calculate the standard deviation of a portfolio consisting of 25 percent stock a and 75 percent stock…

Explanation:

Step1: Identify given variables

$w_A = 0.25, w_B = 0.75, \sigma_A = 0.30, \sigma_B = 0.50, \rho_{A,B} = 0.24$

Step2: State the portfolio variance formula

$$\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\sigma_A\sigma_B\rho_{A,B}$$

Step3: Substitute values into the formula

$$\sigma_p^2 = (0.25)^2(0.30)^2 + (0.75)^2(0.50)^2 + 2(0.25)(0.75)(0.30)(0.50)(0.24)$$

Step4: Calculate each term

$$\sigma_p^2 = 0.005625 + 0.140625 + 0.0135 = 0.15975$$

Step5: Calculate the standard deviation

$$\sigma_p = \sqrt{0.15975} \approx 0.399687$$

Answer:

39.97%