DECISION MAKING UNDER RISK AND
UNCERTAINTY
Dr Simon Naitram
ECON 3075 - Advanced Financial Economics
Shalicia Johnson
408001105
Date: April 8th, 2022.
Abstract
I conducted a study to determine if the individuals' investment decisions are rational or affected
by behavioural bias. In this research, the pattern of preferences followed the Expected Utility
Theory more than the Prospect theory. Therefore, rational thinking influences decision-making
more than behavioural bias.
Introduction
The Decision Theory by Leonard Savage studies and explains how investors make decisions,
how their different choices affect each other, and the decisions investors make when they face
uncertainties.
In Classical economics, the expected utility theory asserts that in decision-making, individuals
act rationally. In Behavioural economics, the Prospect theory, also known as the loss-aversion
theory, argues that investors are loss averse and do not act rationally because behavioural bias
influences their decision-making.
The Expected Utility Theory and Prospect Theory are both descriptive decision theories that
focus on the rules that govern individuals' choices when faced with gambles or investments.
Investors generally desire to avoid risky behaviour or somewhat risky investments, and as a
result, investors typically wish to maximise their returns with the least amount of risk possible.
Due to the differences in investor behaviour, the study of human behaviour exists, and
behavioural economics studies human behaviour.
There is a linear relationship between risk and return because there is a trade-off between risk
and return. The amount of risk an investor will take determines their risk preferences when
investing. All investments involve taking risks, so investors face decisions that involve financial
risk considerations and evaluations before investing under certainty and uncertainty.
According to Markowitz (1952), to obtain an optimal portfolio investment, an individual
considers how to maximise their returns at a given level of risk and minimise their risks at a
given level of return. Markowitz's (1952) theory also states that individuals engage in rational
decision making when investing to achieve the highest return or utility.
Rational decision-making occurs when an individual executes a formal multi-step analysis
process to determine which investment provides the most significant benefit at the lowest cost;
the benefit may include the highest monetary and non-monetary return and risk considerations.
Behavioural finance biases occur when psychological factors affect an investor's investment
decision-making; psychological factors determine how they invest their money. Contrary to
rational decision-making, each individual has emotions, motivations, social pressures, and
behaviours that reflect the inability of some individuals' minds to comprehend and process
information in the decision-making process fully. As a result, behavioural bias occurs when
investing, and it eliminates the occurrence of rational thinking before investing.
Rational thinking and behavioural bias consider risks, but different factors determine these
considerations. If behavioural biases influence an investor's decision-making process, logical
thinking will not occur.
Does rational thinking influence the decision-making process for investors, or is it influenced
more by behavioural biases? This study aims to analyse how investors act, where I studied the
significant factors that influence an investor's decisions. The analysis of the Expected Utility
theory and the Prospect theory is helpful since it helps us to understand how investors make
investment decisions when faced with uncertainty and risks.
.
Theory
In my study, I tested the expected utility theory of Daniel Bernoulli against the prospect theory
proposed by Kahneman and Tversky (1979). The expected utility theory consists of individuals
mathematically calculating the probability of each outcome, times the value of each outcome,
and then adding these totals to determine which investment is better (Palmer n.d.).
The expected utility theory involves rational decision-making under uncertainty. Rational
decision-making occurs when an individual is assumed to have perfect information about their
investment alternatives, so they analyse and evaluate each option to determine which investment
provides the most utility with minimal costs. Individuals who follow the rational decisionmaking model need quantifiable data or information to perform a good data analysis. The
expected utility theory has four axioms that define a rational decision-maker: completeness,
continuity, transitivity and reflexiveness.
In this study, the assumption was that all individuals have the utility function of Bernoulli where
u(x) = √x, and to calculate the expected utility for each problem, I used
.
Contrary to the expected utility theory, the prospect theory is a theory of behavioural economics
and behavioural finance. This theory states that individuals make decisions based on the
available information, the time they have to make the decision, and the cognitive limitations of
their minds. The prospect theory shows investors' choices when faced with risks and uncertainty.
According to the prospect theory, individuals fear losses more than they value gains, and because
of this, investors are generally loss averse. In the photo below, an investor will feel the loss of
$100 more than the gain of $100 due to risk-aversion.
According to the expected utility theory, after analysing and evaluating all the information, they
will choose the investment that maximises their benefits with minimal costs. In the photo below,
an investor will choose investment A under this theory even if investment A is not the optimal
investment.
Rational Choice
16,000
6,000
14,000
5,000
12,000
4,000
10,000
8,000
3,000
6,000
2,000
4,000
1,000
2,000
0
0
Investment A
Investment B
Proposed Returns
Actual Costs
Data
This proposal took a qualitative and quantitative approach using primary data, where I designed
a questionnaire and distributed it to five participants. The questionnaire consisted of seven
questions designed to determine if individuals engage in rational decision-making by following
the expected utility theory while investing or are influenced more by behavioural bias.
