

the second one being true for the risk-takers and so on the pattern continues. The reason for this

is to provide variety for the respondents and not having them choosing all true or all false as they

fill out the questionnaire. Many people tend to choose the same answers after they start to notice

their answer choices are not changing as they are going through a questionnaire or survey.

After the respondents have answered all ten questions one last statement is brought up.

I consider myself to be a risk taker. Agree Neither Agree/Disagree Disagree

This statement was added to the end of the questionnaire in order to compare each respondents’

answers to the way they classy themselves. It will let us know if they underestimated or

overestimated their risk-taking ability.

Note: For further understanding the whole risk-taking questionnaire is illustrated in the appendix.

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Section 3.2 Administered Survey

So far we might assume that there is a correlation between one’s risk and the decision

they made on the investment problem. In order to test this assumption a sample of fifty

university students’ responses were collected. As broad as this can be in order to simplify this

assessment and analyze the data is only based on a particular group of students. Each respondent

is between the age of 20-25 and is qualified as a college senior. To even narrow this a little more

this analysis is based on only stem majors. The reason this study is only focused on stem majors

is to analyze college students who might not have as much knowledge about investing or the

stock market.

Section 3.3 Collection Data

The way the data was collected was not an easy task. The risk-taking questionnaire and

investment problem were created using SurveyMonkey. After they were done each participant

received an email with two links. In the email it was instructed for them to first take the risk-

taking questionnaire before answering the investment problem. The reason for this is for the

participants to be able to think about how risky they are when making decisions and to see if they

consider themselves to be risk-takers before answering the investment question.

After almost two weeks the email was sent only 50% of the participants had responded to

the two surveys. It began to get tricky for data to be collected that a different approach was

created. Instead of sending an email with survey links I copied and pasted the risk-taking

questionnaire and the investment problem into Microsoft Word and printed out copies. As I ran

in to some participants who had not taken the survey I asked them right there and then to take the

two surveys. After collecting the rest of the responses, I manually inputted their responses on to

SurveyMonkey.

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Section 3.4 Analysis of Data

When all the data was collected and input into Survey Monkey histograms were created

in order to have a visual of our results. From the diagram below, we can see that the most chosen

mutual fund was global which is our moderate approach. 54% (27 individuals) chose to invest in

global, 36% (18 individuals) chose aggressive growth, and only 10% (5 individuals) chose

utility.

Figure 3 Investment Problem Results

When each participant took the risk-taking questionnaire a few general questions about their

gender, ethnicity and age were asked.

Figure 4 Gender

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Figure 5 Age

Figure 6 Ethnicity

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We had 26 females and 24 males take the two surveys and out of these 50 individuals

62% were Hispanic or Latino showing the strong Hispanic community University of Houston-

Downtown holds. From the analysis data we also gathered the results about their investment

experience and if they considered themselves risk takers.

Figure 7 Investment Experience

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Figure 8 Risk-taker

Majority of the stem major respondents (62%) claimed to have no investment experience.

Only 38% of the individuals (19) considered themselves risk takers, 36% (18) answered neither

agree/disagree, and 26% (13) considered themselves non-risk takers.

If we were comparing the investment problem answers with the way each individual

classified themselves, we should have had a higher percentage under the answer neither

agree/disagree because of the high percent answer on the mutual fund global.

3.5 Observation

Now that we have collected our data analysis the question whether the participants risk-

taking questionnaire responses correlate with their investment problem responses arises.

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From our data we had 54% of the participants choose global as the mutual fund they

would invest in. If there was a perfect correlation between each person’s answer and their risk-

taking questionnaire we would have 27 individuals classify as moderate risk takers. According to

the question whether the student considers themselves to be risk-takers 38% (19) of them

answered yes and 36% (18) of them classified themselves as moderate but the risk-taking

questionnaire results classified them differently.

Let’s go back to the ten questions risk-taking questionnaire that was taken by each

individual. Even though we did ask each participant if they considered themselves to be risk

takers, a risk score was created based on how the participant answered the ten questions. Each

question that was considered low risk = 1 point, moderate = 2 points, and high risk = 3 points as

illustrated below.

1. I tend to make decisions based on what is most likely to happen.

Mostly true Somewhat true/false Mostly false

1 2 3

The participants are not aware of the scoring of each question. The maximum total a person

could score is a 30 and the minimum would be a 10. The way the scoring was issued was divided

into three categories.

Utility Global Aggressive Growth

Low risk Moderate High Risk

(10-16) (17-23) (24-30)

After calculating each individual’s risk-taking score we came to a surprise. 62% (31) of

the respondents scored in the moderate range, 38% (19) scored in the low risk range, and 0%

scored in the high risk range. Because no one scored as high risk-takers, a second scale was

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created eliminating the middle range leaving respondents to either fall under low or high risk-

takers as illustrated below.

Low risk High Risk

(10-20) (21-30)

When we only looked at low and high risk we get the results that 82% (41) of the

participants were considered low risk takers and 18% (9) classified as high risk takers. We

expected to have a higher score for risk takers since 36% of the individuals chose to go with

aggressive growth. In Table 6 we have a visual representation of the risk score and the

investment chosen by each individual.

Table 6 Risk Score and Investment Chosen

From the table above we can notice that we do not get the correlation we were expecting. When

we look at the risk score with the mid included no one who chose utility scored as low risk

takers. The only correlation we can see is between the individuals who chose global, the

moderate approach and their risk scores. Most of these students fell under the middle or low risk

takers which was what was expected.

