Question

A stock is expected to return 11 percent in a normal economy, 16 percent in a boom, and lose 9 percent in a recession. There is a 20 percent chance the economy will boom and a 10 percent chance of a recession. What is the standard deviation of the expected returns?

Answer 1

The standard deviation of the expected returns is 0.383.

Step-by-step explanation:

To calculate the standard deviation of the expected returns, we first need to compute the expected return for each scenario. The expected return is the weighted average of the returns in each scenario, where the weights correspond to the probabilities of each scenario.

Expected return = (Probability of boom * Return in boom) + (Probability of normal economy * Return in normal economy) + (Probability of recession * Return in recession)

= (0.20 * 16%) + (0.70 * 11%) + (0.10 * -9%)

= 0.20 * 16% + 0.70 * 11% - 0.10 * 9% = 8.2%

Next, we need to calculate the variance of the returns in each scenario, which is the squared difference between each return and the expected return, weighted by the probability of each scenario.

Variance = (Probability of boom * (Return in boom - Expected return)^2) + (Probability of normal economy * (Return in normal economy - Expected return)^2) + (Probability of recession * (Return in recession - Expected return)^2)

= (0.20 * (16% - 8.2%)^2) + (0.70 * (11% - 8.2%)^2) + (0.10 * (-9% - 8.2%)^2)

= 0.20 * (0.0784) + 0.70 * (0.0784) + 0.10 * (0.3364) = 0.1466

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

Standard deviation = sqrt(Variance) = sqrt(0.1466) = 0.383