I acknowledge using [insert tool[s] name] to [what the tool did] on <<Date>>. With the <<prompt>>. What then happened?
For example, I acknowledge using ChatGPT (https://chat.openai.com/) to refine the academic language of my own work. On 1 April 2025, I submitted my entire essay to refine the academic language of my own work. With the prompt: “For the following essay, can you improve the academic tone and accuracy of language, including grammatical structures, punctuation and vocabulary?”.
2. The output produced by AI tools is non-deterministic (ie, another person cannot obtain the same information as you did); thus, citing AI tools is not a source and is inappropriate for an assignment.
Executive Summary
Introduction
A brief overview, the importance in the context of project management and your research objective.
Reflection on the MesoCYBER project (HarmonyHub)
a discussion and self-reflection on how team/group work was used in your HarmonyHub project – this should be linked to relevant literature (both presented in the unit and through additional research).
Literature Review and Analysis
A critical summary of existing academic research on your chosen focus, with an analysis of the key findings and insights from previous studies. You should also identify gaps in the current body of knowledge.
Impact on Project Management at MesoCYBER Solutions
A discussion of aspects of project management in light of Industry 4.0 and this Program of Projects, the benefits and challenges associated with your role. An analysis of predictions on how MesoCYBER will evolve regarding the projects, and implications for all program/project managers in the organization. Recommendations for integrating your discussed methods into the current project management practices.
Conclusion
Summary of key points discussed in the paper and final thoughts.
References
10– 20 academic references (referencing is to be in APA7 format). These also must be cited in-text according to APA 7. – Use the References font style for this section
“ Artificial intelligence is reshaping the kinds of projects
pursue organizations, and the skills project managers need to
deliver them successfully.” (Schmelzer & Walch, 2025)
Task: Individual Reflection and Research Paper – Project
Management
You have just completed a major group simulation project, which involved working continuously with AI Agents to gather project planning requirements, create system interface designs, and respond to changes. In this simulation, the feedback from students highlighted that you were not expecting the changes that occurred throughout the project (need for continuous engagement, taking ownership of your schedules and internal deadlines, changes to requirements, a company acquisition). Each of the tasks in the group project was designed to be centered around the key aspects of a project:
Your assignment concluded with the submission of a report to MesoCYBER Solutions, which provided designs for the interfaces of an innovative application to share best practices in team and group work, as well as a presentation at SydDevCon 2025. You are to use the group assignment as a case example for your final project.
From your interactions with FUTRE from MesoCYBER, your group should have identified the following final requirement for HarmonyHub:
Group Project – Functional Requirements
1. Framework Development:
o Comprehensive Framework: Develop a detailed structure for
capturing and documenting best practices in team and group work.
This framework should include guidelines, templates, and workflows to ensure consistency.
o Links to Literature: Integrate references to relevant literature and
research to validate and support the documented practices. This could involve creating a database of sources and linking them to specific practices.
2. User Interface:
o User-Friendly Design : Create an intuitive and easy-to-navigate
interface that allows team members to input and access best practices effortlessly. The design should minimize the learning curve and enhance user experience.
o Material Design Theme/Style: Utilise a Material Design theme to
ensure a modern and responsive interface. Adhere to MesoCYBER Solutions, color scheme as specified in the MesoCYBER Solutions, Style Guide to maintain brand consistency.
o Input Forms: Design input forms that are both simple and
comprehensive, allowing users to provide detailed information about best practices, including descriptions, steps, benefits, and relevant literature.
o Complies with WCG 2.1 Guidelines.
3. AI Chatbot:
o Develop an AI agent (UI-only) that functions as a chatbot to propose solutions to group challenges.
4. Categorization and Search (UI only):
o Categorisation: Design a robust categorisation system that allows users to classify best practices into relevant categories. This could include tags, labels, and hierarchical categories.
o Tagging: Enable users to tag best practices with keywords to facilitate easier searching and filtering.
o Advanced Search: Develop an advanced search functionality that
allows users to search for best practices using various criteria such as keywords, categories, tags, and associated literature. The search results should be relevant and quickly accessible.