Comparing these results with the investment problem there were 54% (27) individuals

who answered global (the moderate approach) and from the questionnaire only 16 individuals

who scored in the middle answered global. We can see that those who chose global did not score

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very high in the questionnaire they either scored as low risk-takers or in the middle. Even when

we took away the middle range only three individuals fell into high risk -takers. What was also

very interesting was that individuals who chose aggressive growth (the high-risk fund) did not

score high on the risk-taking questionnaire; majority of them fell into the low risk-takers

category.

After looking at each individual’s answers the average for risk scores and a cumulative

average was calculated as illustrated in the tables below. The average risk score for aggressive

growth was 17.44 points, global’s score was 17.26 and to our surprise utility had the highest

average score with 19 points.

Table 7:Average Risk Score

With the cumulative average we can notice that there is not a big difference in the way the

participants scored. Most individuals fell between 15-20 points which explains our high percent

of moderate risk takers.

16

16.5

17

17.5

18

18.5

19

19.5

Aggressive Growth Global Utility

Average Risk Score

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Table 8: Cumulative Average

With all the data collected the results we got were not exactly what was expected but does this

mean there was no correlation found between one’s risk taking nature and the way they make

decisions?

0

5

10

15

20

25

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Cumulative Average

Risk Score Cumuliate Average

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Section 4

Conclusion

Even though the results were not what we expected we can still conclude that a person’s

risk-taking nature does influence the way individuals make decisions. We must keep in mind that

there are other factors that come to play when making decisions under risk. This can explain why

we did not find a perfect correlation between one’s risk taking nature and their investment

decision. It was expected for global to be the most chosen fund and it was with a 54%. For global

we found a good correlation having most of the people who chose this fund fall under the

moderate risk-taking score. There were some downfalls with the results from aggressive growth

and utility which can lead to further research on how individuals are classifying themselves

under risk analysis. Overall, we can conclude that one’s risk-taking nature does influence the

way someone approaches or makes decisions, but it is not the only factor that comes to play.

There are other factors that can influence how an individual makes decisions such as emotions,

age, etc. that can be tested in further research.

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Section 5

Extension/Future Work

There is much room for further work on this project. One extension that I would had

liked to complete is to have had the participants take a pre-and-post survey of the investment

problem. What if the participants became knowledgeable about the different decision-making

strategies, how would they approach the investment problem, would they change their answer,

would we see more people fall from global and go more or less extreme. There are many

questions that arise about how the participants would answer. Making changes to the investment

problem itself could also cause the data to change. The investment problem has high percent

return rates and probabilities, what would had happened if they were to change and it wasn’t as

clear as it was presented. If we created a higher probability for the down fall market would those

who chose aggressive growth or global go for utility to play it safe. Many changes can be made

that can have a big influence in the participant’s answers.

It would also be good to collect more data instead of doing fifty individuals reaching out

to a hundred students, it will provide a better outlook on the correlation. This project was

conducted on stem majors only who were in the age range from 20-25. It would be nice to see

how business majors would had answered the investment problem and compare their risk scores

with the stem majors. Another data collection that would be interesting to see is conducting this

project on different age groups. Older generations are seen as more conservative, would they

lean more to utility rather than global or aggressive growth.

There is a lot that can be done to expand this project. I would like to continue to work on

these different extensions and see the different results and data collection we would get. Working

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on this project allowed me to practice on data collection and analysis. It has been challenging but

highly rewarding to have had the opportunity to work on my senior project.

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Section 6 References

Dartmouth, University of Massachusetts. “Decision-Making Process.” Decision-Making Process

- UMass Dartmouth, www.umassd.edu/fycm/decisionmaking/process/.

Dr. Redl, Timothy. “Decision Analysis .” Lecture and Notes, Sept. 2017, Houston, University of

Houston-Downtown.

“Risk Analysis and Risk Management: Evaluating and Managing Risks.” Decision Making from

MindTools.com, www.mindtools.com/pages/article/newTMC_07.htm.

Taha, Hamdy A. “Chapter 14 Decision Analysis and Games.” Operations Research: an

Introduction, 7th ed., Prentice Hall, 2003, pp. 503–546.

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Appendix – Risk-Taking Questionnaire

Risk-Taking Questionnaire Please, answer the questions below as objectively as you can.

Major: . Gender: .

Age: Ethnicity: .

Which one of the following statements best describes your investment experience? A) I have a fair investment in shares and I check the prices regularly. B) I have a small investment in shares or unit trusts and I hardly ever check what it’s

worth. C) I have never invested in shares or unit trusts

1. I tend to make decisions based on what is most likely to happen.

Mostly true Somewhat true/false Mostly false

2. I am willing to take a chance at failure for the sake of innovation.

Mostly true Somewhat true/false Mostly false

3. I need to have control over the outcome of my work, even if the project is difficult or demanding. Mostly true Somewhat true/false Mostly false

4. I focus more on the big picture rather than the little details. Mostly true Somewhat true/false Mostly false

5. Before making a business decision, I fully research all possible outcomes and likelihood to determine what is the right path to take. Mostly true Somewhat true/false Mostly false

6. I am comfortable in unfamiliar situations. Mostly true Somewhat true/false Mostly false

7. When I make a risky decision, I plan for the worst-case scenario. Mostly true Somewhat true/false Mostly false

8. I perform best under pressure. Mostly true Somewhat true/false Mostly false

9. Before making a decision, I try to anticipate the factors that could influence the outcome. Mostly true Somewhat true/false Mostly false

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10. Before making a final decision, I generally do not have a Plan B in case something goes wrong.

Mostly true Somewhat true/false Mostly false

Do you agree or disagree with the following statement

I consider myself to be a risk taker. Agree Neither Agree/Disagree Disagree