For this assignment, I am required to work on Question 3 (Testing the CAPM only). The raw data and assignment questions have been attached.

Date ASX200 8/31/2012 4387.0 9/30/2012 4517.0 10/31/2012 4506.0 11/30/2012 4649.0 12/31/2012 4878.8 1/31/2013 5104.1 2/28/2013 4966.5 3/31/2013 5191.2 4/30/2013 4926.6 5/31/2013 4802.6 6/30/2013 5052.0 7/31/2013 5135.0 8/31/2013 5218.9 9/30/2013 5425.5 10/31/2013 5320.1 11/30/2013 5352.2 12/31/2013 5190.0 1/31/2014 5404.8 2/28/2014 5394.8 3/31/2014 5489.1 4/30/2014 5492.5 5/31/2014 5395.7 6/30/2014 5632.9 7/31/2014 5625.9 8/31/2014 5292.8 9/30/2014 5526.6 10/31/2014 5313.0 11/30/2014 5411.0 12/31/2014 5588.3 1/31/2015 5928.8 2/28/2015 5891.5 3/31/2015 5790.0 4/30/2015 5777.2 5/31/2015 5459.0 6/30/2015 5699.2 7/31/2015 5207.0 8/31/2015 5021.6 9/30/2015 5239.4 10/31/2015 5166.5 11/30/2015 5295.9 12/31/2015 5005.5 1/31/2016 4880.9 2/29/2016 5082.8 3/31/2016 5252.2 4/30/2016 5378.6 5/31/2016 5233.4 6/30/2016 5562.3 7/31/2016 8/31/2016 9/30/2016 10/31/2016 11/30/2016 12/31/2016 1/31/2017 2/28/2017 3/31/2017 4/30/2017 5/31/2017 6/30/2017 7/31/2017 5433.0 5435.9 5317.7 5440.5 5665.8 5620.9 5712.2 5864.9 5924.1 5724.6 5721.5 5720.6 5743.8 Date ASX200 Bond ETF 6/25/2012 -0.028269 0.039394 9/28/2012 0.068977 0.020308 12/31/2012 0.073968 0.003119 3/28/2013 0.050102 0.002547 6/24/2013 -0.033558 0.003194 9/30/2013 0.081038 0.017587 12/31/2013 0.026919 0.00856 3/31/2014 0.013497 0.00829 6/26/2014 0.004104 0.027092 9/30/2014 -0.023581 0.008401 12/31/2014 0.02189 0.033956 3/31/2015 0.08169 0.01869 6/26/2015 -0.061656 -0.011722 9/30/2015 -0.093275 0.017708 12/31/2015 0.047149 0.000427 3/31/2016 -0.057615 0.013145 6/29/2016 0.048262 0.020317 9/30/2016 0.035445 0.006785 12/30/2016 0.041423 -0.012845 3/31/2017 0.034537 0.008536 6/29/2017 -0.024754 0.006091 Date ASX200 8/31/2012 4387.0 9/30/2012 4517.0 10/31/2012 4506.0 11/30/2012 4649.0 12/31/2012 4878.8 1/31/2013 5104.1 2/28/2013 4966.5 3/31/2013 5191.2 4/30/2013 4926.6 5/31/2013 4802.6 6/30/2013 5052.0 7/31/2013 5135.0 8/31/2013 5218.9 9/30/2013 5425.5 10/31/2013 5320.1 11/30/2013 5352.2 12/31/2013 5190.0 1/31/2014 5404.8 2/28/2014 5394.8 3/31/2014 5489.1 4/30/2014 5492.5 5/31/2014 5395.7 6/30/2014 5632.9 7/31/2014 5625.9 8/31/2014 5292.8 9/30/2014 5526.6 10/31/2014 5313.0 11/30/2014 5411.0 12/31/2014 5588.3 1/31/2015 5928.8 2/28/2015 5891.5 3/31/2015 5790.0 4/30/2015 5777.2 5/31/2015 5459.0 6/30/2015 5699.2 7/31/2015 5207.0 8/31/2015 5021.6 9/30/2015 5239.4 10/31/2015 5166.5 11/30/2015 5295.9 12/31/2015 5005.5 1/31/2016 4880.9 2/29/2016 5082.8 3/31/2016 5252.2 4/30/2016 5378.6 5/31/2016 5233.4 6/30/2016 5562.3 BHP 23.22997 24.73594 24.83703 26.79429 27.06874 26.77258 23.65985 24.17396 25.78557 23.19074 25.60812 26.42876 26.42132 28.62896 28.4237 28.87977 27.8003 29.1763 27.72431 29.45677 28.87933 28.01321 30.18243 28.61403 26.4291 27.24663 24.80759 23.56399 23.47581 26.99798 24.89586 26.68328 26.42952 24.16081 23.6249 22.76744 19.8467 21.66097 17.02202 16.8056 14.44378 14.65079 15.86464 19.79753 18.26581 17.85416 18.68703 CBA 39.64132 41.04868 42.4276 44.1975 45.81104 47.81549 50.10215 54.10974 49.25497 50.96408 54.66962 53.66039 54.59934 58.33329 59.66739 59.65213 