US equity International index equity index returns returns (Weight) (Weight) 0 100% slope of CAL (Sharpe ratio) Exp. Ret port. St.dv 1 2 10% 90% 3 20% 80% 4 30% 70% 5 40% 60% 6 50% 50% 7 60% 40% 8 70% 30% 9 80% 20% 10 90% 10% 11 100% 0% b. Calculate the minimum variance portfolio (only consider the option of investing in equity: international and US equity index). (15 points) c. Calculate the maximum Sharpe ratio portfolio (only consider the option of investing in equity: international and equity index). (15 points) d. Now, suppose your investment advisor suggests adding the risk-free asset to the portfolio. In other words, your investment advisor recommends you to have a portfolio with three assets: risk-free rate, US equity index, and the International Equity Index. Using the following weights of the risk-free asset as the initial guess, estimate the portfolios that maximize the Sharpe ratios of those portfolios. (15 points) US equity International index equity index returns returns (Weight) (Weight) 0 100% slope of CAL (Sharpe ratio) Exp. Ret port. St.dv 1 2 10% 90% 3 20% 80% 4 30% 70% 5 40% 60% 6 50% 50% 7 60% 40% 8 70% 30% 9 80% 20% 10 90% 10% 11 100% 0% b. Calculate the minimum variance portfolio (only consider the option of investing in equity: international and US equity index). (15 points) c. Calculate the maximum Sharpe ratio portfolio (only consider the option of investing in equity: international and equity index). (15 points) d. Now, suppose your investment advisor suggests adding the risk-free asset to the portfolio. In other words, your investment advisor recommends you to have a portfolio with three assets: risk-free rate, US equity index, and the International Equity Index. Using the following weights of the risk-free asset as the initial guess, estimate the portfolios that maximize the Sharpe ratios of those portfolios. (15 points)