8. Assume that you have $50,000 of your own funds to invest. You may borrow and lend at a risk free rate of 6% and/or invest in a well-diversified mutual fund whose performance matches with the market as a whole. The expected annual return of the fund is 16%, and the standard deviation of its annual returns is 20%. On a percentage basis, calculate the risk and the expected return of your investment if you: a) Invest $50,000 in the risk-free asset. b) Invest $50,000 in the market portfolio. c) Invest $25,000 in the risk free asset and $25,000 in market portfolio. d) Borrow $10,000 at the risk free rate and invest $60,000 in the market portfolio. e) Borrow $50,000 at the risk free rate and invest $100,000 in the market portfolio. f) Graph your results. g) Which of these portfolios (if any) is optimal in Markowitz sense? 8. Assume that you have $50,000 of your own funds to invest. You may borrow and lend at a risk free rate of 6% and/or invest in a well-diversified mutual fund whose performance matches with the market as a whole. The expected annual return of the fund is 16%, and the standard deviation of its annual returns is 20%. On a percentage basis, calculate the risk and the expected return of your investment if you: a) Invest $50,000 in the risk-free asset. b) Invest $50,000 in the market portfolio. c) Invest $25,000 in the risk free asset and $25,000 in market portfolio. d) Borrow $10,000 at the risk free rate and invest $60,000 in the market portfolio. e) Borrow $50,000 at the risk free rate and invest $100,000 in the market portfolio. f) Graph your results. g) Which of these portfolios (if any) is optimal in Markowitz sense