56.91486 57.24456 61.50345 62.66297 64.79937 64.23556 66.51491 64.58498 62.18806 66.47488 66.67311 70.74525 73.7848 75.92413 79.56745 75.70834 72.48817 72.52219 74.59238 65.40352 64.81509 68.38918 70.79569 76.23258 70.11829 62.51554 69.4187 68.46433 71.74439 68.9091 71.67027 TLS 2.851738 3.011784 3.135456 3.179105 3.346427 3.339153 3.429078 3.786432 3.603953 3.626763 3.794035 3.725605 3.933066 4.099253 4.004289 4.154648 4.067597 3.996376 4.185248 4.30059 4.399455 4.292351 4.523034 4.580705 4.535831 4.818251 4.8696 5.109229 5.562812 5.451556 5.581706 5.51094 5.502094 5.431328 5.740931 5.104033 5.15669 4.963659 4.926891 5.15669 5.175074 4.82578 4.899315 5.143843 5.364567 5.335777 5.537308 WOW 28.471 29.1145 29.28 29.33 31.24 34.93 33.79 36.41 33 32.81 33.32 35.67 35 34.9 33.69 33.85 34.07 36.07 35.72 37.32 37.53 35.22 36.95 36.16 34.24 36 31.12 30.68 31.78 30.71 29.49 29.48 28 26.96 28.6 26.4 24.84 24.11 23.67 24.5 24.28 22.9 22.1 22.11 22.12 20.89 23.41 7/31/2016 8/31/2016 9/30/2016 10/31/2016 11/30/2016 12/31/2016 1/31/2017 2/28/2017 3/31/2017 4/30/2017 5/31/2017 6/30/2017 7/31/2017 5433.0 5435.9 5317.7 5440.5 5665.8 5620.9 5712.2 5864.9 5924.1 5724.6 5721.5 5720.6 5743.8 19.5582 21.42499 22.37534 23.67499 24.30542 25.83784 24.24723 23.31613 23.72 23.9 23.28 25.85 25.55 66.53706 5.047876 70.00501 5.18 70.96226 4.98 76.04826 5.05 79.68388 5.1 78.95869 5 79.59685 4.82 85.91 4.66 87.4 4.22 79.65 4.4 82.81 4.3 83.73 4.1 80.5 4.15 23.71 23.27 23.65 22.89 24.1 24.6 25.76 26.5 26.88 26.05 25.54 26.7 26.75 Date ASX200 8/31/2012 4387.0 9/30/2012 4517.0 10/31/2012 4506.0 11/30/2012 4649.0 12/31/2012 4878.8 1/31/2013 5104.1 2/28/2013 4966.5 3/31/2013 5191.2 4/30/2013 4926.6 5/31/2013 4802.6 6/30/2013 5052.0 7/31/2013 5135.0 8/31/2013 5218.9 9/30/2013 5425.5 10/31/2013 5320.1 11/30/2013 5352.2 12/31/2013 5190.0 1/31/2014 5404.8 2/28/2014 5394.8 3/31/2014 5489.1 4/30/2014 5492.5 5/31/2014 5395.7 6/30/2014 5632.9 7/31/2014 5625.9 8/31/2014 5292.8 9/30/2014 5526.6 10/31/2014 5313.0 11/30/2014 5411.0 12/31/2014 5588.3 1/31/2015 5928.8 2/28/2015 5891.5 3/31/2015 5790.0 4/30/2015 5777.2 5/31/2015 5459.0 6/30/2015 5699.2 7/31/2015 5207.0 8/31/2015 5021.6 9/30/2015 5239.4 10/31/2015 5166.5 11/30/2015 5295.9 12/31/2015 5005.5 1/31/2016 4880.9 2/29/2016 5082.8 3/31/2016 5252.2 4/30/2016 5378.6 5/31/2016 5233.4 6/30/2016 5562.3 BHP 23.22997 24.73594 24.83703 26.79429 27.06874 26.77258 23.65985 24.17396 25.78557 23.19074 25.60812 26.42876 26.42132 28.62896 28.4237 28.87977 27.8003 29.1763 27.72431 29.45677 28.87933 28.01321 30.18243 28.61403 26.4291 27.24663 24.80759 23.56399 23.47581 26.99798 24.89586 26.68328 26.42952 24.16081 23.6249 22.76744 19.8467 21.66097 17.02202 16.8056 14.44378 14.65079 15.86464 19.79753 18.26581 17.85416 18.68703 CBA 39.64132 41.04868 42.4276 44.1975 45.81104 47.81549 50.10215 54.10974 49.25497 50.96408 54.66962 53.66039 54.59934 58.33329 59.66739 59.65213 56.91486 57.24456 61.50345 62.66297 64.79937 64.23556 66.51491 64.58498 62.18806 66.47488 66.67311 70.74525 73.7848 75.92413 79.56745 75.70834 72.48817 72.52219 74.59238 65.40352 64.81509 68.38918 70.79569 76.23258 70.11829 62.51554 69.4187 68.46433 71.74439 68.9091 71.67027 