Question

Which one of the following statements is correct?
A. A portfolio variance is a weighted average of the variances of the individual securities which
comprise the portfolio.
B. A portfolio variance is dependent upon the portfolio;s asset allocation..
C. A portfolio variance is unaffected by the correlations between the individual securities held in
the portfolio.
D. The portfolio variance must be greater than the lowest variance of any of the securities held in
the portfolio.
E. The portfolio variance must be less than the lowest variance of any of the securities held in the
portfolio.

Answer 1

Answer:

B. A portfolio variance is dependent upon the portfolio's asset allocation.

Explanation:

A portfolio variance is used to determine the overall risk or dispersion of returns of a portfolio and it is the square of the standard deviation associated with the particular portfolio.

Hence, the correct statement among the options given is that, a portfolio variance is dependent upon the portfolio's asset allocation.

The portfolio variance is given by the equation;

$Variance = w^{2}_{1} d^{2}_{1} + w^{2}_{2} d^{2}_{2}+2w_{1}w_{2}C_{OV_{1, 2}}$

Where;

$w_{n}$ = the weight of the nth security.

$d^{2}_{n}$ = the variance of the nth security.

$C_{OV_{1, 2}}$ = the covariance of the two security.