I used a thematic analysis to analyse the data, where I examined, summarised, and interpreted the
data.
Results
To analyse the data in this study, I used linear regressions where the outcome for each question
regresses on rational thinking and behavioural bias. In the following problems, we will analyse
and discuss the study’s results to determine if the expected utility theory affects decision-making
more than behavioural bias.
To understand how individuals engage in decision making when faced with uncertainty and
risks, I presented five participants with the problems below.
Problem 1:
In Problem 1, the utility for Lottery A is 95 utils, and the utility for Lottery B is 94.87 utils. The
pattern of preferences in Problem 1 supports what the expected utility theory predicts since 60%
of the participants chose Lottery A; this is also an implication that .95u(10,000) + .05u(0) > u
(9000). Even though $9000 came with certainty, the participants preferred Lottery A. An
individual who is more affected by behavioural bias (Prospect Theory) will choose Lottery B
since they become more risk-averse when it comes to gains.
Problem 2:
In Problem 2, the utility for Lottery A is 5 utils, and the utility for Lottery B is 70 utils. The
pattern of preferences in Problem 2 supports the expected utility theory since 100% of the
participants chose Lottery B; this is also an implication that u(9000) > .05u(10000)+.95u(0).
Even though with Lottery A, the investor has a chance of receiving an amount greater than nine
thousand dollars ($9000), the participants preferred Lottery B with a certain payoff. The choice
pattern in Lottery B follows the expected utility theory, and this choice is a rational choice.
Problem 3:
In Problem 3, the utility for Lottery A is -31.62 utils, and the utility for Lottery B is -25 utils. If a
person chooses rationally, they will select Lottery B because the number of utils to represent the
loss is less than Lottery A. The pattern of preferences in Problem 3 violates the expected utility
theory since 60% of the participants chose Lottery A which implies that .05u(-2500) + .05u(0) <
u (-1000). According to the Prospect theory, an investor prefers certainty, so they prefer a certain
outcome over an uncertain one. However, an investor will view the lotteries in this problem as a
certainty of losses. As a result, individuals will choose Lottery B because they will select the
riskier alternative to avoid the certainty of loss even when the expected utility of their chosen
lottery is less than the other lottery or lotteries.
Problem 4:
In Problem 4, the utility for Lottery A is 8.37 utils, and the utility for Lottery B is 7 utils. If a
person chooses rationally, they will select Lottery A because the number of utils to represent the
gain is greater than Lottery B. The pattern of preferences in Problem 3 supports the expected
utility theory since 100% of the participants chose Lottery A. The choice of Lottery A implies
that u(70) > .7u(100) + .3u(0). In this question, the expected value of both lotteries is the same,
with a value of seventy (70), but even though the lotteries provide the same expected value,
individuals are different. Therefore, what provides a certain level of satisfaction or utility for one
individual will differ for another individual.
Problem 5:
In the problem above, the utility for Lottery A is 102.87 utils, and the utility for Lottery B is 100
utils. If a person chooses rationally, they will select Lottery A because it provides greater utility
to the investor. The pattern of preferences in this problem violates the expected utility theory and
supports the prospect theory because 80% of the participants chose Lottery B, and Lottery B
provides less utility than Lottery A. Lottery B’s choice shows that u(10000) > .6u(10000) +
.35u(15000) + .05u(0). Investors may fear disappointment, which causes them to become riskaverse and accept an unfavourable investment. Most investors will choose a certain gain since it
is the less risky choice even if it has a lower expected utility; this pattern of preferences follows
the Prospect theory’s certainty effect.
Problem 6:
In Problem 6, the utility for Lottery A is 20 utils, and the utility for Lottery B is 12.24 utils. If a
person chooses rationally, they will select Lottery A because it provides more utility than Lottery
B. The pattern of preferences in this problem supports the expected utility theory since 80% of
the participants chose Lottery A, which implies that u (400) > .5u(600) + .5u(0). Since lottery B
is the riskier investment, a risk-averse individual (Prospect theory) will also choose lottery A
because it provides certainty.
Problem 7:
In the problem above, the utility for Lottery A is 31.62 utils, and the utility for Lottery B is 25
utils. If a person chooses rationally, they will select Lottery A because the number of utils the
investor gains from that lottery is greater than Lottery B. The pattern of preferences in Problem 3
supports the expected utility theory since 100% of the participants chose Lottery A, which
implies that u(1000) > .5u(2500) + .5u(0).
Conclusion
This study concludes that rational decision-making affects an investor more than behavioural
bias based on the preceding analyses. Therefore, the expected utility theory is more accurate in
explaining how individuals engage in decision making when investing under risk and
uncertainty.
Appendix