Please show all work, especially the standard deviation calculation of the portfolio in (a).

Suppose that a fund that tracks the S&P has expected return E[Rm]=8.5% and standard deviation M=17%, and suppose that the T-bill rate is Rf=4.5%. (a) What is the expected return and standard deviation of a portfolio that: i. Is entirely invested in the risk-free asset? ii. Has 50% of its value in the risk-free asset and 50% in the S&P ? iii. Has 125% of its value in the S\&P, financed by borrowing 25% of its value at the risk-free rate? (b) Now consider an investor that has preferences over portfolio returns characterized by: U(RP)=E[RP]2Var(RP) Which of the three portfolios from part (a) will be preferred by the investor with the above utility function? (c) What are the weights for investing in the risk-free asset and the S\&P that produce a standard deviation for the entire portfolio that is twice the standard deviation of the S\&P? What is the expected return on this portfolio? Limit your attention to efficient portfolios. (d) What is the Sharpe ratio of this portfolio and how does it compare to the Sharpe ratio of a 100%S&P investment? (e) What about an investor with preferences characterized by: U(RP)=E[RP]0.5Var(RP) Is her choice the same? Why? In your answer, describe this investor's attitude towards risk relative to the investor in part (b)