The universe of available securities includes two risky stocks A and B, and a risk-free asset. The data for the universe are as follows:

Assets Expected Return Standard Deviation

StockA 6% 25%

Stock B 12% 42%

Risk free 5% 0

The correlation coefficient between A and B is -0.2.

The investor maximizes a utility function U=E(r)^2

(i.e. she has a coefficient of risk aversion equal to 2).

Q9a. Assume that to maximize his utility when there is no available risk-free asset, an investor invest w in stock A and 1-w in stock B. What is the value of w?

Q9b. Further assume that this investor has A=5 and the above risky portfolio in Q9a, containing A and B is the OPTIMAL risky portfolio. The investor wants to maximize his utility when using both risky assets and risk-free asset. How much will he invest in stocks A and B and in risk free assets?