Question

a stock will have a loss of 13 percent in a recession, a return of 11.7 percent in a normal economy, and a return of 26.4 percent in a boom. there is 27 percent probability of a recession, 42 percent probability of normal economy, and 31 percent probability of boom. what is the standard deviation of the stock's returns?

Answer 1

To find the standard deviation of the stock's returns, first calculate the expected return with the given probabilities and returns, then compute the variance, and finally, take the square root of the variance.

Step-by-step explanation:

To calculate the standard deviation of the stock's returns given the different economic scenarios and their probabilities, we first need to find the expected return and then the variance of the returns before taking the square root to find the standard deviation.

The expected return (ER) can be calculated using the formula:

ER = (Probability of Recession × Return in Recession) + (Probability of Normal Economy × Return in Normal Economy) + (Probability of Boom × Return in Boom)

ER = (0.27 × (-13)) + (0.42 × 11.7) + (0.31 × 26.4)

Next, we calculate the variance of the stock's returns, which is the expected value of the squared deviation of each possible return from the expected return, weighted by its probability.

Variance = (Probability of Recession × (Return in Recession - ER)^2) + (Probability of Normal Economy × (Return in Normal Economy - ER)^2) + (Probability of Boom × (Return in Boom - ER)^2)

Finally, the standard deviation is the square root of the variance.