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Score: 0 of 3 pts 17of22 (19 complete) ▼ Hw Score: 72.87%, 18.22 of 25 pts Exercise 2.22 Question Help * Suppose you have some money to invest-for simplicity, $1--and you are planning to put a fraction w into a stock market mutual fund and the rest, 1- w, into a bond mutual fund. Suppose that $1 invested in a stock fund yields R after 1 year and that $1 invested in a bond fund yields Rb, suppose that Rs is random with mean 0 09 (9%) and standard deviation 0.08, and suppose that Rb is random with mean 0.06 (6%) and standard deviation 0.05. The correlation between Rs and is 0.29. If you place a fraction w of your money in the stock fund and the rest, 1-w in the bond fund, then the return on your investment is R= wRs + (1-wjRb Suppose that w 0.57. Compute the mean and standard deviation of R. The mean is □ (Round your response to three decimal places.) The standard deviation is (Round your response to three decimal places.)
2.22 Suppose you have some money to invest-for simplicity, $1-and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 - w, into a bond mutual fund. Suppose that $1 invested in a stock fund yields R, after 1 year and that S1 invested in a bond fund yields Ra, suppose that R, is random with mean 0.08 (8%) and standard deviation 0.07, and suppose that Rb is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between R, and R, is 0.25. If you place a fraction w of your money in the stock fund and the rest, 1 - w, in the bond fund, then the return on your investment is R wR+ (1 -w)R, a. Suppose that w0.5. Compute the mean and standard deviation of R. b. Suppose that w0.75. Compute the mean and standard deviation of R c. What value of w makes the mean of R as large as possible? What is the standard deviation of R for this value of w? d. (Harder) What is the value of w that minimizes the standard deviation of R? (Show using a graph, algebra, or calculus.)
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