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(4) I8 pts] 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 Rs after 1 year and that $1 invested in a bond fund yields Rh. Suppose further that Rs is random with with mean 0.08 (8%) and standard deviation 0.07, and that Rb is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between Rs and Rb 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 RwRb (a) Suppose that w 0.5. Compute the mean and standard deviation of R. (b) Suppose that w-0.75. 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) What is the value of w that minimizes the standard deviation of R?

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Given thab vcRs): (0.04). 0.0016 V an 0.25 オ 0.07 x 0.04 0.0607 Given R (1-u), 2 ati--u) 0.0007 0.0049ん1 t 0.0011 0o8w.to.o5(I.w) ะ o.ost7% (8,S)2十 0.0016x11-0,S) Ltab ,S xa-09. vce): 0.0003 O. 001975 s.d ()004441 o.0125 VCR) = 0.0031153

Von (R) 0,004 △ s) P) o 0007 0.0047 Van (x) itt ruspert to w ㄴ + veu) ((..w) 2-e 2 w ((m).ene 0.0102 i>。

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