Question

Given the following information on a portfolio of Stock X and Stock Y, what is the portfolio standard deviation?

Probability of boom state = 30%

Probability of normal state = 70%

Expected return on X = 14.5%

Expected return on Y = 14%

Variance on X = 0.004725

Variance on Y = 0.0189

Portfolio weight on X = 50%

Portfolio weight on Y = 50%

Correlation between X and Y = -1

Answer 1

3.44%

Working:

a.

Standard deviation of X

=

Variance^(1/2)

=

0.004725^(1/2)

=

0.0687

Standard deviation of Y

=

Variance^(1/2)

=

0.0189^(1/2)

=

0.1375

b.

Portfolio standard deviation

=

(((Weight of X^2)*Variance of X)+((Weight of Y^2)*Variance of Y)+(2*Weight of X* Weight of Y *Standard deviation of X*Standard Deviation of Y*correlation between X and Y))^(1/2)

=

(((.50^2)*0.004725)+((0.50^2)*0.0189)+(2*0.50*0.50*0.0687*0.1375*-1))^(1/2)

=

3.44%