ASSIGNMENT 10
Optimal Portfolio

An individual investor's preferences regarding expected return (E) and risk (s) are represented by the utility function: u(E,s) = aE - 3s². The equation of the efficient frontier is: E = 4.5 + s^0.5.

1. Obtain u₂. What does its sign represent?
   
   
2. Plot the efficient frontier (with expected return on the vertical axis). What is the significance of the vertical intercept?
   
   
3. Let a = 30. What is the expected return and risk associated with the optimal portfolio? [Use FOC and SOC.]
   
   
4. What is the investor's maximum utility? Plot the corresponding indifference curve. Indicate the optimal portfolio on the graph.
   
   
5. Suppose the investor becomes more risk-averse, i.e. she is less willing to take risk. (This might be due to a recent adverse occurrence; e.g., a stock market crash!) How will this affect her optimal portfolio? Using a new value for the parameter a, re-write the investor's optimization problem. Using new FOCs, obtain the return and risk for the new portfolio. Find maximum utility, sketch the indifference curve, and indicate the optimal portfolio. Does the investor's revised portfolio exhibit a higher, or lower, expected return? Explain. On a graph, compare the points of tangency in the two cases.