TLS 2.851738 3.011784 3.135456 3.179105 3.346427 3.339153 3.429078 3.786432 3.603953 3.626763 3.794035 3.725605 3.933066 4.099253 4.004289 4.154648 4.067597 3.996376 4.185248 4.30059 4.399455 4.292351 4.523034 4.580705 4.535831 4.818251 4.8696 5.109229 5.562812 5.451556 5.581706 5.51094 5.502094 5.431328 5.740931 5.104033 5.15669 4.963659 4.926891 5.15669 5.175074 4.82578 4.899315 5.143843 5.364567 5.335777 5.537308 WOW 28.471 29.1145 29.28 29.33 31.24 34.93 33.79 36.41 33 32.81 33.32 35.67 35 34.9 33.69 33.85 34.07 36.07 35.72 37.32 37.53 35.22 36.95 36.16 34.24 36 31.12 30.68 31.78 30.71 29.49 29.48 28 26.96 28.6 26.4 24.84 24.11 23.67 24.5 24.28 22.9 22.1 22.11 22.12 20.89 23.41 FLT 17.99214 21.14579 21.46376 21.46376 24.13481 25.83601 26.71046 30.95272 31.83662 31.89339 36.77511 38.11313 39.16732 43.22748 40.54606 39.59674 39.53012 43.17751 43.71047 45.4352 42.07933 37.57385 40.15204 39.64486 36.13683 36.52606 35.22778 28.42271 32.9449 35.95098 34.54815 38.58575 41.35774 30.30532 31.64689 32.88184 32.07335 35.05557 33.23582 36.84761 36.09939 38.24244 39.93287 37.046 29.78947 29.76119 30.33606 MYR 1.039621 1.256779 1.39499 1.388563 1.600704 1.793558 1.896415 2.170029 1.65625 1.608927 1.811738 1.859054 1.764414 1.768256 2.015815 1.945081 1.789477 1.853133 1.577289 1.664674 1.61219 1.589692 1.709669 1.814646 1.469715 1.518105 1.267696 1.095535 1.216828 1.451591 1.060322 1.168057 1.269628 1.036861 1.066487 1.024168 0.795569 0.867893 1.003502 1.080346 0.935697 1.044184 1.062265 0.957949 1.036621 1.027365 1.235615 COH 57.57713 61.0412 64.65102 67.82353 69.22118 60.74109 58.94257 57.57375 56.31722 53.84778 53.29805 50.04326 54.09097 52.67789 52.30225 52.69577 51.1843 51.24691 52.11444 53.65958 54.73845 56.41159 58.19445 66.33163 63.55219 68.46448 64.82037 72.41615 77.35573 84.27114 84.37367 78.85056 83.4894 75.56945 86.05395 80.21771 78.69972 85.32156 90.52048 91.68111 89.94495 98.30924 98.12699 105.213 117.5234 118.0883 129.2689 7/31/2016 8/31/2016 9/30/2016 10/31/2016 11/30/2016 12/31/2016 1/31/2017 2/28/2017 3/31/2017 4/30/2017 5/31/2017 6/30/2017 7/31/2017 5433.0 5435.9 5317.7 5440.5 5665.8 5620.9 5712.2 5864.9 5924.1 5724.6 5721.5 5720.6 5743.8 19.5582 21.42499 22.37534 23.67499 24.30542 25.83784 24.24723 23.31613 23.72 23.9 23.28 25.85 25.55 66.53706 5.047876 70.00501 5.18 70.96226 4.98 76.04826 5.05 79.68388 5.1 78.95869 5 79.59685 4.82 85.91 4.66 87.4 4.22 79.65 4.4 82.81 4.3 83.73 4.1 80.5 4.15 23.71 23.27 23.65 22.89 24.1 24.6 25.76 26.5 26.88 26.05 25.54 26.7 26.75 34.72768 34.28474 33.11602 32.65648 30.60323 29.2735 28.19799 28.2371 31.45 35.76 38.3 43.5 44.76 1.263382 1.078271 1.128156 1.22417 1.324984 1.161761 1.209768 1.166562 1.11 0.865 0.835 0.76 0.74 137.2259 137.3136 126.1784 117.0473 120.8437 123.4272 128.7323 133.3471 139.88 146.59 155.45 142.85 140.17 JBH 6.650139 7.515304 7.28069 7.588631 7.258698 9.494973 11.47535 12.4394 11.72412 13.06914 14.44524 14.66299 16.57037 17.24265 16.13531 17.00543 14.23702 14.53766 15.47749 15.93145 14.97398 15.10599 16.44323 13.92559 13.03235 13.21001 13.09154 13.3624 14.17481 14.79251 16.34267 17.14801 19.1263 17.05179 16.90292 16.63161 17.12012 16.09823 17.3083 17.49656 20.99223 