Question

If you have one security with an expected return of 7% and a standard deviation of 2% and a second security with an expected return of 13% and a standard deviation of 2.4%, what would be the standard deviation of a portfolio that consists of 30% of the first security and 70% of this second security if the correlation coefficient between the two securities is -.30?

Answer 1

Standard deviation of portfolio ?p = ? [(W1^2 * ?1^2 + W2^2 * ?2^2 + 2*W1*W2*?1 *?2 *Cov(1, 2)]

Where,

W1 = weight of security 1 in portfolio = 30% or 0.3

W2 = weight of security 2 in portfolio = 70% or 0.7

E (r1) = Expected return of security 1 = 7% or 0.07

E (r2) = Expected return of security 2 = 13% or 0.13

The standard deviation of security 1, ?1 = 2% or 0.02

The standard deviation of security 2, ?2 = 2.4% or 0.024

Cov (1,2) is the correlation coefficient between two securities = - 0.30

Therefore,

Standard deviation of portfolio ?p =? [0.3^2*0.02^2+0.7^2*0.024^2 +2* 0.3*0.7*0.02 * 0.024 *(-0.3)]

=? [0.000036 + 0.00028224 -0.00006048]

= ? [0.00025776]

= 0.016054906 or 1.605%