Group Project – Non – Functional Requirements
1. Performance:
o Scalability: Ensure the system can scale to accommodate a growing number of users and best practices without performance degradation.
o Response Time: Optimise the system to provide quick response times for all user interactions, including inputting, searching, and accessing best practices.
o Ensure the AI tools respond quickly and accurately to user inputs.
2. Usability:
o Intuitive Navigation: Design the interface to be intuitive, with clear
navigation paths and user-friendly elements. Conduct usability testing to identify and address any pain points.
o Accessibility: Ensure the system is accessible to all users, including those with disabilities. Follow accessibility standards and guidelines to make the system inclusive.
o The AI chatbot should be easy to interact with and provide straightforward, actionable suggestions.
3. Reliability:
o Uptime: Aim for high availability with minimal downtime. Implement robust infrastructure and backup systems to ensure the system is
reliable and always available when needed.
o Error Handling: Develop comprehensive error handling mechanisms to manage and resolve any issues that arise during system use.
4. Security:
o Data Protection: Implement strong security measures to protect
sensitive data. This includes encryption, secure authentication, and regular security audits.
o User Privacy: Adhere to data protection regulations and best
practices to ensure user privacy. Provide clear privacy policies and obtain user consent where necessary.
5. Compliance:
o Regulatory Compliance: Ensure the system complies with relevant data protection regulations and industry standards, including GDPR and any other applicable regulations.
o Audit Trails: Maintain detailed audit trails to track changes and access best practices. This helps maintain and accountability
transparency.
The presentation at SydDevCon2025 was a huge success , and MesoCYBER Solutions will now initiate a new program of projects under the ‘MesoInnovate 4.0’ portfolio. The first project will be to develop the actual HarmonyHub system, along with a suite of complementary applications from the perspective of Industry 4.0 that will be created as future projects. You have been promoted to Program Manager in MesoCYBER’s PMO , overseeing projects in this new program (sub-task: compare the skills required to be a program manager, SFIA , to those of a project manager, SFIA ).
Your task is to conduct independent research and write a report on your plans for the ‘MesoInnovate 4.0’ portfolio of works , which will be tabled at the next C-Suite meeting run by FUTRE . This assessment encourages you to explore and analyze recent academic literature (peer-reviewed and published within the last 5 years) on emerging practices in project management (with a particular focus on the portfolio’s mission) and relate it to the MesoCYBER case study. This will help you stay updated with the latest advancements and prepare you to apply innovative practices in your future career. It will enhance your research and analytical skills, contributing to your career development.
What is Industry 4.0 – the concepts behind the Portfolio?
Industry 4.0, also known as the Fourth Industrial Revolution, refers to the ongoing transformation of traditional manufacturing and industrial practices through the integration of smart technologies. It builds on the digital revolution by combining cyber-physical systems, the Internet of Things (IoT), cloud computing, and Artificial Intelligence (AI) to create intelligent, interconnected, and automated business environments.
Industry 4.0 is reshaping teamwork by facilitating more intelligent, interconnected, and adaptable collaboration. The emergence of digital tools, cloud platforms, and real-time data sharing allows teams to operate seamlessly across different locations and time zones, thereby supporting remote and hybrid work models. Decision- making is increasingly data-driven, with analytics and dashboards offering shared insights that enhance collaborative problem-solving. As roles evolve, team members are required to develop new digital and analytical skills, fostering more agile and cross-functional team structures. Furthermore, collaboration between humans and machines is increasingly prevalent, necessitating teams to adjust to working alongside AI systems and autonomous technologies. Although these advancements enhance efficiency and innovation, they also pose challenges, such as digital fatigue, cybersecurity risks, and the need to maintain strong interpersonal relationships in virtual settings.
To accomplish this:
You must consider how you will define your role as ‘MesoInnovate 4.0’ Program Manager and what aspects of Project Management your role will focus on.
Remember, you are conducting a detailed analysis and presenting your findings in a written report.
The report should cover the following aspects:
• Executive Summary
• Introduction: A brief overview, the importance in the context of project management, and your research objective.
• Reflection on the MesoCYBER p project: a discussion and self-reflection on how team/group work was used in your HarmonyHub project – this should be linked to relevant literature (both presented in the unit and through additional research).
