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)[tex]^{2}[/tex] x 0.25[tex]^{2}[/tex]] + [0.50[tex]^{2}[/tex] x 0.16[tex]^{2}[/tex]] + [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
Answer:
14.82%
Explanation:
The standard deviation of a portfolio is the [tex]\sqrt{variance }[/tex]
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
= [tex]\sqrt{Wx^{2} } Sdx^{2} + Wy ^{2}Sdy^{2}+2Wx*Sdx * Sdy* Wy *R[/tex] -- 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
[tex]\sqrt{(0.5^{2} }*0.25^{2} ) + (0.5^{2}*0.16^{2}) + ( 2 * 0.5 *0.25 *0.16*0.5 *0 )[/tex]
= [tex]\sqrt{0.015625 + 0.0064} = \sqrt{0.022025}[/tex]
therefore standard deviation of new portfolio = 0.1482 = 14.82%
