UNSW Sydney SCHOOL OF RISK AND ACTUARIAL STUDIES ACTL3182: ASSET-LIABILITY AND DERIVATIVE MODELS AND ACTL5109: FINANCIAL ECONOMICS FOR INSURANCE AND SUPERANNUATION TERM 3 2020 ASSIGNMENT DUE DATE: 13th OF NOVEMBER 2020 11:59pm 1 The Assignment Task and Instructions Construction of a self-managed superannuation fund using mean-variance port- folio theory [100 marks] With the defined contribution (DC) superannuation plan being the dominant retirement saving initiative in Australia, it is critical for superannuation contributions to be invested in asset classes matching each individual’s needs. The superannuation guarantee system in Australia mandates employers to sufficiently support their employees through payroll contributions to employee’s chosen superannuation fund. Each employee is responsible for choosing appropriate asset classes upon which the contributions can be invested in. Contrary to this, research on financial literacy shows that majority of employees across various sectors irrespective of age choose the “default” option which may not be reflective of their risk preference. Research shows that very few individuals have any idea of what constitutes such default options, with even fewer individuals having the knowledge of switching among investment options during the accumulation phase. As an actuary, you are smarter and you wish to structure your own self-managed superannuation fund premised around mean-variance portfolio theory of Harry Markowitz with your investment horizon spanning across your working life. Your wish is for this fund to be predominantly Australian equities and some exposure to fixed income and international stocks. Using your knowledge of the markets, pick 20 stocks from the Australian Securities Exchange (ASX) that can form your dream portfolio. Page 1 of 6 You are expected to provide a paragraph for each stock justifying why you have included it in your portfolio. Download the daily closing prices for each stock for the period from the beginning of January 2015 to the 31st of January 2020. You can download the closing prices from any reliable data sources such as Bloomberg, Datastream, Yahoo Finance among others. For the same time frame, download the daily closing levels for the following two in- dexes; the S&P/ASX 200 Index and the FTSE 100 Index. (Note that you can ignore any minor misalignments in trading days associated with say, public holidays.) Download the exchange rates for the Australian dollar against the Great British Pound from the Reserve Back of Australia website. You are expected to extract rates for a time frame matching the period of your share price data when responding to relevant parts below. Access the 3-month Overnight Indexed Swap (OIS) rates for Australia from the spreadsheet located on the Assignment Folder of the Course website. For con- venience in what follows, the OIS will be adopted as the proxy for the 3-month treasury bill rates, that is, each OIS rate will be assumed to be the corresponding treasury bill rate for that period. Use the downloaded data and the treasury bill rates to answer the following series of questions in either excel or “R” or any other programming environments where you will be able to submit your source files: Use the ASX stocks to answer Questions 1 - 7 below. 1. Plot the cumulative continuously compounded returns for each stock in your port- folio. 2. Compute the per annum expected return and standard deviation for each stock in your portfolio. 3. What are the weights of each stock in ASX stock only portfolio yielding an expected return of 14% p.a.? 4. Graph the minimum variance frontier for short sales allowed combinations of your stock portfolio. Page 2 of 6 5. Plot on the risk (standard deviation), expected return space each of the stocks in your portfolio. Which stocks are mean-variance efficient? 6. Find the weights for the short sales allowed, minimum variance portfolio (MVP). 7. Show that an equally weighted portfolio lies inside the minimum variance frontier. Questions 8 - 11 involves the ASX Stocks and the FTSE 100 Index. 8. Use daily data for the FTSE 100 index and the exchange rate to compute daily continuously compounded returns for a “typical” United Kingdom (UK) stock de- nominated in Australian dollars. Compute annual expected returns and standard deviation of returns for this typical UK stock. (Here you are treating the FTSE 100 index as a typical UK stock). 9. Add the UK stock to your 20 stock short sales allowed portfolio. Identify the best portfolio with an expected return of 14% p.a. How much risk was eliminated with the addition of the UK asset? 10. Plot on the same figure, the minimum variance frontier for (a) the 20 asset short sales allowed portfolio, (b) the 21 asset portfolio (includes the UK asset). 11. Using the 21 assets, compute the short sales allowed weights in the best portfolio with an expected return of 14% p.a., where the weight in the UK asset is restricted to be less or equal to 5% of the portfolio. Questions 12 - 16 involves the ASX Stocks. 