1.   Submission  deadline: The assessment  links will be accessible  on Moodle from 10:00 AM, 18th January to 23:55 PM, 29th January, Sydney Time.

.    You may  attempt the assessment  at  any time  during the provided  window, but please note that the assessment will close sharply at 11:55 PM on January 29th. For instance, if you begin your attempt at 11:25 PM on January 29th, you will have only 30 minutes to complete the task.

.    Please plan your time accordingly and avoid waiting until the last minute. Please be aware that any failure to submit due to technical issues near the deadline will not be considered a valid reason for applying for special consideration.

.    Late submission: Late submissions without prior approval for special consideration will incur a 5% mark deduction for each day or part thereof (including weekends) beyond the due date and time.

2.   Submission  format:

.    Please  submit BOTH questionnaire  and Excel work. If you only submit  one of them, you will not be able to receive any marks for this assessment. Both of these links can be found in the Moodle section "Assessment - iLab: Data Exercise"

.    Questionnaire:  To submit your solutions for each question, please use the "Data exercise Questionnaire" link. For successful submissions:

i.   Please   report   your   solutions   as   decimals   (not   percentages)   exactly following the example provided in the questionnaire.

ii.   Only  ONE  attempt  is  allowed.  So  please  prepare  your  solutions  ready before you start the questionnaire to avoid any technical issues.

iii.   Your  attempt  will   be  submitted   if  and  only   if  you   click   "Submit questionnaire". Please note that you cannot make any further changes and

resubmit the questionnaire after you click the submission button.

iv.   All the questions should be attempted (i.e., no questions left blank).

.    Excel:  Please   submit   your  Excel   spreadsheet  via   the  "Data  exercise  Excel submission" link.

i.   Your marks will be determined by your answers in the questionnaire rather than the Excel file. However, the Excel file may be used/investigated by grader if any clarification  or checking of your solutions  is required. The Excel file does not require a specific format, as long as it is clear and easily understandable. For clarity, you might consider creating separate sheets for different questions and labeling them appropriately.

3.   About enquiries: If you have questions regarding this assessment, please raise them on Moodle discussion  forum.  However,  please  keep  in  mind  that  this  assessment   is   one  of  the individual assessments for this course (i.e., please treat it as a takehome exam). Therefore, only clarification-type questions (e.g., the ambiguity of the question) will be answered.

4.   The total mark of this assessment is 54. It accounts for 20% of the final mark for this course.

You are evaluating  a  portfolio  of U.S. equities  drawn from the  S&P500.  The  five  stocks in

your portfolio have the FactSet identifiers as follows:

.    Assume the annualised risk-free rate is 3% for this assessment

.    The monthly return data can be found in the Excel “Data pool” on Moodle

NOTE:

.    Annualized aveTage TetuTn  =   12 × AveTage monthly TetuTn

.    Annualized vaTiance =  12 × vaTiance of monthly TetuTns

.    Annualized standaTd deviation  =  SQRT(Annualized vaTiance) =  SQRT( 12) × standaTd deviation of monthly TetuTns

.    Annulaised ShaTpe Tatiop   = AnnualizedAnnualized(aveTage Te)tstandaTd(uTn p−An)ndevia(uliaz)t(e)io n(d R)isk  FTee Tate

p

Gift mark for assigned group number.

Q1: what  is  your assigned  group  number  which  can  be found on the first page of your instruction file? (2 marks)

For Q1 to Q46: using the monthly data from 2014 Jan to 2018 Dec for the portfolio construction. Please calculate the annualised average return and annualised variance of your assigned stocks and S&P 500 index over the sample period (i.e., 2014 Jan to 2018 Dec), and check your basic summary statistics with the solutions  provided  in  the  excel  “Data  pool”  before  you  start  solving  the questions.  Your calculation  of  the  basic  summary  statistics   will  not  be  marked  but  the purpose of this step is to make sure you do not make naive mistakes  (e.g., copy and paste errors) at the very beginning of this assessment.

1.   Markowitz optimization

.    For the group of stocks assigned to you, form the minimum  variance frontier. What is

the minimum attainable annualised standard deviation of the portfolio:

Q2: at an annualised average return level of 0% (1 mark)

Q3: at an annualised average return level of 15% (1 mark)

Q4: at an annualised average return level of 30% (1 mark)

.    Calculate the portfolio weight for Global Minimum Variance Portfolio (GMVP). What is GMVP portfolio weight? What is the annualised expected return and annualised standard deviation of GMVP?