19.83596 22.02059 20.5171 21.77784 22.50619 24.22454 WES 26.83408 27.23355 27.84448 28.86271 29.45008 32.13661 32.35081 34.90185 31.5783 31.86798 32.64057 32.72102 34.29372 35.82789 35.34244 36.2647 34.58487 35.36713 34.86778 36.15451 36.70471 35.41806 37.26339 36.66237 37.02434 38.76318 35.74521 36.34942 36.34942 40.36987 38.25522 38.03766 37.99415 33.96499 36.94117 34.85263 35.53738 35.70954 34.51349 37.70297 38.21038 35.41959 38.80896 40.04486 38.04121 37.54498 40.19466 QBE 10.56589 10.75355 8.925937 8.8933 9.725518 10.91673 11.0228 11.02377 13.2005 12.44194 13.5303 12.53264 12.31613 12.42527 13.13888 9.663164 9.646373 10.76297 10.76297 9.854746 9.684543 9.250527 9.361158 9.803685 10.11292 10.00017 9.419066 9.722628 9.202237 11.26645 11.30982 12.1741 13.01829 12.14744 12.97386 11.68536 11.705 12.0319 11.32361 11.43258 9.879782 9.598281 9.907023 10.53009 11.74837 9.670688 10.3601 27.72656 27.87971 27.32154 26.63826 26.98471 26.60939 25.81062 24.7 24.69 23.12 23.37 26.01 25.37 39.73588 42.59411 39.60962 40.35333 40.70104 38.88524 41.53167 45.07 43 42.7 40.12 40.73 40.68 9.368479 9.000751 9.678956 10.82222 12.0333 12.11081 11.92672 12.48866 12.87 12.9 11.81 11.85 11.93 Finance Discipline Group UTS Business School 25721 Investment Management AssignmentPart I Spring 2017 1. The assignment should be completed in groups of 3-4 students (your group does not need to be in the same class). All group members receive the same mark. 2. Help: For consultation times, please check UTSOnline and the subject outline. Note that email is not an efficient way for asking questions about the assignment; please post any questions on the UTSOnline discussion board. 3. Due date: A hard copy of the assignment should be brought and submitted in the assignment box marked \"FINANCE6\" located in Building 8, Level 5, by 5:00pm Friday 8th September 2017. Late submissions will not be accepted and no soft copy is required. 4. Complete a cover sheet (available on UTSOnline) with all the signatures from your group members and attach it to a printout of your answers. 5. The assignment computations are to be done in Excel, but the solutions may be pasted into Word and formatted for submission. The final report, including all text, tables and figures should be printed out on A4 paper with a minimum font size of 12 and double spacing. Also, the final report (excluding the cover sheet) should not exceed 10 pages in length. Subject Coordinator: Lei Shi In this assignment you will look at mean-variance optimization, statistical arbitrage and testing the CAPM. In order to help you do this you will find an Excel workbook called AssignmentPart1Data.xlsx on UTSOnline. 1 Data Description The Excel worksheet contains monthly closing prices from 31-August-2012 to 31-July-2017 for 10 Australian publicly listed companies and also for the ASX200 index. It also has the quarterly returns for an Australian Semi-Government Bond ETF. Note that you are to use the price or return data under each tab for the corresponding parts of each question. 