Construct a tangency portfolio using the stocks only

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Reference no: EM131676328 , Length: 4

Applied Portfolio Management

Select 5 Australian listed companies in the ASX200 or 5 US companies in the S&P500 and download their monthly adjusted closing prices. The adjusted closing price is adjusted for dividends, stock splits and so on.

This makes the adjusted closing price reflect total returns, not capital returns only. A good source of adjusted closing prices is Yahoo Finance. Ensure that each of the companies have at least 120 months of adjusted closing price data so that the GFC which started in 2007 is included. Do not mix US and Australian companies since we don't want to complicate the assignment with foreign exchange considerations.

If you chose Australian stocks, download the ASX200 accumulation index or if you chose US stocks, download the S&P500 accumulation index monthly closing prices provided on MQ ilearn. Each countries' government bond yields are also provided. Match the accumulation index, government bond yields and stock data so that the dates correspond. There is a demonstration spreadsheet on MQ ilearn called ‘vlookupExample.xlsx' which might help you start.

The shares you selected will be referred to as the shares, the ASX200 or S&P500 as the market portfolio, and the Australian or US federal government bonds as the bond. All of them will be referred to as the assets, so there are 7 assets (5 stocks, the market portfolio and the bond).

Question 1: Convert the assets' monthly adjusted closing prices (or yields to maturity in the case of the bonds) into discretely compounding monthly returns compounding per month, also called monthly net discrete returns or effective monthly returns (r_(eff monthly) = r_(discrete monthly)=(p_1-p_0)/p_0 ).

Do not use monthly continuously compounding returns. Report the discrete monthly returns' historical arithmetic average, geometric average, standard deviation and variance for each of the assets. Report your results in a clearly labelled table with units. For this and all of the following questions, use the discretely compounded monthly returns.

Note that the Australian and US government bond yields provided by Bloomberg are expected future annual yields to maturity (YTM's), not past historical prices.

Therefore you should convert the annual YTM's into monthly past historical returns. For an example of how to do that. The ‘approximate solution' using the duration-bond-price-change formula will suffice.

Question 2 : Report the assets' covariance of returns matrix in a table. Also report the assets' correlation of returns matrix in a table. Note that the assets include the stocks, market portfolio and bond.

Question 3a : Comment on the bond's risk and discuss if it can be seen as a risk free security. Consider the different risks that Australian or US government bond investors are exposed to and which are or aren't significant. Use academic references to support your answer.

Question 3b : For the purpose of an investor trying to make a portfolio allocation decision using Markowitz mean-variance optimization, a risk free rate is needed. What risk-free rate would you recommend that the investor use? Outline the rationale for your decision. Use academic references to support your answer.

Question 4a :Graph two Markowitz bullets on the same chart using the stocks only, and then all assets (stocks, market and bond). Do not assume that the bond is risk free. Label each portfolio possibility frontier (Markowitz bullet) appropriately. Depict the stocks, market portfolio and bond as points on the graph and label them too. Assume that all assets can be short-sold.

Question 4b: Repeat with short selling not allowed.

Question 5: From this question onwards, assume that the bond is a risk free security in the sense that its standard deviation of returns is zero. Use the risk free rate that you recommended in the prior question.

Question 5a: Construct a tangency portfolio using the stocks only. Ignore the market portfolio. Assume that the bond is risk free and short selling is allowed. Repeat with short selling not allowed.

Report the return, standard deviation, variance, Sharpe ratio and weights in each stock using a table with one row or column for each the three portfolios: short-selling allowed tangency portfolio; non-short selling tangency portfolio; and the market portfolio. You can leave the weights of the stocks in the market portfolio (ASX200 or S&P500) blank or include the adjusted weights calculated in the Black-Litterman question.

Question 5b: Plot the three Capital Allocation Lines (CAL's) from the bond through the two tangency portfolios (short and non-short selling) and the market portfolio (ASX200 or S&P500) on a graph of return versus standard deviation.

