Assume that an investor holds the market portfolio M which is the most optimum portfolio with an expected return E(R_M)=15% and standard deviation _M = 12%. However the maximum risk tolerance of the investor is only 8%. Assume 10 year government bonds give a risk free yield of 7%.

1. How much weight should the investor put in risk free assets to meet his risk tolerance but maximize his utility?
2. The investor is indifferent between the above portfolio and a real estate asset having returns of 10% and standard deviation of _B = 2%. What is the risk aversion coefficient?

For the above risk aversion, how much return should the risk free asset have given (instead of 7% above), for the investor to be indifferent between the market optimal portfolio, real estate and the risk free asset?