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 -1 < ρA,B < 1, then a portfolio that consists of stock A and stock B MUST have a variance _________. Assume no short selling allowed.

A. Greater than 0.6

B. Less than 0.8

C. Greater than 0.8

D. Less than 0.64

E. Not enough information

ANS: D

Answer 1

Standard deviation of stock A(SDa) =0.6

Standard deviation of stock B(SDb) =0.8

Let the weight of Stock A in Portfolio be W1 and weight of stock B be W2

So variance of the portfolio ,

= (W1 * SDa)^2 + (W2 * SDb)^2 + 2*(W1 * SDa) * (W2 * SDb) * Correlation coefficient

The variance will be highest when Correlation coefficent is 1 and weight of Stock B is 100% ( Since Stock B has higher Standard deviation)

So in that case W1 will be 0 and W2 will be 1

So Vaiance of portfolio = (W2 * SDb)^2 = (1* 0.8)^2 = 0.64

So When correlation coefficient is 1, variance is highest i.e 0.64

Here since it is mentioned that correlation coefficient is less than 1, so variance must be lesser than 0.64

Si the correct answer is option D) Thanks:)