Reference no: EM131676328

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len1676328

10/12/2017 1:51:47 AM

f. Suppose that the contribution marks for each member are 1st draft: A receives a score of 32 from B and 24 from C; and 2nd draft: A receives a score of 32 from B and 16 from C. Then the average score of A is ((32+24)/2 + (32+16)/2)/2 = 26. In this case, the mark rewarded to A is the same as that rewarded by the marker of the report. g. Non-performing members will be removed from the group if the average peer assessment score in the first peer assessment is 8 or lower. Evicted members will submit a report on all questions of the assignment on an individual basis. The assignment questions might be changed to make them clearer and avoid confusion. Any change will be announced on iLearn, so please regularly check ilearn announcements and your emails. This report is worth 20% of your final grade.

len1676328

10/12/2017 1:51:22 AM

Score: 0 - Very bad, 1 - Bad, 2 - Average, 3 - Good, 4 - Excellent. c. Members with average scores of 19 or higher will receive the mark given to the assignment report by the marker. d. A student with an average score lower than 19 will receive a downscaled mark. For example, a student with average score of 10, and the mark given to the report is 80, then the student receives a mark of (10/19)*80 = 42. e. To provide an example of how the average score is calculated, consider a group of 3 members A, B, C. In this group, A can assess B and C for their contributions in each submission; B can assess A and C for their contributions, and C can assess A and B for their contributions.

len1676328

10/12/2017 1:50:44 AM

5. Peer assessment of other members’ contributions a. Group members will evaluate each others’ contributions after the submission of the milestone report in Week 8 and the final submission of the assignment in Week 10. b. For each submission, each group member assesses other members’ team work performance based on the following 8 criteria using scores 0 to 4: i. Make commitments to do task assignments ii. Complete assigned tasks on time iii. Do their fair share of work iv. Produce work of an acceptable quality v. Act in a cooperative fashion vi. Actively participate in the team vii. Help to promote a climate of trust and mutual respect viii. Handle conflicts in an open and constructive fashion

len1676328

10/12/2017 1:50:25 AM

e. Address all the issues raised in the assignment. f. List all the references you have used and refer to them in the text using the Harvard referencing style. g. The maximum number of pages for the Word report is 10 pages. Reports that are not proof-read will be marked down. Grammar and sentence structure are important. Default margin spacing, 12 Arial font size and 1,5 line spacing should be used, the same as this document. h. There should be no appendices. All tables, graphs and explanations that you refer to should be embedded alongside the text that answers the question. 4. Use of iLearn Group Discussion Space a. Students should use the iLearn discussion space setup for each group. b. All group members should document their progress in the discussion space. c. Draft of assignment answers completed by individuals should be uploaded to the discussion space as proof of individual contribution. d. If there is a dispute about members’ contributions, only the evidence in the discussion space will be looked at. We do not accept evidence from social media, i.e Facebook, Wechat, MySpace, Tinder etc.

len1676328

10/12/2017 1:50:18 AM

3. For final submission on Midday Monday 16 Week 10: a. You will have to submit two documents: a written Word document that answers the assignment questions and an Excel file in which you present your calculated solutions for each question in a separate sheet. b. Marks are allocated based on answers provided in the Word document only. Solutions presented in Excel but not in Word document will receive zero marks. Numerical results and graphs presented in the Word document but not supported by calculations in Excel will receive zero marks. c. Word report must be text recognizable. Reports that are not text recognizable and cannot be scanned by Turnitin will not be marked and will score zero marks. d. The assignment must be structured by using the question number in the subheadings. You do not need to repeat the question text. Answer questions in the prescribed order.

len1676328

10/12/2017 1:50:06 AM

1. Each group has a minimum of 2 and a maximum of 4 members. All group members are equally responsible for the entire submitted assignment. Groups must be formed and registered by 12 noon Monday 11 on iLearn. 2. Each group has to submit a milestone report by Midday Friday 6 Week 8. The milestone report should contain: a. Distribution of responsibilities among group members. b. A group project journal to record all the activities that have happened since the group was formed. c. Tasks and target timeline that group members will need to adhere to before the assignment due date. d. Answers for Question 1 to 5 at a minimum. You should really try to finish all questions from 1-8 at this late stage. e. Report on any non-contributing members. Please note that non-contributing member will be advised to undertake the assignment by himself.

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