Stock Market Indices and Statistical Analysis

The Dow Jones Industrial Average

The monthly closing values of the Dow Jones Industrial Average (DJIA) for the period beginning in January 1950 are given in the Excel _le tab named Dow. According to Wikipedia, the Dow Jones Industrial Average, also referred to as the Industrial Average, the Dow Jones, the Dow 30, or simply the Dow, is one of several stock market indices created by Charles Dow. The average is named after Dow and one of his business associates, statistician Edward Jones. It is an index that shows how 30 large, publicly owned companies based in the U.S. have traded during a standard trading session in the stock market. It is the second oldest U.S. market index after the Dow Jones Transportation Average, which Dow also created.

The Industrial portion of the name is largely historical, as many of the modern 30 components have little or nothing to do with traditional heavy industry. The average is price-weighted, and to compensate for the effects of stock splits and other adjustments, it is currently a scaled average. The value of the Dow is not the actual average of the prices of its component stocks, but rather the sum of the component prices divided by a divisor, which changes whenever one of the component stocks has a stock split or stock dividend, so as to generate a consistent value for the index.

Along with the NASDAQ Composite, the S&P 500 Index, and the Russell 2000 Index, the Dow is among the most closely watched benchmark indices for tracking stock market activity. Although Dow compiled the index to gauge the performance of the industrial sector within the U.S. economy, the index's performance continues to be influenced not only by corporate and economic reports, but also by domestic and foreign political events such as war and terrorism, as well as by natural disasters that could potentially lead to economic harm.

a) Plot a time-series chart of closing values. What kind of trend do you observe? You will notice a few dips in the trend. Try to identify what those two dips corresponded to. You might have to research on the internet as to which macroeconomic events occurred during those times. Identifying dips carries no credit, which means that I just want you to try. If you are wrong, no worries. No points will be deducted. But your time-series chart should be correct.

b) Find the geometric mean rate of return over the entire period from January 1950 through October 2021.

c) Create a histogram of returns. Comment on the shape of the histogram.

In 2011 there were 232.2 million cell phone subscribers in the United States. By 2017 the number of subscribers increased to 265.9 million. What is the geometric mean annual percent increase for the period? Further, the number of subscribers is forecast to increase to 276.7 million by 2020. What is the rate of increase from 2017 to 2020? What can you say about the rate of increase?

Listed in the Excel _le Waiting Times are the fifty wait times (minutes) at 10 AM for the rides. “It's a Small World" and “Avatar Flight of Passage" at one of the theme parks in the Disney World. Do the two rides appear to have different amounts of variation? Compare using both standard deviation and the coefficient of variation. Which ride's waiting times have lower relative variation?

Citibank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. The data are available on the Excel file ATM. Verify using the Empirical Rule like we did in the class to check if the number of customers is normally distributed (bell shaped). Please note that the percentages don't have to exactly match the Empirical Rule percentages. It is very rare for the percentages to exactly match the percentages from the Empirical Rule. Just use rough approximations. Create a histogram to see if the data looks approximately bell-shaped.