Normal Distribution

Normal Distribution

One theory about the daily changes in the closing price of a stock is that these changes follow arandom walk – that is, these daily events are independent of each other and move upward or downward in a random manner – and can be approximated by a normal distribution. To test this theory, collect the opening and closing prices of stocks from for your favorite company or brand.

Initial Post:

  1. Choose your favorite company or brand and search finance.yahoo.com with that company name and “historical stock prices.” Download the stock history for this company for the past 6 weeks by selecting the appropriate dates and clicking on “Download to Spreadsheet” at the bottom of page.
  2. Calculate the daily change in the closing stock prices by taking the difference between the closing and opening price for the day. This is the daily stock change.
  3. Calculate the mean and standard deviation of the daily stock changes by running the Descriptive Statistics in Excel Data Analysis. Share the summary table.
  4. Consider the mean, median and mode (if it exists). Is your daily stock change distribution right skewed (median < mean), left skewed (mean < median), or symmetric (mean ≈ median)? What other considerations would you look at to determine whether or not this distribution is approximately normally distributed?

See Example post.

First response: Read a classmate’s response. Consider investing in your classmate’s stock and assume that the daily change is normally distributed. Using Normal.xlsx, your classmate’s mean and standard deviation, determine the probability for the daily change of this stock to have:

  1. A decrease of 0.5 point or more (X ≤ -0.5)?
  2. An increase of more than 0.5 point (X > 0.5)?
  3. A decrease of more 1 point or more (X ≤ -1)?
  4. An increase of more than 1 point (X > 1)?

See Example post.

Second Response: Read a different classmate’s response. Consider investing in your classmate’s stock and assume that it is normally distributed. If you wanted to be 95% sure of what the daily change would be, what range for a daily change would you expect? Use Normal.xlsx.

See Example post.