To determine the range of returns with a 68 percent probability, we need to apply the concept of one standard deviation around the mean in a normal distribution. A 68 percent probability in a normal distribution represents one standard deviation from the mean in either direction.

Given:

• Mean (average return) = 9.83%
• Standard Deviation = 18.81%

Calculation:

The range of returns with a 68 percent probability would be: $\text{Range} = \text{Mean} \pm \text{Standard Deviation}$ So, $9.83\% - 18.81\% = -8.98\%$ $9.83\% + 18.81\% = 28.64\%$

Expected Range

The expected range of returns with a 68 percent probability is: $-8.98\% \text{ to } 28.64\%$

Answer:

The correct choice is: −8.98% to 28.64%

Would you like further details on this calculation or have any other questions?

Here are five related questions to expand on this topic:

1. How would the range change with a 95 percent probability?
2. What does the standard deviation represent in this context?
3. How can you calculate the probability of a return falling outside one standard deviation?
4. How would the mean return affect the expected range?
5. How does standard deviation relate to risk in finance?

Tip: In finance, a higher standard deviation often suggests greater volatility or risk associated with an asset's returns.