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

Explanation:

Step1: Identify given variables

$$w_A = 0.25, w_B = 0.75, \sigma_A^2 = 0.09, \sigma_B^2 = 0.25, \text{Cov}_{A,B} = 0.036$$

Step2: State portfolio variance formula

$$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \text{Cov}_{A,B}$$

Step3: Substitute values into formula

$$\sigma_p^2 = (0.25)^2(0.09) + (0.75)^2(0.25) + 2(0.25)(0.75)(0.036)$$

Step4: Calculate individual terms

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

Step5: Sum terms for variance

$$\sigma_p^2 = 0.15975$$

Step6: Calculate standard deviation

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

Answer:

0.3997 (or 39.97%)