$1.$ What are the two main concerns faced by the investor under Portfolio Theory?$2.$ What is the typical utility function equation used for investor portfolio choice problem?$3.$ What is the price of risk $($A$)?$ What does a positive value of A $($A $>0)$ imply about an investors risk aversion? What does a negative value of A $($A $<0)$ imply about an investors risk aversion? What does a zero value of A $($A $=0)$ imply about an investors risk aversion?$4.$ Holding all else constant what would happen to an investors utility if the expected return of the risky portfolio $($E$($rp$)$ increases$\mathrm{.}5.$ Given the price of risk, the expected return of the risky portfolio $($E$($rp$))$ and the standard deviation of the risky portfolio p can you calculate the utility received from the portfolio?$6.$ Given the price of risk $($A$)$ and a given level of utility from a risky portfolio, can you draw an indifference curve?$7.$ Given an indifference curve identify the areas that represent higher levels of utility. Given an indifference curve identify areas that represent lower levels of utility. $8.$ Using calculus how is the optimal portfolio derived? What is the formula to determine the proportion of an investors total portfolio $($y$)$ that should be invested in the risky asset $?9.$ What are the determinants that affect the proportion of an investors total portfolio $($y$)$ that should be invested in the risky asset?$10.$ What is covariance? What is the formula to calculate the covariance of two returns?