Examine the benefits of international diversification.
For financial assignments, you need to use excel and calculations to complete 4 questions. You need to download the relevant data through the channel I gave you. Check out the excel I gave you to do the rules for homework data. Finally answer 4 questions written in words and excel. I need to do exactly what the assignment requires.
Requirements: 24
IMPORTANT
Projects MUST be completed in groups of minimum four and maximum five students.
Although this is a collaborative group project, each group member is responsible for the solution to the entire project. Every group should submit only one solution to the project.
Your report must agree with class notes in terms of notation and methodology. Each question should be answered separately with detailed steps.
Your report should be written in a professional manner (a Word or PDF document rather than an Excel file), accompanied by a description of methodology for all questions. You should clearly state the equations you use for each question along with tables with the data/answers you are asked to compute. Other tables (such as ETF and T-bill data provided for the project) and all your Excel work should only be provided electronically in Excel format.
Your written report must contain the names of all group members on the cover page.
Your project will be graded based on the quality of your report, the validity of any assumptions you make (if required at all), and the efficiency with which you solve various problems. Your report should be a standalone report with all required information in it. Answers absent in the report but included in the Excel file will not be graded.
Your written report and all your supporting spreadsheet material (Excel file) are due at the beginning of class
In this project you will examine the benefits of international diversification. For this purpose, you will need to download total return index (TRx) data from Bloomberg for the following exchange traded funds (ETFs) for a 121-month period:
North-American Assets
US stocks (Vanguard Total Stock Market Index ETF, ticker: VTI),
US bonds (iShares 20+ Year Treasury Bond ETF, ticker: TLT),
Canadian stocks (iShares S&P/TSX 60 Index ETF, ticker: XIU)
International equity
Vanguard FTSE Developed Markets ETF (VEA) tracking the investment performance of the FTSE Developed All Cap index excluding US equities; however, it does have Canadian equities, and
Vanguard FTSE Emerging Markets ETF (VWO) tracking the performance of companies located in emerging markets around the world, such as China, Brazil, Taiwan, and South Africa.
The 121-month period is from June 30, 2013, to June 30, 2023. The ETF data should be downloaded in the form of the total return index, which means that the log-change in the index is the total continuously compounded return (dividends included) on the ETF. All values must be in Canadian dollars.
(5) Calculate the annualized mean rate of return and variance for these five ETFs. Use a table to present your results. You can copy these tables from your spreadsheets. Include only relevant results necessary to answer the question (e.g., do not insert columns of return data downloaded from Bloomberg or other intermediate Excel work into your report). Explain how you compute these results (e.g., formulas used and any other relevant information). The same rules apply to the remaining parts of the project.
(5) Calculate the historical covariance matrix for these five ETFs from monthly returns in part (a) and then annualize the matrix as discussed in the lab.
(10) Find the (global) minimum-variance portfolio (GMV) weights (using Solver) for the North American portfolio: US stocks + US bonds + Canadian stocks. Provide an intuitive explanation for the composition of the (global) minimum-variance portfolio. Specifically, explain the resulting allocation of money in the GMV across the three asset classes.
(15) You will also need to download both bid and ask yields on the Canadian 3-month T-bill (our proxy for the risk-free asset) from Bloomberg (see data retrieval instructions). Find corresponding bid and ask prices (see lecture notes on Canadian T-bill quotations). Find the midpoint of the bid-ask price range for each month. Finally, use the midpoint price to compute the effective yield (again, see T-bill-related class notes) for each month.
Use the sample average of the effective T-bill yield over the 120-month period as an estimate of the risk-free rate of return. Find the composition of the tangency portfolio based on the North American assets, i.e., US stocks + US bonds + Canadian stocks. To do this, solve a system of linear equations as discussed in class:
Compute weights of the three asset classes in the tangency portfolio from the Z’s and find expected return, volatility, and the Sharpe ratio of the tangency portfolio. Use a table (tables) to present your results.
(10) Derive the efficient frontier for US stocks, US bonds, and Canadian stocks and plot it. Instead of minimizing standard deviation for a set of given expected returns to trace the frontier, use the two-fund separation principle discussed in the lab to build the efficient frontier. Also, plot (on the same diagram) the capital allocation line (CML) that represents all combinations of the risk-free asset and the optimal risky portfolio from part (d).
(15) Now, add the international ETFs. Using the same technique as in (e), derive the efficient frontier for the portfolio of all five ETFs: US stocks, US bonds, Canadian stocks, and International Equity (VEA and VWO) and plot it. Assume the same risk-free rate of return as in part (e). Also, plot (on the same diagram) the capital allocation line (CML) that represents all combinations of the risk-free asset and the optimal risky portfolio for the 5-ETF case.
(5) Is any of your five ETFs in part (f) dominated (inferior in mean-variance sense) by any of the other ETFs (why?). If so, what role do the dominated assets play in your portfolio from part f?
(5) Superimpose the efficient frontier in (e) on the efficient frontier plot from (f).
(5) What are the portfolio weights of each of the three North American ETFs on the efficient frontier (CML) constructed from the three North American ETFs and the risk-free asset for σ = 15%?
(5) What are the portfolio weights of each of the five asset classes on the efficient frontier (5-ETF CML) for σ = 15%?
(5) Compare the efficient frontiers (the 3- to the 5–ETF CMLs) from (e) and (f) at σ = 15%. What is the estimated increase in expected return gained from international diversification at σ = 15%?
(15) Suppose that your client’s utility function in mean-variance space is given by:
U = E(r) – (A/2)2.
After she completed an asset allocation questionnaire, you estimate that this client has a risk aversion coefficient A = 15.
1. (5) Find the proportion of her money (investment weight) she should optimally allocate to each of the five ETFs and to the risk-free asset (the Treasury bill).
2. (10) Compute the client’s optimal indifference curve and superimpose it on the 5-ETF efficient frontier chart from part (f).
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