2 Question 1 (Mean-variance optimization - 10 marks) You have been approached by a client who is interested in investing in equities. After some questionnaires, you discover that you client's utility function can be approximated by a quadratic utility, 1 A > 0. U (E[rq ], Var[rq ]) = E[rq ] AVar[rq ], 2 (a) Based on the monthly closing prices provided, estimate the expected return E[rp ] and variance Var[rp ] of ASX200 per annum (p.a.). Note that you should first compute the continuously compounded returns by using ln(Pt+1 /Pt ), then compute the sample average and sample variance of the monthly returns. Finally, to annualize the estimates, multiply the sample average and sample variance by 12. [1 mark] (b) Given that the 1-year term deposit rate is 2.3% p.a. and the risk aversion coefficient is given by A = 4, suppose your client only invests in ASX200 and the 1-year term deposit, compute the portfolio weights (wp , 1wp ), expected return E[rq ] and standard deviation q for the optimal portfolio q . What is the maximum utility (or risk-adjusted return) that can be achieved? Then, briefly explain why is it not optimal to allocate 100% of capital to either the risk-free security or the equity index. [1 mark] (c) Plot the capital allocation line (CAL) in the (, E[r]) space for in the range of 0%30%, you should also indicate the position of the optimal portfolio q . Furthermore, on the same graph, also plot the indifference curve that corresponds to the maximum utility achieved by the optimal portfolio q . Based on the indifference curve plotted, briefly explain why a higher utility cannot be attained by a portfolio different from q . [2 marks] (d) Based on the quarterly returns provided for the ASX200 and the Australian SemiGovernment Bond ETF, estimate the expected return and variance p.a. using the same approach as in Part (a). Moreover, also estimate the correlation coefficient. Then, suppose your client only invests in ASX200 and the Bond EFT, by using the Solver add-in in Excel, work out the portfolio weights (wE , wD ), expected return E[rq ] and standard deviation q for the optimal portfolio q (assume A = 4). What is the maximum utility that can be achieved? Briefly explain why is it not optimal for any risk-averse investor to allocate all her capital to debt (Hint: you may want to compute the expected return of the minimum variance portfolio.). [2 marks] (e) Plot the investment opportunity set (IOS) in the (, E[r]) space that represent all the possible portfolios attainable by investing in ASX200 and the Bond ETF. You should also indicate the positions of ASX200, the Bond ETF and the optimal portfolio q . On the same graph, also plot the indifference curve which corresponds to the maximum utility that can be achieved by q . [2 marks] 3 (f) Suppose now your client invests in the ASX200, Bond ETF and the 1-year term deposit, work out the portfolio weights (wE , wD ), expected return E[rT ] and standard deviation T for the tangent portfolio that maximizes the slope of the CAL when combined with the risk-free security. Plot the CAL together with the IOS from Part (e) in the (, E[r]) space, also indicate the positions of ASX200, Bond ETF and the tangent portfolio T . Suppose your client has a target expected return of E[rq ] = 0.06 p.a., what is the minimum standard deviation q ? How do you construct this portfolio? Finally, indicate this portfolio q on the graph. [2 marks] 4 Question 2 (Statistical Arbitrage - 5 marks) You are now discussing statistical arbitrage by investing in long-short portfolios with another client. (a) Let rk be the monthly (continuously compounded) return of stock k and rM the monthly return of ASX200. Based on the single index model (SIM), rk = k + k rM + k , estimate the k and k for BHP, CBA, TLS and WOW respectively. [1 mark] (b) Compute the return variance p.a. k2 for each individual stock, and decompose it into 2 2 systematic risk k,sys and idiosyncratic risk ,k . Also, estimate the expected stock returns p.a. [1 mark] (c) Construct an arbitrage portfolio P using the following strategy. First, invest either 100% or -100% in BHP, i.e., wBHP = 1 or wBHP = 1. Then, decide on the portfolio weights of ASX200 and the risk-free security (assume the risk-free rate is 2.3% p.a.), such that portfolio weights sum up to zero and the beta of the arbitrage portfolio is zero. What is the expected return, variance and utility of portfolio P (Assume risk aversion A = 4)? [1 mark] (d) Replace BHP with each of the other 3 stocks and repeat the exercise in part (c). Which arbitrage portfolio should the investor choose and why? [1 mark] (e) Briefly explain why a statistical arbitrage opportunity may not be desirable for a riskaverse investor even if the expected return is positive. [1 mark] 5 Question 3 (Testing the CAPM - 5 marks) Your client from Question 2 is quite skeptical about the profitability of the strategy that you've recommended. The client argues that if the market is efficient and the CAPM holds, then the only way to earn a higher risk premium is to take on more systematic risk (measured by beta). (a) Based on the adjusted closing prices for BHP, CBA, TLS, WOW, FLT, MYR, COH, JBH, WES, QBE and ASX200, estimate the stock betas k and the annualized expected returns E[rk ]. Plot the SML predicted by the CAPM, also indicate the positions of the 10 individual stocks and of ASX200 (you can treat ASX200 as a proxy for the market portfolio and assume the risk-free rate is 2.3% p.a.). Are the positions of the individual stock consistent with the CAPM prediction? Why or why not? [1.5 marks] (b) Based on the stock beta estimates and expected returns of the 10 stocks from Part (a), run the following linear regression E[rk ] = + k + k , where E[rk ] is the dependent variable and k is the independent variable. Essentially, you are trying to explain the variation in expected stock returns by variation in the stock betas. Report the estimates for and and their p values. Plot the best-fitted line together with the SML from Part (a), you should also indicate the positions of the 10 stocks. Finally, comment on the regression results in terms of the observed risk-return relationship. [2 marks] (c) Plot the CML and indicate the positions of the 10 individual stocks in the (, E[r]) space. Are the positions of the individual stocks consistent with CAPM, why or why not? Finally, explain to your client why the market may not be perfectly efficient and therefore arbitrage opportunities may exist. [1.5 marks] 6