Q5: GMVP portfolio weight in STOCK 1 (1 mark)

Q6: GMVP portfolio weight in STOCK 2 (1 mark)

Q7: GMVP portfolio weight in STOCK 3 (1 mark)

Q8: GMVP portfolio weight in STOCK 4 (1 mark)

Q9: GMVP portfolio weight in STOCK 5 (1 mark)

Q10: GMVP annualised average return (1 mark)

Q11: GMVP annualised standard deviation (1 mark)

.    Calculate the portfolio weight for the Optimal Risky Portfolio (P*). What is the P* portfolio

weight? What is the annualised expected return and annualised standard deviation of P*?

Q12: P* portfolio weight in STOCK 1 (1 mark)

Q13: P* portfolio weight in STOCK 2 (1 mark)

Q14: P* portfolio weight in STOCK 3 (1 mark)

Q15: P* portfolio weight in STOCK 4 (1 mark)

Q16: P* portfolio weight in STOCK 5 (1 mark)

Q17: P* annualised expected return (1 mark)

Q18: P* annualised standard deviation (1 mark)

.    Suppose your utility function is U = E(r) 一 3σ2 . Form an optimal complete portfolio by combining P* with the risk-free asset. What is the portfolio weight on each of individual asset in this optimal complete portfolio? What is the max utility score that you can achieve?

Q19: complete portfolio weight in STOCK 1 (1 mark)

Q20: complete portfolio weight in STOCK 2 (1 mark)

Q21: complete portfolio weight in STOCK 3 (1 mark)

Q22: complete portfolio weight in STOCK 4 (1 mark)

Q23: complete portfolio weight in STOCK 5 (1 mark)

Q24: complete portfolio weight in Risk-free asset (1 mark)

Q25: Utility score is? (1 mark)

2.   Short Selling Constraint

.    Construct the GMVP and P* with the short selling constraint:

Q26: GMVP(with short selling constraint) annualised average return (1 mark)

Q27: GMVP(with short selling constraint) annualised standard deviation (1 mark)

Q28: P*(with short selling constraint) annualised average return (1 mark)

Q29: P*(with short selling constraint) annualised standard deviation (1 mark)

Q30: Compare the GMVP that you construct without and with short-selling constraints. Make comments  on their performance  and  explain  why short  selling  constraints  may  affect  the

optimization procedure (3 marks)

Q31: Compare the P* that you construct without and with short-selling  constraints.  Make comments  on their performance  and  explain  why short  selling  constraints  may  affect  the

optimization procedure (3 marks)

3.   SIM Optimization

.    Estimate  the Single Index Model ai  and βi, for each  stock in your portfolio using the

regression equation:

Rit  = a i  + βiRMt  + εit

where Rit  and RMt   are the excess return for individual stocks and S&P 500 index

Q32: What was the lowest beta out of your 5 stocks? (1 mark)

Q33: What was the highest beta out of your 5 stocks? (1 mark)

.    Decompose the total variance using σi(2)  = βi(2)σM(2)  + σε(2)  for all 5 stocks

Q34:What was the lowest σε2  out of your 5 stocks? (1 mark)

Q35: What was the highest σε2  out of your 5 stocks? (1 mark)

.    Construct GMVP and P* under the SIM.

Q36: GMVP annualised average return (1 mark)

Q37: GMVP annualised standard deviation (1 mark)

Q38: P* annualised average return (1 mark)

Q39: P* annualised standard deviation (1 mark)

Q40: Briefly describe and comments on the key differences between the Markowitz and SIM optimization procedure (hint: You should point out the additional assumption that SIM made on the variance-covariance matrix construction, and provide your own opinion on whether the assumption fits the data or not) (4 marks)

4.   Treynor-Black Model

.    Explore  the  potential  mispricing  opportunities   of  the  5  individual  stocks  under  the Treynor-Black Model. Form a new optimal risky portfolio (New P*) by combing the 5 individual stocks and S&P 500, what is your optimal portfolio weights on each stock and

S&P 500 in your new optimal risky portfolio:

Q41: STOCK 1 (1 mark)

Q42: STOCK 2 (1 mark)

Q43: STOCK 3 (1 mark)

Q44: STOCK 4 (1 mark)

Q45: STOCK 5 (1 mark)

Q46: S&P500 (1 mark)