Capital Market Theory

Consider an investor with current wealth w, who maximizes the expected utility of her wealth in period 1 and whose utility function is given by: u(w) = -exp(- 3w). She may invest in a risk-free asset that pays r; = 1.5% and in a risky asset with payoff per unit. The price of the risk-free asset at time 0 is normalized to be equal to $1 and the risky asset's current price is $9. x is normally distributed with a mean of $11 and a variance of 3. She will also receive a random income (normally distributed with a variance of 2) in period 1; the correlation between i and is: -0.345. 1. Find the amount invested in the risky asset. Explain your result. 2. Interpret the demand for the risky asset in the context of the two funds theorem. Consider an investor with current wealth w, who maximizes the expected utility of her wealth in period 1 and whose utility function is given by: u(w) = -exp(- 3w). She may invest in a risk-free asset that pays r; = 1.5% and in a risky asset with payoff per unit. The price of the risk-free asset at time 0 is normalized to be equal to $1 and the risky asset's current price is $9. x is normally distributed with a mean of $11 and a variance of 3. She will also receive a random income (normally distributed with a variance of 2) in period 1; the correlation between i and is: -0.345. 1. Find the amount invested in the risky asset. Explain your result. 2. Interpret the demand for the risky asset in the context of the two funds theorem