• Literature Review and Analysis: A critical summary of existing academic
research on your chosen focus, with an analysis of the key findings and insights from previous studies. You should also identify gaps in the current body of knowledge.
• Impact on Project Management at MesoCYBER: A discussion of aspects of project management in light of Industry 4.0 and this Program of Projects, the benefits and challenges associated with your role. An analysis of predictions on how MesoCYBER will evolve regarding the projects, and implications for all program/project managers in the organization. Recommendations for integrating your discussed methods into the current project management practices.
• Conclusion: Summary of key points discussed in the paper and final thoughts.
• References: A minimum of ten (10) and an upper limit of twenty (20)
academic references correctly used and referenced in the report (APA7).
Note : Code used for each analysis must be included in your response.
1) [10 marks] Multidimensional wine
The Wine dataset contains the results of a chemical analysis of wine samples grown in the same region of Italy. While all samples come from a single region, they originate from three distinct grape cultivars. The dataset includes various chemical properties used to assess the composition and quality of the wines.
The measured variables are:
a. Alcohol
b. Malic acid
c. Ash
d. Alkalinity of ash
e. Magnesium
f. Total phenols
g. Flavonoids
h. Nonflavonoid phenols
i. Proanthocyanins
j. Color intensity
k. Hue
l. OD280/OD315 of diluted wines
m. Proline
Note : Do not use the cultivar information (do not use the column “Class”) in your analysis for this item.
A) [3 marks] Cluster Analysis
Perform a cluster analysis. What method did you select? Justify your choice. (Maximum: 100 words).
B) [3 marks] Metric Multidimensional Scaling (MDS)
Perform a metric MDS analysis. Did you apply any preprocessing to the dataset? What distance metric did you choose? Justify your decisions. (Maximum: 100 words).
C) [4 marks] Comparison to Cultivars
Does your analysis (A and B) support the existence of three distinct cultivars? Why or why not? Provide a critical interpretation. (Maximum: 200 words).
2) [10 marks] Wine testing
As wine growers are interested in distinguishing between cultivars, they want to know whether it is possible to reliably discriminate between them based on their chemical composition. Carry out a Discriminant Analysis by following the steps below. For each question, justify your answers.
A) [3 marks] Canonical Discriminant Analysis.
Split the dataset into a training and testing set. Perform an adequate Discriminant Analysis using all variables. Briefly interpret the canonical functions and the separation achieved between cultivars (maximum: 200 words).
B) [1 marks] Classification Accuracy
Apply the discriminant model to the testing subset. What is the overall classification error rate? Based on this result, would you trust the model’s performance? Briefly explain (maximum: 100 words).
C) [2 marks] Stepwise Discriminant Analysis
Conduct a Stepwise Discriminant Analysis on the training set. How many variables are selected, and which ones? Briefly describe the procedure cultivars (maximum: 100 words).
D) [4 marks] DA with Selected Variables
Using only the subset of variables selected in (c), repeat the Analysis on the training set, and test it on the testing set. Compare the results of the full-variable and stepwise-variable analyses. Which model performs better in terms of error rate or interpretability? Which one would you recommend for future use? Briefly explain (maximum: 200 words).
INFS6004 Digital Business Transformation Assignment 1 2025
News Research & Analysis – Specification
This assignment assesses skills in research and critical analysis required for an independent learner able to keep up to date with the latest practices in digital transformation and change.
You are required to submit a brief written business report on a company based on no less than THREE news articles, which are relevant to INFS6004, with your original description and original analysis of a company’s digital transformation presented in the article.
Marks: 15% of unit assessment. Note: Individual assignment
Due date: 21 March 2025, before 11:59 pm, submit the assignment through INFS6004 CANVAS site.
Requirements: A maximum of 700 words (+ 10% allowance) in a business report
Report: Your report includes a report title page with the company name and your name and SID, followed by the company and news articles summary, analysis, conclusion, and Appendix. The Appendix lists the references you used with sufficient details for a reader to locate each reference directly.
A THREE marks penalty will apply for the report with less than THREE news articles.
Activities & Deliverables
• Search for at least THREE news articles on a company of interest to you that presents details on a digital transformation relevant to INFS6004 that meets Assignment 1’s requirements and Marking Guide.