12. Using the 20 ASX stocks, compute the short sales allowed weights for the best portfolio with an expected return of 14% p.a., where the sum of the weights of Technology stocks is restricted to be at most 20%. 13. Using the 20 ASX stocks, compute and plot the short sales allowed minimum vari- ance frontier where the sum of the weights of Technology stocks is restricted to be at most 20%. Compare this frontier with the unrestricted frontier. 14. Using the 20 ASX stocks, compute the weights associated with a short sales not al- lowed portfolio yielding a return of 14% p.a. Comment upon the differences between this weight vector and its short sales allowed equivalent. Page 3 of 6 15. Compare and contrast the MVP weights for (a) the short sales allowed and (b) the short sales not allowed portfolios consisting of ASX stocks. 16. Following on from 15. above, overlay the short sales allowed minimum variance frontier on the short sales not allowed minimum variance plot. Where does the short sales not allowed restriction cause the greatest and least increase in optimal portfolio risk? Questions 17 - 22 involves the ASX Stocks, the FTSE 100 Index and the Treasury Bills. 17. For the period from beginning of January 2015 to the 31st of January 2020, compute daily holding period returns for the 3-month Treasury bill rates (you need to research on how to compute holding period returns for bills). What is the per annum average return and standard deviation of the treasury bill returns? 18. Plot no short sales allowed minimum variance frontier for a portfolio consisting of 20 ASX stocks plus the treasury bills. 19. Compare the composition and risk associated with the no short sales portfolios, with a target return of 14% p.a., constructed from (a) 20 stocks, (b) 20 stocks plus 90-day treasury bills. 20. Compare the composition and risk associated with the no short sales minimum variance portfolios constructed from (a) 20 stocks, (b) 20 stocks plus 90-day treasury bills. 21. Plot the minimum variance frontier for the 21 stocks (20 ASX stocks plus the UK asset) and the 90-day treasury bills, no short sales allowed portfolio (a) unconstrained, (b) with the constraint that equity comprises 88% of the portfolio. Page 4 of 6 22. Examine and plot on a histogram the weights of a no short sales allowed portfolio consisting of 21 assets and the 90-day treasury bills, with a target return of 14% p.a. (a) unconstrained, (b) with the constraint that equity comprises 88% of the portfolio. Questions 23 - 25 look at the proposition that expected return is pos- itively related to systematic risk. This notion is central to the capital asset pricing model (CAPM). The next question estimates an Australian security market line (SML) using the 20 stocks. 23. Using the S&P/ASX200 index, calculate betas for the 20 stocks. 24. Decompose each stock’s risk into a systematic and unsystematic component. Com- ment upon your results. 25. Estimate a SML by regressing expected return for the 20 stocks. Based on the SML, which stocks seem overpriced and which seem underpriced? What is the implied risk free rate? 2 Submission Requirements You are expected to submit two files: 1. A PDF file that justifies your selection of stocks (see the first page). In the file you must also summarise key findings from your analyses. The page limit for this file is 5 pages excluding cover page and appendices (Times News Roman font, 12pt font size, 1.5 line spacing). 2. An Excel spreadsheet/ R markdown that contains your analyses and answers for above questions. Marks will be awarded based on the presentation and clarity of your PDF file and your Excel spreadsheet/ R markdown as detailed in the assess- ment criteria below. Make sure that your responses in either the spreadsheet/ R markdown file are easy to follow. The best way would be to organise the responses chronologically (e.g. each question per “Sheet” on your spreadsheet). Page 5 of 6 3 Assignment Submission Procedure Assignment reports must be submitted via the Moodle submission box that will be ac- tivated on the Course Website. Students are reminded of the risk that technical issues may delay or even prevent their submission (such as internet connection and/or computer breakdowns). Students should then consider either submitting their assignment from the university computer rooms or allow enough time (at least 24 hours is recommended) be- tween their submission and the due time. Late Submission The submission deadline is 11:59pm of the 13th of November 2020. Late submissions will be dealt with according to the school policy as detailed in the course outline. 4 Assessment Criteria Your assignment report will be assessed using the following criteria: 1. Clear and concise justification of stock selection and summary of key findings in the PDF file. [25 marks] 2. Accurate presentation of results in excel or R. [50 marks] 3. Presentation of solutions in excel or R. [20 marks] 4. Follow the formatting and page limit requirements. [5 marks] Page 6 of 6
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