Behavioural Finance
Coursework
General Information
Answer All the questions and submit your solutions and comments
in a document.
The document should not exceed 2000 words. The word count ex_x005f cludes tables, figures (with associated legends), equations, footnotes,
endnotes, and references.
Ensure your final document is saved as a PDF file.
Question 1.
Let’s considerthe utility of the wealth. Mathematically, the utility of wealth
can be defined in various ways. One commonly employed mathematical
function is the power function. In this context, the utility, denoted as u(·),
derived from wealth w can be expressed as u(w) = awb
.
a) Use the provided dataset, named Utility.xlsx, to estimate the wealth
utility function and generate the corresponding plot.
[10 Marks]
Suppose Sophia adopts the estimated function from part a) for the utility
associated with her wealth levels and considers a scenario with two states
of the world. If the first state occurs, her wealth will be w1, and if the sec ond state occurs, her wealth will be w2. The probabilities associated with
these wealth levels are denoted as p1 and p2, respectively. This scenario is
defined as P(p1, w1, w2) where p2 = 1 p1.
b) Calculate the expected utility of the following scenarios:
P1(0.6, 400, 800),
P2(0.8, 5000, 2000),
P3(0.4, 6000, 3000).
[10 Marks]
c) Based on the results from parts a) and b), discuss Sophia’s risk at titude. Provide a comprehensive explanation and justification for
your answer, taking into account the implications of the utility func tion estimated in part a) and the scenarios introduced in part b).
[15 Marks]
Question 2.
Consider the experiment in which subjects are presented with the follow ing two prospect situations:
In Situation 1, a noteworthy percentage of subjects choose Prospect A over
A*, whereas in Situation 2, a substantial number express a preference for
Prospect B* over B.
Do you agree that these preferences align with the axioms of the expected
utility theory Provide a comprehensive explanation and justification for
your answer and comment on your findings. [15 Marks]
2
Question 3.
On a sunny day, Mike attends the final match between two footbal
l teams—Team
A and Team B—competing for a cup trophy, and he is deciding which team
to bet on before kick-off. He has gathered information from the previous
20 final matches between the two teams. Team B has won 8 times, and
Team A has won 12 times. Additionally, he found that out of Team B’s 8
wins, 6 occurred on sunny days, and it was sunny only three times when
Team B lost. Given this information, Mike is certain, with 75 percent con fidence, that Team B will win the cup trophy today.
Do you agree with him Provide a comprehensive explanation and jus tification for your answer and comment on your findings. [15 Marks]
Question 4.
Prospect Theory aims to enhance our understanding of decision-making
under uncertainty. Let’s consider the value function, v(·), under prospect
theory, which is as follows:
v(x) = ( x
0.8 if x ≥ 0,
2( x)
0.5 if x < 0,
(1)
where x denotes gains or losses against a reference point.
a) Create a graphical representation of the value function and explain
its key features in comparison to the expected utility theory. Analyse
how the shape of the curve reflects individuals’ preferences and risk
attitudes, highlighting any deviations or nuances that distinguish it
from the typical utility functions seen in expected utility theory.
[15 Marks]
b) Suppose there are two outcomes, x1 and x2, each associated with
probabilities p1 and p2 respectively. Using the value function, exam ine which of the following prospects in P(p1, x1, x2) is preferred:
P1(0.6, 8000, 5000),
P2(0.7, 6000, 2000).
where p2 = 1 p1. Provide a comprehensive explanation and justi fication for your answer and comment on your findings.
3
[10 Marks]
c) According to the prospect theory people tend to weight outcomes by
transformed probabilities or decision weights. They are computed
using the weighting function w(·) which is as follows:
w(p) = p
δ
[p
δ (1 p)
δ
]
1/δ
.
where p denotes a probability. Given the parameter, δ = 0.5, examine
which of the following prospects would be preferred by people:
P1(0.02, 10000, 0),
P2(1, 70, 0).
Provide a comprehensive explanation and justification for your an swer and comment on your findings.
[10 Marks]
4