• To reduce the risk of plagiarism, the news articles need to be published after 1st January 2023.
• Prepare and submit a brief review in a business report format that addresses Assignment 1’s requirements and Marking Guide.
• Marks are awarded for consistency with the business report structure, format and requirements, your own original description and your own original analysis.
• Copies of the major news articles used in your report must be included. The Appendix and References are NOT included in your word count.
Notes:
1. All reports need to be carefully checked prior to submission to ensure there are no spelling or grammatical errors.
2. All references should adhere to the guidelines laid out in the APA Referencing Guide:
Assignment 3: Ol in Context: ORGANISATIONAL CASE STUDY
INTRODUCTION TO THE CASE STUDY
CONTEXT: ORGANISATIONAL TRANSFORMATION WITH AI TECHNOLOGIES
Over the past 18 months Al, and generative Al in particular, has emerged as a radical game changer for all organizations. Machine learning, data analytics and other Al technologies are reshaping the way organizations go about their business and are profoundling reshaping organizational processes, structures and systems (Faraj, Pachidi & Sayegh, 2018).
The fundamental nature of Al technologies are also raising deep ethical questions about organizational responsibility in their design, development and deployment. Australia, like many other countries, is looking into what regulatory guardrails are needed to support safe and responsible Al innovation and adequately manage their risks and negative impacts on individuals, communities and societies (DISR, 2023). With the European Union’s Al Act coming into force on 1 August 2024 and being fully applicable from 2 August 2026, organizations have two years to put in place the systems for risk assessment, compliance with accountability and transparency requirements, and other oversight and monitoring mechanisms (Blackman & Wasiliu-Feltes, 2024; Nicoud, 2024; Wade & Yokoi, 2024).
For your Case Study we are asking you to explore your organization in depth to understand how it is looking to leverage Al technologies and manage the associated digital transformation.
We want you to apply an Ol perspective to analyze how your chosen organization is approaching Al innovation, and what that means in terms of structural changes and/or the development of new products, services, practices and processes.
Finally we want you to consider an aspect of organizational innovation from the perspective of complexity, and to suggest, based on your research, ways that models or theories introduced through the Ol unit can contribute to Al-driven organizational innovation and transformation
This assessment task addresses the following subject learning objectives (SLOs): 1 and 2.
Task
In this assignment, students will giveadataexplorationreporton theirworkintheproject. Their group willdescribe theresultsof their dataexplorationandfeatureengineeringbyusing theSAS Viya tool. Thereport shouldcover thebusinessproblems,characteristics of thedata,and transformation of the data.Thereportshouldbestructured andpresentedinline withprofessional industryreport format.
Length
15pagesmax in an11 or12-point font.
Criteria Linkages(Please insert addition rowsin table where required)
AssessmentCriteria
Weight(%)
SLO
GA
1
Depth of understanding ofthebusiness problem andquality of data exploration results.
100%
1,2
D,E
2
3
4
5
6
Assessment Task 1: Data Exploration
Objective: The main objective of this assessment task is to apply data exploration and feature engineering techniques to real-world business problems.
Relevant Learning Objectives :
• Subject Learning Objectives: SLO 1
• Course Intended Learning Outcomes: CILO D.1
Format:
• Type: Report
• Work: Group assignment, but each member will be individually assessed.
Weightage: 30% of the overall grade.
Task Description: Students are required to:
1. Form groups of 2-3 (you may increase group size at max of 5 members based on your tutor’s choice) members.
2. Select a dataset similar with the COMMSDATA (in SAS Viya Course) or any other
existing datasets is available for classification task. Selecting a right dataset is key in this assignment. Please ensure to select a large dataset (over 1000 data points).
3. Select a predictive business analytics task based on the chosen dataset.
4. Collaboratively analyze both the chosen business problem and its associated dataset.
5. Submit a report, detailing:
o The business problem they aim to solve.
o Characteristics of the chosen dataset.
o Data transformation processes applied.
o Proposed method to address the data mining problem.
Additionally, the report should also describe:
• The composition of the group.
• Roles and responsibilities of each team member.
• A proposal for addressing the data mining problem.
• A comprehensive plan outlining how they intend to solve the problem.
