Question

An investment has an average return of 9.5%. The standard deviation of returns on this investment is 23.69%. Given this information, what is the range of return 99% of the time

Answer 1

The range of return 99% of the time for an investment with an average return of 9.5% and a standard deviation of 23.69% would be from -61.57% to 80.57%, calculated using the empirical rule for a normal distribution.

Step-by-step explanation:

To calculate the range of return 99% of the time for an investment with an average return of 9.5% and a standard deviation of 23.69%, we can use the concept of empirical rule or z-scores associated with a normal distribution. The empirical rule states that approximately 99% of data falls within three standard deviations from the mean in a normal distribution. Thus, the range is given by:

• Lower bound = Mean - 3 × Standard Deviation
• Upper bound = Mean + 3 × Standard Deviation

In this case:

• Lower bound = 9.5% - 3 × 23.69% = -61.57%
• Upper bound = 9.5% + 3 × 23.69% = 80.57%

Therefore, the range of return 99% of the time would be from -61.57% to 80.57%.