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
Stock A	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).

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.

a) What is the value of w?

Further assume that this investor has A=5 and the above risky portfolio in a) 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?

Weight in stock A?

Weight in stock B?

Weight in risk-free asset?