What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 22%. Stock B has a standard deviation of 16%. The portfolio is equally weighted and the correlation coefficient between the two stocks is .35.

15.7%

Explanation:

Given the following ;

Sa = standard deviation of stock A = 22%

Sb = standard deviation of stock B = 16%

Cc = correlation coefficient between the stock A and B = 0.35

Sp = portfolio standard deviation

Wa = weight of stock A

Wb = weight of stock B

However, WA and Wb are equal

Therefore, Wa = Wb = 0.5

Portfolio standard deviation(Sp) involving two stocks or asset as in above is evaluated using the formula;

Sp = sqrt(Wa^2Sa^2 + Wb^2Sb^2 + 2WaWbSaSbCc)

Sp = sqrt(0.5^2×22%^2 +0.5^2× 16%^2 + 2×16%×22%0.5×0.5×0.35)

Sp = sqrt((0.5^2×0.22^2) + (0.5^2×0.16^2) + ( 2×0.16×0.22×0.5×0.5×0.35))

Sp =sqrt(0.02466)

Sp = 0.1570

Sp = 15.7%

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