The expected returns of stocks 1,2, and 3 are 8%, 9%, and 12% respectively. The variances of stocks 1,2, and 3 are .04, .06, and .08 respectively. the three stocks are uncorrelated. the risk free rate is 4%.

a) calculate the tangency portfolio weights of these three stocks and the mean, SD, and sharpe ratio of the tangency portfolio.

b) if my risk avcersion is 10% standard deviation, what investment portfolio should I invest in? what is the maximum sharpe ratio i can achieve if i am only williong ot face a 10% standard devation? what is the expected return on this portfolio?