Question

Stock X has a standard deviation of 25 percent per year and stock Y has a standard deviation of 16 percent per year. The correlation between stock X and stock Y is zero. You have a portfolio of these two stocks wherein stock X has a portfolio weight of 50 percent. What is your portfolio standard deviation?

Answer 1

Answer:

14.82%

Explanation:

The standard deviation of a portfolio is the $\sqrt{variance }$

standard deviation of stock X = 25%

standard deviation of stock Y = 16%

weight of X = 50%

weight of Y = 50%

correlation coefficient = 0

therefore portfolio standard deviation

= $\sqrt{Wx^{2} } Sdx^{2} + Wy ^{2}Sdy^{2}+2Wx*Sdx * Sdy* Wy *R$    -- equation 1

Wx = weight of stock x

Wy = weight of stock y

Sdx = standard deviation of stock x

Sdy = standard deviation of stock y

R = correlation coefficient

back to equation 1

$\sqrt{(0.5^{2} }*0.25^{2} ) + (0.5^{2}*0.16^{2}) + ( 2 * 0.5 *0.25 *0.16*0.5 *0 )$

= $\sqrt{0.015625 + 0.0064} = \sqrt{0.022025}$

therefore standard deviation of new portfolio = 0.1482 = 14.82%

Answer 2

Answer:

The portfolio standard deviation is 14.82%

Explanation:

The portfolio standard deviation would be calculated by finding out the variance of the portfolio and taking the square root of it.

Variance of the portfolio = [(1 - .50)$^{2}$ x 0.25$^{2}$] + [0.50$^{2}$ x 0.16$^{2}$] + [2 x (1 - 0.50) x 0.50 x 0.25 x 0.16 x 0]

= [0.25 x 0.0625] + [0.25 x 0.0256] + [0]

= 0.015625 + 0.0064

VarPort = 0.022025

Std DevPort  = √0.022025

Std DevPort = 0.1482 = 14.82 percent