Suppose you have two assets x and y with the following properties: Asset x: E[r_x] = 0.1, sigma_x = 0.1 Asset y: E[r_y] = 0.2, sigma_y = 0.2 If the correlation between the two assets is rho_xy = -1, what proportions of assets do you have to invest into both of them in order to get a risk-free portfolio? Now suppose that the correlation of the assets is rho_xy = 0. What is the expected return and the volatility of a portfolio that consists in 50% asset x and 50% asset y? Suppose that there is a third asset z with the following properties: Asset z: E[r_z] = 0.10, sigma_z = 0.11 Furthermore, this asset is perfectly correlated with asset x. What is the optimal fraction any investor should invest into the asset z? Suppose that an investor can also borrow or lend at an interest rate of 16 percent. Given that he can borrow or lend, what proportions of the common stock portfolio should be invested in x, y and z if he cannot short sell any of the risky assets, i.e. having negative portfolio weights of the asset? Would the results change if he could short sell one asset? Why? Give a short answer, no calculation needed