# ETF5952 QUANTITATIVE METHODS FOR RISK ANALYSIS

ETF5952 QUANTITATIVE METHODS FOR RISK ANALYSIS

Semester 2, 2019
ASSIGNMENT 2 • This assignment comprises 25% of the assessment for ETF5952. This is an individual, NOT a
syndicate, assignment. On the Assignment Cover Sheet, read the references to plagiarism and
collusion from University Statute 4.1. Part III – Academic Misconduct. • Deadline: 1PM, Oct 21 on Monday, 2019 • Submission:
1. Your assignment must be typed and you must submit a printed “hard copy” with an
Assignment Cover Sheet (from the “ASSIGNMENTS” section of Moodle). Submit it in
your class/tutorial before the due time, or submit it to your tutor’s mailbox, 5th floor H
Block. For each day that it is late, 10% of Assignment’s allocated marks will be
deducted. Do not submit your assignment in a folder and staple A4 pages.
2. Name your assignment: Surname-Initials_A2.docx or Surname-Initials_A2.pdf (eg.
Trump-DJ_A2.docx) and Upload this file to Moodle (as a backup) – as follows:
• Go to the “ASSIGNMENTS” section.
• Click on the “ASSIGNMENT 2” link to upload.
• The following message will appear momentarily, “File uploaded successfully.”
(To later confirm your upload was successful, go to the “ASSIGNMENTS” section and
click. On the “Assignment 2” uploading link. The uploaded file’s name will be shown.)
Note: DO NOT submit any Excel files. You may upload ONE file only. Retain your
marked assignment until after the publication of final results for this unit.
• Your tutor will NOT print or mark your assignment from Moodle.
• You are required to
o Answer all questions.
o Write your answer succinctly and include big tables and figures as appendices with
appropriate labels. (If you have trouble pasting figures and tables in your document,
you could print them out separately.)
• If you find possible typos or mistakes in this Assignment, please contact a lecturer or tutors
to clarify the questions for you. Also, if you have any other questions, please use
consultation time.
Plagiarism
Intentional plagiarism amounts to cheating in terms of University Statute 4.1. Part III – Academic Misconduct.
Plagiarism: Plagiarism means to take and use another person’s ideas and or manner of expressing them and to
pass these off as one’s own by failing to give appropriate acknowledgement. This includes material from any
source, staff, students or the Internet – published and unpublished works.
Collusion: Collusion is unauthorised collaboration with another person or persons.
Where there are reasonable grounds for believing that intentional plagiarism or collusion has occurred, this
will be reported to the Chief Examiner, who may disallow the work concerned by prohibiting assessment or
refer the matter to the Faculty Manager.
Question 1 (20 marks = 5+5+10)
XYZ produces the following figure, given the price of oil being equal $1.50. 1. Suppose that XYZ is risk neutral. Obtain the optimal choice and the corresponding expected monetary value (EMV). 2. Suppose that XYZ use the Maximin criterion to choose an area. Obtain the optimal choice and the corresponding EMV. 3. XYZ conducts a sensitivity analysis regarding probabilities of #1 of all three areas. The next page presents a spider figure, in which #1(F3), #1(F5) and #1(F7) indicates probabilities of #1 for Area 1, 2 and 3, respectively. a. Explain why the three lines cross at the centre (no more than 25 words). b. The red line, #1 (F5), becomes flat if changes are -10% or below. Explain why (no more than 25 words). Question 2 (30 marks = 5+10+5+10) Use the file, aribnb_MEL.csv, which contains data on houses/apartment listed in Airbnb in Melbourne. The data set contains the following variables: • price: price • bathrooms: the number of bathrooms • accommodates: the number of accommodates • bedrooms : the number of bedrooms • review_scores_rating: rating score • room_type: type of room 1. Estimate and report a linear regression model with the dependent variable of price and with regressors of bathroom, accommodates, bedroom, and review_scores_rating. Explain carefully an effect of bedrooms on price (no more than 30 words). 2. Create a dummy variable which takes 1 if room_type is Entire home/apt and zero otherwise. Then, Estimate and report the linear regression model in 1 additionally with the dummy variable. Explain carefully an estimated coefficient of the dummy variable (no more than 30 words). (Hint: To create a dummy variable in R, you can use (data_name$variable_name == value), which gives you TURE or FALSE, and also if value
is character, you have use double quotation.)
3. From Assignment 1, we know that the price contains outliers and it is better to mitigate
outliers’ effect. For this end, we consider an application of log transformation. Try to
estimate the linear regression model with the dependent variable of log price and the
same regressors as in 3. Explain whether it is possible and why (no more than 30 words).
4. To implement the idea explained in 3, we decided removing observations causing the
trouble. Estimate and report a linear regression model. Explain carefully an effect of
bedrooms on price (no more than 30 words.)
1000
1100
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1300
1400
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1700
1800
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2000
Change in Input (%)
Spider Graph of Decision Tree 'Aucution'
Expected Value of Entire Model
#1 (F3)
#1 (F5)
#1 (F7)
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
Expected Value
Question 3 (25 marks = 5+10+10)
We use a data set for analysing chronic kidney disease. The data set comes from the
Machine Learning Repository1, while the data set, kidney-clean.csv, at Moodle is cleaned up.
The outcome of interest is “class”, which takes “ckd” for chronic kidney disease and
“notckd” otherwise. For classification, we consider blood pressure (bp) and diabetes
mellitus (dm).
1. Obtain and report summary statistics of the three variables: class, bp and dm.
2. Estimate and report a logit model to predict chronic kidney disease with the regressors:
bp and dm. Use “glm” function. Given the estimation result, explain contributions of the
two factors (regressors) to kidney disease (no more than 15 words).
3. Estimate and report a CART model for predict chronic kidney disease with the same
regressors above (you can report only a tree figure). Using all information obtained from
the estimated tree, explain each end node (leaf) (no more than 30 words for each node).
Question 4 (25 marks =5+10+10)
We analyse returns (%) from a portfolio consisting of the index of Australia's top 200 companies
(ASX200) and a hypothetical safety asset. The data set, asx.csv, contains monthly return rate on
ASX200. Use the data on “return” to answer questions.
1. Report means, standard deviations and Value-at-Risk 5% of the monthly returns in the data set.
2. Consider a relatively safe financial asset, which has a half of average return of ASX200 but a half
of its standard deviations. To access financial portfolio based on pairs of ASX200 and the safe
asset, obtain simulation outcomes under the assumption that the pair follow normal
distributions with parameters estimated in 1. Let their correlation coefficient is -0.5. Consider
the three cases:
a. 0.5 ASX200 and 0.5 Safe Asset
b. 0.2 ASX200 and 0.8 Safe Asset
c. 0.8 ASX200 and 0.2 Safe Asset
To report simulated outcomes (1000 iterations), present a table that includes means, standard
deviations, minimum, maximum and VaR5%. Compare portfolios a-c and explain which portfolio
is the most risky or the least risky (50 words or less).
3. Suppose that you want to maximize the expected return from the portfolio that consists of two
financial products out, while restricting the VaR5% to be -4% or higher. Obtain the optimal portfolio
and report a table including your portfolio choice (weight), its mean return, minimum, maximum and
standard deviation. (You can choose any pair as long as you can satisfy the restriction).
1 https://archive.ics.uci.edu/ml/datasets/Chronic_Kidney_Disease