Suppose that you have $100,000 to invest for one year. Suppose further that Treasury bills yield 5%. One alternative is to buy Treasury bills. There is then no risk and the expected return is 5%. Another alternative is to invest the $100,000 in a stock. To simplify things, we suppose that the possible outcomes from this investment are as shown in Table 1.1. (a) (b) Table 1.1 One-Year Return from Investing $100,000 in a Stock Probability (d) 0.05 0.25 0.40 0.25 0.05 Return +50% +30% +10% -10% -30% What is the mean and standard deviation of 1-year returns on the stock? Suppose we invest $70,000 in the stock and invest $30,000 in Treasury bills. What is the mean and standard deviation of 1-year returns of the portfolio? (c) Let be the proportion of $100,000 to invest in the stock and 1-2 be that to invest in the Treasury Bills. For = 0,0.1,0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, find the mean and standard deviation of 1-year returns of the portfolio. Plot a scatter plot between the mean returns and the standard deviation of returns. Explain why the scatter plot is a straight line. What is the slope and y-intercept of the line in terms of the mean and standard deviation of 1-year returns on the stock and the risk-free return?