On a single chart, plot the value of $1 invested in each of the five ETFs over time. i.e.. for all t, plot the cumulative return series for each index: TV t = (1 + r_{1})(1 + r_{2}) ...(1+r t ) What patterns do you observe? (II-VI) Imagine that you are an investor on Jan 1st, 2014, and using the historical data up to that date (2008.1.1-2013.12.1) Please use excess returns for all analyses. II. Draw the mean-variance frontier in annual terms using the five ETFs assuming short-selling is not allowed. (using 2008.1.1-2013.12.1) , where annual mean = monthly mean x 12, annual covariance = monthly covariance x 12 You first need to find annual mean and covariance matrix. Please try 7 different target mean returns, 2%, 4%, 5%, 5.5%, 6%, 8%, 10%. III. What are the optimal weights for the following strategies? (using 2008.1.1-2013.12.1) ⚫ maximum SR portfolio assuming short-selling is allowed ⚫ maximum SR portfolio assuming short-selling is not allowed ⚫ minimum global variance portfolio .1/N IV. What would the SR of your portfolio using four different strategies be over the next 9 years (out-of-sample test, 2014.1.1-2022.9.1)? V. Apply "All Weather Portfolio" weights, (0.3, 0.4, 0.15, 0.075, 0.075) to your portfolio, what would the SR of your portfolio be over the next 9 years (2014.1.1-2022.9.1)? VI. Imagine that you are a portfolio manager in charge of asset allocation. Write a short executive summary (around 200 words) directed to the CIO discussing four different approaches and all weather portfolio, their performance, and your recommendation for asset allocation.