3. (10 pt) You are interested in investing in the following 4 sectors of the economy: (1) Agricultural, (2) Manufacturing, (3) Energy, and (4) Financial. Your trusted investment firm offers 4 ETFs (Exchange Traded Funds) that closely mimic the performance of each sector. You are also given the following estimates for the mean, standard deviation and correlation of annualized returns of the ETFs. ETF Agricultural Manufacturing Energy Financial 0.08 0.12 0.15 0.06 0.08 0.10 0.13 0.1 o Manufacturing Energy Financial 0.5 0.0 0.4 -0.1 0.0 Agricultural Manufacturing Energy 0.3 Hint: When answering the following questions, you may refer to formulas presented during the class. Your are also allowed to workout matrix manipulations (e.g. matrix inversion and multiplication) by a computer. (a) (2 pt) What is the minimum variance portfolio of the 4 ETFs? (b) (2 pt) Find the parametric formula for the efficient frontier, if only investing in the ETFs is allowed. (c) (2 pt) Which efficient portfolio provides a return 4 times that of the minimum variance portfolio? (d) (3 pt) Assume that the effective rate of interest is 3% per annum, find the mutual fund in the one fund theorem. Find the efficient frontier when investing risk-free is allowed in addition to investing in the ETFs. (e) (1 pt) Which efficient frontier is superior (in M-V sense)? The one you found in part (b), or the one you found in part (d)? Explain your answer. 3. (10 pt) You are interested in investing in the following 4 sectors of the economy: (1) Agricultural, (2) Manufacturing, (3) Energy, and (4) Financial. Your trusted investment firm offers 4 ETFs (Exchange Traded Funds) that closely mimic the performance of each sector. You are also given the following estimates for the mean, standard deviation and correlation of annualized returns of the ETFs. ETF Agricultural Manufacturing Energy Financial 0.08 0.12 0.15 0.06 0.08 0.10 0.13 0.1 o Manufacturing Energy Financial 0.5 0.0 0.4 -0.1 0.0 Agricultural Manufacturing Energy 0.3 Hint: When answering the following questions, you may refer to formulas presented during the class. Your are also allowed to workout matrix manipulations (e.g. matrix inversion and multiplication) by a computer. (a) (2 pt) What is the minimum variance portfolio of the 4 ETFs? (b) (2 pt) Find the parametric formula for the efficient frontier, if only investing in the ETFs is allowed. (c) (2 pt) Which efficient portfolio provides a return 4 times that of the minimum variance portfolio? (d) (3 pt) Assume that the effective rate of interest is 3% per annum, find the mutual fund in the one fund theorem. Find the efficient frontier when investing risk-free is allowed in addition to investing in the ETFs. (e) (1 pt) Which efficient frontier is superior (in M-V sense)? The one you found in part (b), or the one you found in part (d)? Explain your
