Calculate the variance of a portfolio (sigma^2_p) where company A has weight 0.5 and has variance of 4, while company B has weight 0.5 and has variance of 9.The correlation between their returns is 0.5.

Variance of the portfolio is 4.75.

Explanation:

The variance of the portfolio can calculated using the following portfolio variance formula:

Portfolio variance = (WA^2 * VA) + (WB^2 * VB) + (2 * WA * SDA * WB * SDB * CFab) (1)

Where;

WA = Weight of Stock A = 0.50

WB = Weight of Stock B = 0.50

VA = Variance of Stock A = 4

VB = Variance of Stock B = 9

SDA = Standard deviation of stock A  = VA^0.5 = 4^0.5 = 2

SDB = Standard deviation of stock B  = VB^0.5 = 9^0.5 = 3

CFab = The correlation between stock A and stock B returns = 0.50

Substituting all the values into equation (1), we have:

Portfolio variance = (0.50^2 * 4) + (0.50^2 * 9) + (2 * 0.50 * 2 * 0.50 * 3 * 0.50)

Portfolio variance = 4.75

Therefore, variance of the portfolio is 4.75.