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CASE 1-3
Find the sample proportion of the years when nominal annual returns were negative.
Using this sample proportion as the probability of a negative nominal return in any year and assuming the occurrence of a negative nominal return in one year of a 10-year period is independent of occurrences in other years of the 10-year period, derive a theoretical probability distribution on the number of years with negative returns over a 10-year period.
In the data provided, there are 10-year periods with six years of negative returns. Based on your theoretical distribution, what is the probability of having six or more years of negative returns over a 10-year period?
In the data provided there are 10-year periods with only one year of negative returns. Based on your theoretical distribution, what is the probability of having one or fewer years of negative returns over a 10-year period?
In your Word/pdf document, discuss whether the occurrences of one or six years of negative returns observed are reasonably possible if the assumptions of your probability model are valid.
CASE 1-4
Treating nominal annual returns as occurrences from a normally distributed population, create a normal distribution model of nominal annual returns using the mean and standard deviation you derived in CASE 1-2.
Using your normal distribution model, find the probability of a negative return in a single year. Compare this the observed proportion of negative returns you found in CASE 1-3. Again, using your normal distribution, find the probability that the nominal annual return will be 10% or greater and compare this to the sample proportion in the data set. Comment on these results in your Word/pdf document.
Assuming nominal returns in one year of a 10-year period are normally distributed and independent of annual nominal returns in other years of the period, derive a distribution on the average nominal annual return over a 10-year period. How likely is it that the average annual return over a 10-year period will be negative? How likely is it that the average annual return over a 10-year period will be 10% or greater?
Display your numerical analysis on the Excel worksheet for CASE 1-4. In your Word/pdf document discussion for this case, include a short statement to a general investor about what they can expect if they invest money in an S&P 500 mutual fund or ETF over 10 years.
Find the sample proportion of the years when nominal annual returns were negative.
Using this sample proportion as the probability of a negative nominal return in any year and assuming the occurrence of a negative nominal return in one year of a 10-year period is independent of occurrences in other years of the 10-year period, derive a theoretical probability distribution on the number of years with negative returns over a 10-year period.
In the data provided, there are 10-year periods with six years of negative returns. Based on your theoretical distribution, what is the probability of having six or more years of negative returns over a 10-year period?
In the data provided there are 10-year periods with only one year of negative returns. Based on your theoretical distribution, what is the probability of having one or fewer years of negative returns over a 10-year period?
In your Word/pdf document, discuss whether the occurrences of one or six years of negative returns observed are reasonably possible if the assumptions of your probability model are valid.
CASE 1-4
Treating nominal annual returns as occurrences from a normally distributed population, create a normal distribution model of nominal annual returns using the mean and standard deviation you derived in CASE 1-2.
Using your normal distribution model, find the probability of a negative return in a single year. Compare this the observed proportion of negative returns you found in CASE 1-3. Again, using your normal distribution, find the probability that the nominal annual return will be 10% or greater and compare this to the sample proportion in the data set. Comment on these results in your Word/pdf document.
Assuming nominal returns in one year of a 10-year period are normally distributed and independent of annual nominal returns in other years of the period, derive a distribution on the average nominal annual return over a 10-year period. How likely is it that the average annual return over a 10-year period will be negative? How likely is it that the average annual return over a 10-year period will be 10% or greater?
Display your numerical analysis on the Excel worksheet for CASE 1-4. In your Word/pdf document discussion for this case, include a short statement to a general investor about what they can expect if they invest money in an S&P 500 mutual fund or ETF over 10 years.