Problem 1. The annual rate of return of a bond fund over the last 8 years are (in \%) as follows: 0.5315.2932.6823.962.658.4019.497.13 Calculate the arithmetic and the geometric mean rate of return of the fund. Problem 2. A project requires investments of $1,000 and $1,176 at the end of the first year and the third year, respectively, and generates income of $2,170 at the end of 2 years. Find the internal rate of return of the project. Problem 3. The following shows the return and standard deviations of three stock indices: US, Germany, and Japan: The correlation matrix of the three stock indices is as follows: You construct a portfolio of the three markets with 15% weight in US, 40% weight in Germany and 45% weight in Japan. Calculate the expected return and standard deviation of the return of the portfolio. Problem 4. A stock fund has an expected return of 0.16 and variance of 0.0784 . A bond fund has an expected return of 0.08 and variance of 0.0196 . The correlation between the two funds is -0.3 . (a) What is the expected return and standard deviation of the portfolio with 80% in the stock fund and 20% in the bond fund? (b) What is the expected return and standard deviation of the portfolio with 20% in the stock fund and 80% in the bond fund