Question

The standard deviation of stock A is .60, while the standard deviation of stock B is .80. If the correlation coefficient for A and B is positive, then a portfolio that consists of 50% of stock A and 50% of stock B MUST have a standard deviation _________. Assume no short selling allowed.

a) Less than 0.5

b) Greater than 0.7

c) Greater than 0.5

d) Less than 0.6

e) Not enough information

Answer 1

e. Not enough information. Correlation amount is not given and also no mean is given. Cov xy means Covariance can't be calculated because of this. The formula for calculating Portfolio standard deviations is;

Here W stands for weight which is given in the problem and sigma indivates standard deviation. Cov for Covariance. In the question it is mentioned that there is a positive correlation. No amount is given a positive correlation may be above 0 upto 1. If it is mentioned that perfect correlation is there we could assume it as 1. Bu only positive correlation is mentioned. Upto 0.5 lower positive correlation. 0.5- +1 will ne highly positive correlation.