have $1M to invest. Assume the S&P500 index is the market portfolio, and that it has a risk premium of 5% over the risk-free rate and a volatility of 16%. Short-term Treasury bills are trading at a yield of 2%.

(a) What is the Sharpe ratio of the S&P 500?

(b) want to maximize returns subject to a portfolio volatility of 12%. consider investing in a combination of the S&P 500 and T-bills. Given willingness to accept a volatility of 12%, what is the expected return on the portfolio?

(c) Your friend tells you that he has analyzed Apple stock and strongly believes it has an expected return higher than that on the S&P 500, and he encourages you to shift some of your assets from the S&P 500 to a direct investment in Apple stock. Assume your friend is right about the expected return, and assume the CAPM holds. How do you react?