Problem 3 (32 points) Suppose that you are interested in investing in a portfolio consisting of...

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Problem 3 (32 points) Suppose that you are interested in investing in a portfolio consisting of stocks and bonds. You have already decided to invest in an equity fund that is indexed to the S&P 500, but are not sure whether to invest in Government bonds or Catastrophe ("Cat") bonds. The Cat bonds are riskier than Government bonds because Cat bond investors must forfeit interest and principal payments if a Category 4 or 5 hurricane hits Florida. The following table summarizes the expected returns and standard deviations for these securities: Security Cat Bonds Expected Return Standard Deviation 8% 15% Equity Fund 12% 20% Gov't Bonds 5% 8% The correlation between Cat Bond returns and Equity Fund returns is -.1, whereas the correlation between Government Bond returns and Equity Fund returns is .10. A. (10 points) Suppose you would like to earn 10% on your portfolio. What is the standard deviation of a portfolio consisting of Cat Bonds and the Equity Fund that would have an expected return of 10%? B. (10 points) What is the standard deviation of a portfolio consisting of Government Bonds and the Equity Fund that would have an expected return of 10%? C. (12 points) Suppose the riskless rate of interest is 3%, and you can borrow or lend against either of the portfolio combinations described in parts A and B above. Which of these two portfolio combinations is preferred by arbitrarily risk averse investors? Justify your answer. Problem 3 (32 points) Suppose that you are interested in investing in a portfolio consisting of stocks and bonds. You have already decided to invest in an equity fund that is indexed to the S&P 500, but are not sure whether to invest in Government bonds or Catastrophe ("Cat") bonds. The Cat bonds are riskier than Government bonds because Cat bond investors must forfeit interest and principal payments if a Category 4 or 5 hurricane hits Florida. The following table summarizes the expected returns and standard deviations for these securities: Security Cat Bonds Expected Return Standard Deviation 8% 15% Equity Fund 12% 20% Gov't Bonds 5% 8% The correlation between Cat Bond returns and Equity Fund returns is -.1, whereas the correlation between Government Bond returns and Equity Fund returns is .10. A. (10 points) Suppose you would like to earn 10% on your portfolio. What is the standard deviation of a portfolio consisting of Cat Bonds and the Equity Fund that would have an expected return of 10%? B. (10 points) What is the standard deviation of a portfolio consisting of Government Bonds and the Equity Fund that would have an expected return of 10%? C. (12 points) Suppose the riskless rate of interest is 3%, and you can borrow or lend against either of the portfolio combinations described in parts A and B above. Which of these two portfolio combinations is preferred by arbitrarily risk averse investors? Justify your answer.