There is an investment opportunity set where the optimal risky portfolio O has expected rate of return of 10% and volatility (or standard deviation) of 20%, and cash yields a risk free rate of 2%.

a) One investor chooses to invest 50% in the portfolio O and 50% in cash. Compute the expected return and volatility of her portfolio, and its Sharpe ratio.

b) A second investor has an expected rate of return target of 12%. Compute the composition of her portfolio, and its Sharpe ratio.

c) A third investor has a volatility target of 15%. Compute the composition of her portfolio, and its Sharpe ratio.