Problem 5. You are interested in investing in the following 4 sectors of the economy: (1) Agri- cultural, (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 μ 0.12 0.08 0.06 0.15 σ 0.10 0.08 0.1 0.13 Manufacturing Energy Financial Agricultural Manufacturing Energy 0.5 -0.1 0.4 0.0 0.3 0.0 Hint: Perform matrix manipulations (e.g. matrix inversion and multiplication) by a calculator, or software such as MATLAB or MATHEMATICA, or on-line tools such as https://matrixcalc.org/en/ found by searching "Matrix calculator" on Google. (a) (3 points) What is the minimum variance portfolio? (Round to the nearest thousandth) (b) (4 points) Find σy as a function of μy for any portfolio V on the Minimum Variance Line. (Round to the nearest thousandth) (d) (3 points) Assume that the risk-free return is 3%. Find the market portfolio μм and σм. Find the Capital Market Line when investing risk-free is allowed in addition to investing in the ETFs. (Round to the nearest hundredth)