a) Suppose you have a project that has a 7 chance of doubling your investment in a year and a.3 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment? Greta, an elderly investor, has a degree of risk aversion of A=3 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain. 1) If the correlation coefficient between annual portfolio returns is 0.3, what is the annual covariance? 2) With correlation of 0.3, what is the covariance between the 3-year returns? 3) Repeat Problem a, using an annual correlation of 0.3. (If you cannot calculate the 3-year covariance in Problem 17, assume it is 0.05.)