3. An investor puts some money into each of two stocks labeled A and B: $500 in

Question

3. An investor puts some money into each of two stocks labeled A and B: $500 in to stock A and $1000 in to stock B. The mean rates of return for the stocks are HA = 0.15 and tig-012. So, if one puts a dollar into stock A, the expected profit at the end of the year is S0.15. The standard deviations of the rates of returns are 0A = 0.05 and, 0.03. (a) Find the mean and standard deviation of the total amount the investor earns in one year, assuming the rates of return are independent random variables (b) Find the mean and standard deviation of the total amount the investor earns in one year, assuming that the rates of return are positively correlated with a correlation coefficient of 0.5

Explanation / Answer

Proportions of stocks: W(A) = 500/1500 = 1/3; W(B) = 2/3

a)

Mean return = 1/3*0.15 + 2/3*0.12 = 0.13 = 13%

Std deviation of return = sqrt( 0.05^2 + 0,03^2 ) = 0.0583

Mean of total amount earned = 0.13*1500 = $195

Std deviation of amount earned = 0.0583*1500 = $87.45

b)

Mean return = 1/3*0.15 + 2/3*0.12 = 0.13 = 13%

Std deviation of return = sqrt( 0.05^2 + 0,03^2 +2*0.5*0.05*0.03) = 0.07

Mean of total amount earned = 0.13*1500 = $195

Std deviation of amount earned = 0.07*1500 = $105

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