·         This assignment comprises 20% 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: 5pm on Friday, 20 October, 2017
·         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, 5^th 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 stapleA4 pages.
2.       Name your assignment: Surname-Initials_A3.docx or Surname-Initials_A3.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 3” 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  This includes material from any source, staff, students or the Internet – published and unpublished works.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 (45 marks = 15(=5+5+5)+ 30 (=10+5+5+10) )
 
 
A bank manager considers an investment strategy. She has three options: a stock for a big company, a bond and a stock for a start-up company, whose stock returns are denoted by SB, BB, and SS, respectively. It is known that SB and BB follow normal distributions: SB~N(8%,10%) and BB~N(2%,1%) and SB and BB have a correlation of -0.5. SS are independent of both SB and BB, and has discrete distribution:
 

 

1. Using @Risk or equivalent software, simulate returns of SB, BB and SS and fill out the following summary statistics of simulated data. Use percentage returns up to 2 decimal points (for instance, 3.99%). 

 
 

Standard deviations
Interquartile Range

 
 

2. The bank manager asks you which investment you recommend among the following four strategies.

 

 

1. For each investment strategy, report a histogram of simulated returns and also report a table including summary measures (Minimum, Maximum, Mean, 90% CI, Mode, Median, Std Dev).

 

2. Among four strategies, which one is the best and the worst strategy in terms of average return?

 

3. Which one is the safest strategy in terms of standard deviations?

 

4. Under some bank regulation, the bank manager maintains the Value-at-Risk 5% of the portfolio return being -2.5% or above. Find a portfolio that satisfies the regulation and achieve an average return of 4% or above. Report your portfolio and simulation outcomes (histogram, mean and 5% percentile). 

 
 
 
 
Questions 2 (40 marks=5 + 5 + 10 + 10 + 10)
 
Suppose that you were wondering whether to open a café. There are two choices: Strategy #1 is not to open (Not IN) and Strategy #2 is to open (IN). The table below shows unit price and cost per customer and a fixed cost per day in dollars (note: you have to pay the fixed cost, such as a rent every day regardless of the number of customers.)
 

Strategy	#1	#2
Decision	Not IN	IN
Unit Price	0	3.5
Unit Cost	0	1.5
Fixed Cost	0	500

 
The number of customers varies according to weather condition and you consider the following probability table.
 

	Probability	#Customer
Sunny	0.75	600
Rainy	0.25	260

 
If you do not open a café, then you can invest your asset into a fixed income security, which generates a return of $380 per day.
 
1.  Fill out a table below regardingrisk profiles for profitsaccording to strategies and weather conditions. [Hint: profit is given by # customers * (unit price – unit cost) – fixed cost.]
 

Strategy	#1	#2	Probability
Sunny
Rainy

 
 
2. Obtain Expected Monetary Value (EMV) for two strategies.
 

Strategy	#1	#2
EMV

 
3. Draw a decision tree by using PrecisionTree software. [Hint: your tree has four end nodes.]
 
4. Conduct a one-way sensitivity analysis by varying the probability of being sunny. Use base-value +/-25% with 11 steps. [Hint: your original file has to set up the probability of rain as a formula of (1 - the probability of being sunny), rather than a value of 0.25.] Report a sensitivity graph and a strategy region graph (EMV and variations in the probability) and discuss which strategy is the best in terms of EMV (30 words or less). 
 
5. Conduct a two-way sensitivity analysis by varying the probability of being sunny (0.75) and the fixed investment return per day ($380). Use a base value +/-25% with 11 steps for both variables. [Hint: To refer a fixed return ($380) for the sensitivity analysis, you can choose only one cell. Thus, before doing this analysis, you should link another cell to the cell that you will use for this analysis. In other words, if you put a value of $380 in two cells, the software does not recognize that they are the fixed cost. Please wait for Week 10 lecture.]Report a figure of strategy region.Also, discuss which strategy is the best in term of EMV when the probability of being sunny is 60% (50 words or less).
 
Questions 3. (15 marks = 5 + 5 + 5)
 
This question asks you to generate X-bar charts, using a file, X-bar-chart-data.xlsx. The file contains 50 averages of subsamples following N(2,3) and the ones following N(2,6). The subsample size is 5 (n=5). 
 
 
1. Report a X-bar chart using averages of subsample generated by N(2,3). Here, assume that the standard deviation (σ = 3) is known and use 2-sigma deviation. You report only the chart but you may follow steps below:
 
Step 1: obtain the average of 50 averages of subsample from N(2,3).
Step 2: Obtain the UCL and LCL with the sample size n =5 and 2-σ deviation.
Step 3: plot 50 subsamples from N(2,3) with values obtained in Step 1-2.
 
 
2. Report a X-bar chart, that has averages of subsample generated by N(2,6) with the UCL and LCL obtained in Step 1-2 above.
 
3. Can the X-bar chart detect a change of distribution in 2?Explain (no more than 50 words).