Question

Woodpecker, Inc., stock has an annual return mean and standard deviation of 12.2 percent and 42 percent, respectively. What is the smallest expected loss in the coming month with a probability of 5.0 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.)

Smallest expected loss %

Answer 1

The smallest expected loss in the coming month with a probability of 5.0 percent is 21.07 percent.

Step-by-step explanation:

To calculate the smallest expected loss with a probability of 5.0 percent, we'll use the concept of z-scores. First, we find the z-score corresponding to the 5.0 percent probability by using the standard normal distribution table or calculator. For a 5.0 percent probability, the z-score is approximately -1.645 (rounded to 3 decimal places).

Next, we'll apply the formula for finding the expected loss, considering the annual return mean and standard deviation. The formula for expected loss using z-scores is Loss = Mean return + (Z-score * Standard deviation). Given the mean return of 12.2 percent and a standard deviation of 42 percent, we substitute these values into the formula: Loss = 12.2 + (-1.645 * 42).

Calculating this, we get Loss = 12.2 - 69.09, which results in -56.89 percent. However, a loss cannot be negative in this context, so we take the absolute value to get the positive smallest expected loss, which is 56.89 percent. Therefore, the smallest expected loss with a 5.0 percent probability is 56.89 percent.

Answer 2

To find the smallest expected loss with a probability of 5.0 percent, we can use the z-score formula and calculate the corresponding loss value. The smallest expected loss is -62.59 percent.

Step-by-step explanation:

To find the smallest expected loss with a probability of 5.0 percent, we need to calculate the z-score corresponding to this probability and then use it to find the corresponding loss value.

The z-score is calculated using the formula: z = (x - mean) / standard deviation

Let x be the loss value we want to find, the mean is 12.2 percent, the standard deviation is 42 percent, and the z-score is -1.645 for a 5.0 percent probability.

Substituting these values into the formula, we have: -1.645 = (x - 12.2) / 42

Solving for x, we find: x = -1.645 * 42 + 12.2

Therefore, the smallest expected loss with a probability of 5.0 percent is -62.59 percent (rounded to 2 decimal places).