Question

a stock will have a loss of 13 percent, or a return of 11.7 percent, or a return of 26.4 percent. the probabilities of these three states of the economy are 27 percent, 42 percent, and 31 percent, respectively. what is the standard deviation of the stock's returns?

Answer 1

The standard deviation of the stock's returns is 6.385%.

Step-by-step explanation:

To find the standard deviation of the stock's returns, we need to calculate the weighted average of the squared deviations from the expected return. We can start by calculating the expected return:

Expected Return = (Loss * Probability of Loss) + (Return1 * Probability of Return1) + (Return2 * Probability of Return2)

Expected Return = (0.13 * 0.27) + (0.117 * 0.42) + (0.264 * 0.31)

Expected Return = 0.0351 + 0.04914 + 0.08184

Expected Return = 0.16608 or 16.608%

Next, we can calculate the variance:

Variance = (Loss - Expected Return)^2 * Probability of Loss + (Return1 - Expected Return)^2 * Probability of Return1 + (Return2 - Expected Return)^2 * Probability of Return2

Variance = (0.13 - 0.16608)^2 * 0.27 + (0.117 - 0.16608)^2 * 0.42 + (0.264 - 0.16608)^2 * 0.31

Variance = 0.00123784 * 0.27 + 0.0016630672 * 0.42 + 0.0098256584 * 0.31

Variance = 0.00033428768 + 0.000698928864 + 0.003043209104

Variance = 0.004076425648 or 0.4076%

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard Deviation = sqrt(Variance)

Standard Deviation = sqrt(0.004076425648)

Standard Deviation = 0.06385 or 6.385%