Final answer:
To calculate the range of returns with a 95% probability for an asset with a mean return of 10.88% and a standard deviation of 20.90%, we use the empirical rule. The range is between -30.92% and 51.68%, meaning option 4) 51.68% is the upper limit of expected returns with a 95% probability.The correct option is D.
Step-by-step explanation:
The question is asking us to calculate the range of returns you should expect to see with a 95 percent probability, given an asset's average return and standard deviation. This involves using the concept of a normal distribution and standard deviation to find the range in which 95% of the returns are expected to fall.
To find this range, we can use the empirical rule, which states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean. The formula to calculate the range is Mean ± 2 * Standard Deviation.
So, for a mean (μ) of 10.88% and a standard deviation (σ) of 20.90%, we calculate the range as follows:
- Lower Range = μ - 2σ = 10.88% - 2 * 20.90% = 10.88% - 41.80% = -30.92%
- Upper Range = μ + 2σ = 10.88% + 2 * 20.90% = 10.88% + 41.80% = 51.68%
Hence, with a 95% probability, the range of returns we should expect to see is between -30.92% and 51.68%.