Explanation

To calculate the standard deviation of Stock B, we first need to find the variance and then take the square root.

Step 1: Calculate the expected return of Stock B (E[R_B])

From the probability matrix:

• P(R_B = 50%) = 40%
• P(R_B = 20%) = 30%
• P(R_B = -30%) = 30%

$E[R_B] = (0.50 \times 0.40) + (0.20 \times 0.30) + (-0.30 \times 0.30)$ $E[R_B] = 0.20 + 0.06 - 0.09$ $E[R_B] = 0.17$

Step 2: Calculate the variance of Stock B (Var[R_B])

$Var[R_B] = E[R_B^2] - (E[R_B])^2$

First, calculate E[R_B^2]: $E[R_B^2] = (0.50^2 \times 0.40) + (0.20^2 \times 0.30) + ((-0.30)^2 \times 0.30)$ $E[R_B^2] = (0.25 \times 0.40) + (0.04 \times 0.30) + (0.09 \times 0.30)$ $E[R_B^2] = 0.10 + 0.012 + 0.027$ $E[R_B^2] = 0.139$

Now calculate variance: $Var[R_B] = 0.139 - (0.17)^2$ $Var[R_B] = 0.139 - 0.0289$ $Var[R_B] = 0.1101$

Step 3: Calculate standard deviation

$\sigma_B = \sqrt{0.1101} \approx 0.3318$

This is closest to 0.33, which corresponds to option C.