8. (60 points) You have decided that you are going to invest in the following ETF assets (which are already portfolios themselves): the S&P-500 index (Symbol: SPY), the NASDAQ-100 index (Symbol: NDX) and the Russell 3000 (Symbol: RUA). Using the internet to find price data for the SPY, NDX and RUA (daily starting 1 Jan. 2009 to 1 Jan 2020). Estimate the following measures for these indexes: The monthly and annual expected return and standard deviation for SPY; The monthly and annual expected return and standard deviation for NDX; The monthly and annual expected return and standard deviation for RUA; Using the monthly returns, estimate the correlation of returns among the three assets (correlation matrix). Please answer the following questions: (a) If you decide that you would like to have an expected return of 13%, what portfolio of the previous three assets would you choose? (b) If you decide that you would like to be exposed to a risk of 12% (in terms of standard deviation), what portfolio of the previous three assets would you choose? (c) What would be the minimum risk in terms of standard deviation) that you can get if you want to have expected returns of: 5%, 9%, 11%, 14%, 17%. (d) Find the minimum variance portfolio. (c) Draw the efficient frontier in this market. (f) If you have the opportunity to invest in the risk-free rate yielding 3%, what portfolio of risky assets would you pick? 8. (60 points) You have decided that you are going to invest in the following ETF assets (which are already portfolios themselves): the S&P-500 index (Symbol: SPY), the NASDAQ-100 index (Symbol: NDX) and the Russell 3000 (Symbol: RUA). Using the internet to find price data for the SPY, NDX and RUA (daily starting 1 Jan. 2009 to 1 Jan 2020). Estimate the following measures for these indexes: The monthly and annual expected return and standard deviation for SPY; The monthly and annual expected return and standard deviation for NDX; The monthly and annual expected return and standard deviation for RUA; Using the monthly returns, estimate the correlation of returns among the three assets (correlation matrix). Please answer the following questions: (a) If you decide that you would like to have an expected return of 13%, what portfolio of the previous three assets would you choose? (b) If you decide that you would like to be exposed to a risk of 12% (in terms of standard deviation), what portfolio of the previous three assets would you choose? (c) What would be the minimum risk in terms of standard deviation) that you can get if you want to have expected returns of: 5%, 9%, 11%, 14%, 17%. (d) Find the minimum variance portfolio. (c) Draw the efficient frontier in this market. (f) If you have the opportunity to invest in the risk-free rate yielding 3%, what portfolio of risky assets would you pick