Assessment Criteria: Assignments will be evaluated based on:
1. Description of business problem
2. Quality and feasibility of the proposal and plan.
3. Data exploration and initial findings:
-Quality of pre-processing
– Quality of initial findings
4. EDA Visualisation
Submission Details:
• Format: Electronic copy
• Platform: Canvas for report and SAS Viya (in Exchange Folder) for upload the pipeline
• Maximum Length: 15 pages (using 11 or 12-point font)
• Due Date: 11.59pm, Friday 8 September 2023
• Feedback Timeline: Feedback with marks will be provided within 2 to 3 weeks after submission.
The following table specifies the weights and values per unit of five different products held in storage. The quantity of each product is unlimited.
Product (i) Weightperunit(wi)Valueperunit(vi)
1
7
9
2
5
4
3
4
3
4
3
2
5
1
0.5
A plane with a weight capacity of 13 is to be used, for one trip only, to transport the products. We would like to know how many units of each product should be loaded onto the plane to maximize the value of goods shipped.
Use dynamic programming to find the optimal solution. Please provide the following details (a) describe clearly the stages, (b) states, (c) allowable decisions at each state in each stage, etc. Finally, please state what the optimal quantity of each product to be loaded to the plane is.
Problem 2
Suppose (by some miracle) that you have access to a particular company’s stock prices over the next 10 days, and they are as follows:
DayPrice
1
7
2
3
3
2
4
8
5
11
6
9
7
5
8
10
9
6
10
4
It is the start of Day 1, and you do not own any shares. At the start of each day, you can either purchase one share or sell any shares that you have on hand (as many as you like, but not more than you own), or do nothing. Suppose that shares are worthless after Day 10 (the company goes bankrupt on Day 11). Your goal is to maximize profit over the 10-day period.
Please solve the above problem by formulating a dynamic program following the steps below
a) What are the states and stages associated with this problem?
b) What is the set of feasible actions associated with stage n and state s ? How much is gained/lost by taking each action?
(Hint: It may be easier to let your action be the number of shares you have at the end of day n , rather than the number of shares you buy or sell on that day)
c) How can the optimization function be interpreted here? That is, given a stage n and a state s , what is fn* (s)?
d) Formulate the above problem as a dynamic program and solve it using GAMS/Python. Write the optimal sequence of actions below, and the profit that these yields
1.You can open this “ipynb”file using VSCode.You may need to download Jupyter extension.
2.You should read the requirements carefully and complete the codes in specific parts.You should not modify any other content except your codes.
3.Assignment2’s deadline is October 20.Please submit your codes in time.No delay is allowed.
AutoGrading:
1.YOU MUST NAME YOUR NOTEBOOK USING ONLY YOUR STUDENT NUMBER(eg, 24018121r.ipynb).OTHERWISE AUTOGRADING WILL NOT WORK.
2.You can only write your codes in the specific code cells and within a certain range.Write all the codes in a single function and return the final result.
3.You can not modify the function names and parameters.
4.You better not modify anything related to otter and grader.check(…).
5.You can test and print the results in the test cell when writing your assignment, but make sure that the solution code in the specific code cells does not contain any print statements.
6.Violating the above rules may lead to unpredictable results, such as a 0 mark.
Question 1(25pts)
Create a program with a function called compare_digit_sums(s).This function takes a string s as its parameter.If s can be converted to a floating-point number, the function returns the integer part (in t)of the number if the sum of the digits in the integer part is less than or equal to the sum of the digits in the fractional part.If the sum of the digits in the integer part is greater,it returns the fractional part.If s cannot be converted to a floating-point number,it returns “Invalid input”.
Requirements
1.The functionality of the program and function should be correct.
2.You should implement the function compare_digit_sums.
Assumptions
1.We assume that the input string consists solely of eleven specific characters:0,1,2, 3,4,5,6,7,8,9 and .when calling the function.Situations involving other
characters in s,such as a6 or le5,are not considered.
Question 2 (25 pts)
Design a function get_passenger_list.This function has three parameters:
· existing_passengers :it is a list representing the names of passengers currently on board.
· boarding_passengers :it is a list representing the names of passengers boarding at this station.
·alighting_passengers: it is a list representing the names of passengers alighting at this station.
