Obtain the daily unadjusted closing prices of each of the 30 stocks in the Dow Jones Industrial Average for the year 2017. There were no stock splits during that period. (There is a text file linked on the website for the book that lists the stock symbols for the stocks in the DJIA during that period. As time goes on, some of these symbols may become invalid. In that case, the exercise can be modified in one of two ways, either of which will preserve the intent of the exercise. One way, is just to change the year 2017 to the most recent full year. In that case, the list of companies may not be the same. The other way is just to remove the invalid stock symbols the list, and to use fewer than 30 stocks.)

(a) Determine the first principal component of these 30 variables.

(b) Now compute the correlation between the daily closes of the first principal component and the daily closes of the DJIA for 2017.

(c) Form a market index based on the first principal component of the Dow 30 stocks as a market index. Normalize your index so that it was 100 on the first trading day of 2017 . Plot the daily closes of your index and of the DJIA for the two years 2017 and 2018 , on a single graph with the indexes normalized so as to have the same value on the first trading day of 2017.

(d) From a practical standpoint, why might a market index based on a principal component of the prices of a set of stocks not be desirable?