Market portfolio consists only of stock A and B. Stock A has expected return of 10% and volatility of 10%. Stock B has expected return of 15% and volatility of 20%. Both stock returns are uncorrelated. Risk-free rate is zero. There are only two investors in the market. Each investor has investment wealth of $1. Outstanding number of shares is one share for each stock. Each investor has the following quadratic expected utility: = 2 Var(), = 1,2. 1 = 10, 2 = 15 4 .

1. If investor 1 demands only stock A and risk-free asset, and investor 2 demands only stock B and risk-free asset, then what are market demands for stock A and B what are the equilibrium stock prices of A and B?

2. Under the assumption of 1, is the market portfolio efficient?

3. If both investors demand both stocks and risk-free asset. What are the equilibrium stock prices of stock A and B? Is the market portfolio efficient?

4. Based on the results from 2 and 3, is the market portfolio always efficient? Under what condition is the market portfolio efficient?