Problem 1: Attitude to risk and return, leverage and risk You total wealth is $20,000. A project can earn 30% or lose 10% with probability 0.5. Your utility of wealth has the shape U(W) = Log(w). You wonder whether to invest your total wealth into it! a) What is the $CE of your total wealth if you undertake the project? Do you do it? b) You can borrow $B at 0%. What is the maximum Bmax you can borrow without risking bankruptcy. In Figure 1 plot your expected wealth vs the amount borrowed for B E [O, Bmax] c) Now write the simple formula of your $CE as a function of $B. In Figure 4, Use R to plot $CE vs the $B. Have B go from $0 to $Bmax. d) How much would you borrow optimally to increase your expected utility? Show that point on your Figure 2. Problem 1: Attitude to risk and return, leverage and risk You total wealth is $20,000. A project can earn 30% or lose 10% with probability 0.5. Your utility of wealth has the shape U(W) = Log(w). You wonder whether to invest your total wealth into it! a) What is the $CE of your total wealth if you undertake the project? Do you do it? b) You can borrow $B at 0%. What is the maximum Bmax you can borrow without risking bankruptcy. In Figure 1 plot your expected wealth vs the amount borrowed for B E [O, Bmax] c) Now write the simple formula of your $CE as a function of $B. In Figure 4, Use R to plot $CE vs the $B. Have B go from $0 to $Bmax. d) How much would you borrow optimally to increase your expected utility? Show that point on your Figure 2