1. You are interested in investing in the following 5 sectors of the economy: (1) Agricultural, (2) Manufac- turing, (3) Energy, (4) Financial and (5) Construction. Your trusted investment firm offers 5 ETFs (Exchange Traded Funds) that closely mimic the performance of each sector. You are also given the following estimates for the mean, variance and correlation of annualized returns of the ETFs ETF Agricultural Manufacturing Energy Financial Construction 0.08 0.08 0.12 0.10 0.15 0.13 0.06 0.10 0.20 0.10 Manufacturing Energy Financial Construction Agricultural Manufacturing Energy Financial 0.3 0.4 0.0 0.2 0.0 0.2 0.5 0.0 0.1 0.0 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 calculator or softwares such as MATLAB or MATHEMATICA (a) (2 points) Find the mean vector and the covariance matrix of the 5 ETFs. (b) (3 points) What is the minimum variance portfolio of the 5 ETFs? What is its mean return and risk? (c) (3 points) Assume that the effective rate of interest is 3% per annum. Find the mutual fund in the one fund theorem, its mean return and risk. (d) (2 points) Find the efficient frontier when investing risk-free is allowed in addition to investing in the ETFs