It is used to predict the list of passengers on the train after it has passed through a station. Importantly, the function can be invoked without specifying values for the
boarding_passengers(or alighting_passengers) parameters when no passengers board (or alight)at a station.If a passenger in the alighting_passengers is not found in the
existing_passengers ,the function returns the string ‘Invalid input’.Otherwise,it returns a list of passenger names on board,sorted in ascending order .
Question 3 (25 pts)
Create a function called find_longest_word_length . This function takes a paragraph as input and calculates the length of the longest word in the paragraph. The paragraph will contain only letters(both uppercase and lowercase)and four non-letter characters:newline (n),period(.),comma(,),and space().These characters separate words.The function returns the length of the longest word.
Question 4 (25pts)
Create a function find_parentheses.This function calculates the total number of parentheses pairs in an expression,regardless of the parentheses’nesting depth.The function takes a string parameter expression,which is an arithmetic expression containing numbers,operators(+, a , * , / ) ,and parentheses((,)).The function returns the total number of matched parentheses pairs.If the expression contains unmatched parentheses (ie, more left parentheses(than right parentheses),or vice versa,or if a first right parentheses)appears before a left parentheses(),the function returns None
This course covers the essential concepts of programming for students who desire to understand computational approaches to problem solving using live code examples and in-class exercises in Python, Bash scripting and High Performance Computing (HPC) environments.
Description
This 1 unit course covers the essential concepts of computer programming to an audience with little to no prior programming experience but a desire to understand computational approaches to problem solving. It is fully geared to use live code examples and in-class exercises — bringing the ideas to life, but without bogging down too much in computer idiosyncrasies. We recommend that you bring a laptop or tablet to lecture each week to follow along with the work.
Expectations and Goals
This course is divided in 3 main aspects: Foundations of Programming, Foundations of Computational Data Science. Our new Data Scientists will get comfortable with a myriad of programming/scripting languages and technologies, and learn to use them to solve the problem at hand. Therefore, this course will be a healthy blend of Python, Bash scripting and High Performance Computing (HPC), along with modeling techniques.
Prerequisites and Course Materials
Prerequisites
During the first half (5 weeks) of the therm, students must independently familiarize themselves with the following concepts using the provided materials and optional in-person training opportunities (workshops, seminars, etc.):
● the Linux (UNIX) operating system, file system and the BASH command line interpreter
● High-Performance Computing at Dartmouth – Andes, Polaris, and Discovery
○ Knowledge Base Article (KBA)
Textbook and software
There is an optional free on-line textbook for the course, Project Python. This is the textbook used as CS1 lecture notes. Reading the text and doing the exercises in it is encouraged but not necessary to do well in this course. More material as needed during the term.
For Python, we will be using “notebook environments”, either local (Jupyter Notebooks viaAnaconda) or online (Dartmouth JHub). For Bash scripting and to access HPC environments, you will be required to use FastX. Windows PC users will also want to install MobaXterm.
Course Schedule
Foundations of Programming and Computational Data Science
You will be required to complete any three of the following four questions within 24 hours. Your work should be done by yourself, do not use gpt or other forms of AI tools, if you are not clear about the meaning of a question, just write your understanding of the question, we will have a professional review teacher to score your calculation results, please remember that some questions may not be calculated correctly. But as long as you write out your own thinking process is also OK, remember never use AI, once found using AI will not work with you for life! Good luck!
Question 1
Consider a stylized two-period portfolio choice problem with a representative agent. The agent’s preference is given by the following:
U(C) = u(C0) + E[u(C1)], (1)
where u(c) = −e −γc, and γ > 0.
The agent faces the following constraints at each period:
C0 + hp ≤ W0, (2)
C1 ≤ W1 + hX, (3)
where h is the portfolio choice that the agent chooses at time 0. The per capita endowment at time 0 and time 1 are given by: W0 = 1, W1 = (3, 6, 9).
At time 1, there are three equally likely states.
The payoff matrix X is given by:
(4)
where Xjs denotes the payoff of asset j (row) in state s (column).
