What range of returns should you expect to see with a 68 percent probability?
What is the most you should expect to lose in any given year with a probability of 2.5 percent?
A.) The range of returns you should expect with a 68 percent probability is -8.76% to 30.18%.
Option C.
B.) The most you should expect to lose in any given year with a 2.5 percent probability is -12.94%.
Option A.
Range of Returns with 68 Percent Probability
To determine the range of returns you should expect to see with a 68 percent probability, we can use the concept of one standard deviation. In a normal distribution, approximately 68 percent of the data falls within one standard deviation of the mean. Given that the asset has an average return of 10.71 percent and a standard deviation of 19.47 percent, we can calculate the range as follows:
Lower Range = Average Return - (Standard Deviation)
Lower Range = 10.71% - (19.47%)
Lower Range = -8.76%
Upper Range = Average Return + (Standard Deviation)
Upper Range = 10.71% + (19.47%)
Upper Range = 30.18%
Therefore, with a 68 percent probability, you should expect returns within the range of -8.76% to 30.18%.
The correct answer is -8.76% to 30.18%.
Expected Loss with 2.5 Percent Probability
To determine the most you should expect to lose in any given year with a probability of 2.5 percent, we can use the concept of the left-tail probability. Given the average return of 11.51 percent and a standard deviation of 24.45 percent, we want to find the value at the 2.5th percentile, which represents the loss you would expect to exceed only 2.5 percent of the time.
Using statistical tables or a calculator, we can find this value, which corresponds to the left-tail probability of 2.5 percent. The value is approximately -12.94%.
Therefore, the most you should expect to lose in any given year with a 2.5 percent probability is -12.94%.
The correct answer is -12.94%.
So Option C is correct for A and Option A is correct for Part B.