What is the standard deviation of a portfolio of two stocks given the following dа ta: 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.

Answer: 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%

15.7%

Explanation:

The standard deviation of a portfolio of two stocks given the following dа ta: 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.

Standard deviation = √

(0.50) 2 (0.22) 2 + (0.50) 2 (0.16) 2 + 2 (0.35) (0.22) (0.16) (0.5) (0.5) = 0.157

0.157 = 15.7%