Suppose you have some money to invest for simplicity, $1-and you are planning to

Question

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 Rb, suppose that Rs 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 Rs and Rb is 0.24. 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-w)R, Suppose that w = 0.48. Compute the mean and standard deviation of R. The mean is 0.065. (Round your response to three decimal places.) The standard deviation is 0.039 Roundour response to three decimal places.)

Explanation / Answer

here R =0.48Rs+0.52Rb

mean of R =E(R) =0.48*E(Rs)+0.52*E(Rb) =0.48*0.08+0.52*0.05=0.064

std deviaiton of R =((0.48*0.07)2+(0.52*0.04)2+2*0.48*0.52*0.24*0.07*0.04)1/2 =0.0436

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