Please answer the following questions:
1. Is the market complete? Why or why not?
2. What are the agent’s absolute and relative risk aversion?
3. Describe the agent’s optimization problem carefully (eg, choice variables, constraints).
4. What are the optimal consumption and portfolio allocation? Explain.
5. What is the pricing kernel?
6. Derive the pricing equation that allows one to price any asset j in this model.
7. What is the risk-free rate?
8. What is the price of asset 2 with payoff (1 2 3)?
Question 2
Consider a stylized asset pricing model with two periods. The representative agent’s preference is given by
V (C) = v(C0) + E[v(C1)], (5)
where
and γ ≠ 1. The agent’s endowment at time 0 is W0 = 1. Assume the market is complete.
1. For a random consumption z, with ln
derive the exact risk compensation function ρ(y, z).
2. How does the exact risk compensation function vary with y, σz, and γ? Interpret your results.
3. The distributional assumption for C1 continues to hold as in part 3. For this question, further assume γ = 2 and σc = 1%. There is a risky security j with expected excess return E[rj − rf ] = 5%. What can you say about the volatility σj of this risky security?
Question 3
Consider a single-period binomial tree of firm value Vt, where t = 0, 1. Suppose the firm value Vt evolves from time 0 to time 1 as follows:
• With probability p, the up state of the world is realized, and V1 = uV0
• With probability 1 − p, the down state of the world is realized, and V1 = dV0
Assume that the market is frictionless and dynamically complete. Also, assume u > d. Denote rf as the riskfree rate. For illustration, the binomial tree is given below:
For the following questions, assume V0 = 1, u = 1.6, d = 0.7, p = 0.2, rf = 0.02..
1. Given that the market is complete, we will have two Arrow securities, one corresponding to each state. Compute the prices of these two Arrow securities. Interpret your results.
Now, we extend the binomial tree to two periods, with the same setting.
Similar to setting in the lecture, we extend the state space from period 1 to period 2. That is, there are two states up and down (with same probabilities p and 1 − p) possible from each of the period 1 state realizations. Now, we have four states of the world at the end of period 2: uu, ud, du, and dd. In other words, the time 2 firm value is given by: V2(s) = sV0, where s = uu, ud, du, dd.
Again, for illustration, the binomial tree is given below:
2. What are the four period 0 Arrow prices for the four states at period 2?
3. Consider the manager of the firm has the option to make an initial investment at time 0, with an up-front cost I0 = αV0. The investment only pays off at period 2. In particular, conditional on investment, firm value at time 2 will be: sV0 in uu state, mV0 in ud and du states, and fV0 in dd state. What is the net present value of this investment project at time 0? Under what conditions will the manager choose to make the investment at time 0?
4. Now, assume that the manager chooses not to exercise the option to invest at time 0. However, the manager can learn the prospect of the project as time evolves. In particular, at time 1, the manager re-evaluates the prospect of the investment project. state. Under what conditions should the manager choose to invest at time 1? Note that the context under which the manager makes the decision depends on which state is realized at time 1.
Question 4
Consider a continuum of investors i, with mean-variance preferences:
There are N risky assets with payoff vector
and a common initial endowment w0. The supply of the assets is the vector x¯ + x, where x¯ is known and
All shocks are independent and normally distributed in this economy. Suppose that investors get a signal vector of the form s = z + yf + ei where
is an N × 1 vector that is independently and identically distributed across investors. z and y are known parameters, common to all investors.
1. Is s an unbiased signal about f? If not, what transformation of s is required to make it unbiased?
2. What is V [f|s]? Is this matrix diagonal? After updating their beliefs with their signal, do agents believe that asset payoffs are conditionally uncorrelated across assets? Why or why not?
3. What is E[f|s]?
4. What is the dispersion (cross-sectional variance) in the beliefs from part 3? In other words, what is E[(E[f|s] − E¯[f|s])2], if E¯[f|s] := RE[f|si ]di is the average agent’s belief?
5. What is the market return in this model?
6. Suppose that the price vector is a linear function of the payoffs f and the supply noise x: p = A + Bf + Cx. Does the CAPM price assets in this economy? Justify your answer.
7. What is E[f|s, p]?
8. What is V [f|s, p]?
9. What is the optimal portfolio choice of investor i? Is this portfolio on the mean-variance frontier?
10. Express the market clearing condition (equate supply and total demand
