Question

An asset has an average return of 10.31 percent and a standard deviation of 22.65 percent. What is the most you should expect to earn in any given year with a probability of 2.5 percent?

A. 55.61%
B. 78.26%
C. 44.29%
D. 66.94%
E. 32.96%

Answer 1

To find the most you should expect to earn with a 2.5% probability, calculate the z-score for a one-tailed distribution at 97.5%, which is 1.96, and apply it to the formula for returns in a normal distribution. The correct expected return is 55.61%, corresponding to answer A.

Step-by-step explanation:

To answer the question of what is the most you should expect to earn in any given year with a probability of 2.5 percent given an asset with an average return of 10.31 percent and a standard deviation of 22.65 percent, we need to utilize the concept of z-scores from statistics.

In standard normal distribution, a z-score corresponding to the top 2.5 percent of returns (meaning there's a 2.5 percent probability of earning more than this return) is typically around 1.96 when looking at a two-tailed distribution. Since we are looking at a one-tailed distribution (the top end), we use the z-score for 97.5 percent, which is approximately 1.96. To calculate the return corresponding to this z-score, we use the formula: return = mean + (z-score * standard deviation).

Therefore, the calculation would be: 10.31% + (1.96 * 22.65%) = 55.61%. So, the correct answer is A. 55.61%.

Answer 2

To find the most you should expect to earn in any given year with a probability of 2.5 percent, we can use the concept of standard deviation. The most you can expect to earn is the average return plus 2.5 times the standard deviation. In this case, the most you should expect to earn is 66.94 percent.

Step-by-step explanation:

To find the most you should expect to earn in any given year with a probability of 2.5 percent, we can use the concept of standard deviation. The most you can expect to earn is the average return plus 2.5 times the standard deviation.

In this case, the average return is 10.31 percent and the standard deviation is 22.65 percent. So, the most you should expect to earn is 10.31 plus (2.5 times 22.65), which is 10.31 plus 56.625, equal to 66.935.

Rounded to the nearest hundredth, the most you should expect to earn is 66.94 percent.