One of the first measures of stock prices was the average developed by Charles Dow.1 Initially, the average consisted of the stock from only 11 companies, but it was later expanded to include more firms. Today, this average is called the Dow Jones Indus- trial Average (ticker symbol: ^DJI) and it is probably the best known and most widely quoted average of stock prices.
The Dow Jones Industrial Average is a simple price-weighted average. Initially, it was computed by summing the price of the stocks of 30 companies and then dividing by 30. Over time, the divisor has been changed so that substitutions of one firm for another (e.g., replacing GM and Citigroup with Travelers and Cisco Systems in 2009) or a stock split has no impact on the average. If the computation were simply the sum of the current prices of 30 divided by 30, the substitution of one stock for another or a stock split would affect the average.
To see the possible impact of substituting one stock for another, consider an aver- age that is computed using three stocks (A, B, and C) whose prices are $12, $35, and
$67, respectively. The average price is $38. For some reason, the composition of the average is changed. Stock B is dropped and replaced by stock D, whose price is $80.
The average price is now $53 [($12 1 67 1 80)/30]. The substitution of D for B has caused the average to increase even though there has been no change in stock prices. To avoid this problem, the divisor is changed from 3 to the number that does not change the average. To find the divisor, set up the following equation:
1$121671802
X 5$38.
1In 1882 Edward Jones joined Charles Dow to form a partnership that grew into Dow, Jones and Company. Information on the Dow Jones averages may be found at www.djindexes.com.
Solving for X gives a divisor of 4.1842. When the prices of stocks A, C, and D are summed and divided by 4.1842, the average price is
1$121671802
4.1842 5$38,
so the average price has not been altered by the substitution of stock D for B.
A similar situation occurs when one of the stocks is split. (Stock splits and their im- pact on the price of a share were covered in Chapter 8.) Suppose stock D is split 2 for 1 so its price becomes $40 instead of $80 (two new shares at $40 5 one old share at $80).
The investor’s wealth has not changed; the individual continues to hold stock worth a total of $159 ($12 1 67 1 40 1 40). The price average, however, becomes ($12 1 67 1 40)/4.1842 5 $28.44 instead of $38. According to the average, the stock is worth less.
The average has been affected by something other than a price movement—in this case, the stock split. Once again, this problem is solved by changing the divisor so that the average price remains $38. To find the divisor, set up the following equation:
1$121671402
X 5$38.
Solving for X gives a divisor of 3.1316. When the individual prices of stocks A, C, and D are summed and divided by 3.1316, the average price is
1$121671402
3.1316 5$38, so the average price has not been altered by the stock split.
While the Dow Jones Industrial Average is adjusted for stock splits, stock dividends in excess of 10 percent, and the substitution of one firm for another, no adjustment is made for the distribution of cash dividends. Hence, the average declines when stocks like ExxonMobil go ex-div (pay a dividend) and their prices decline. (The reason for a stock’s price to decline when the firm pays a dividend was explained in Chapter 8.)
The failure to include dividend payments means that the annual percentage change in the Dow Jones Industrial Average understates the true return. This failure to include the dividend can have an amazing impact when compounding is considered. Suppose the average rises 8 percent annually when dividends are excluded but the return is 10 percent when dividends are included and reinvested. (The dividend yield on the Dow Jones Industrial Average was 2.85 percent as of January 2012.) Over 20 years, $1,000 grows to $4,661 at 8 percent but to $6,728 at 10 percent. If the time period is extended to 50 years, these values become $46,902 and $117,391, respectively.2
This understatement of the true annual return is, of course, true for all stock indexes that do not add back the dividend payment. The bias is greater for those indexes that cover
2One study found that from its inception through December 31, 1998, the Dow Jones Industrial Average grew from 40.94 to 9,181.43, for a 5.42 percent annual growth rate. However, if dividends had been reinvested, the Dow Jones would have been 652,230.87, for an annual growth rate of 9.89 percent. See Roger G. Clarke and Meir Statman, “The DJIA Crossed 652,230,” Journal of Portfolio Management (winter 2000): 89–93.
the largest companies, since they tend to pay dividends. Although some small cap stocks do distribute dividends, they tend to pay out a smaller proportion of their earnings, and the dividend constitutes a small, perhaps even trivial, part of the total return.
The Dow Jones Industrial Average for the period from 1950 through 2011 is pre- sented in Figure 10.1, which plots the high and low values of the average for each year.
During the 1970s, the Dow Jones Industrial Average (and the stock market) certainly did not experience steady growth. (In 1970 and in 1974 the Dow Jones Industrial
fIGuRE 10.1
Annual Price Range of the Dow Jones Industrial Average, 195022011
1980 1975 1970 1965 1960 1955 1950
Year 9,000
8,000 7,000 12,000 11,000 10,000 13,000 15,000 14,000
6,000 5,000 4,000 3,000 2,000 1,000
0 1985 1990 1995 2000 2005 2010 2015
Source: http://stockcharts.com/freecharts/historical/djia1900.html.
Average even fell below the high achieved in 1959.) The period from 1985 through 1999, however, showed a different pattern, as stock prices soared and the Dow Jones Industrial Average rose to 11,497 at the end of 1999. This continual growth came to a crashing end in 2000, when the average declined 6.2 percent and continued to de- cline through 2002. Even in 2005, the Dow Jones Industrial Average traded 15 percent below the 1999 closing.
The Dow’s performance in 2008 was even worse! After reaching a high in excess of 14,200 in 2007, the Dow collapsed in 2008. The low for 2008 barely exceeded the low for 2002 and was less than the high achieved in 1997. This performance by the Dow stocks suggests that many investors were worse off in 2008 than they were in 1997. If an investor purchased the components of the Dow during 1997, the value of the stocks would be less in 2008 than their cost in 1997!
During 2009, the Dow continued to decline and fell to 6,440 in March, for an additional decline of 26 percent in less than three months. From this nadir, the Dow rebounded, reached a high of 10,606, and ended the year at 10,494. While the Dow recouped the losses experienced during late 2008 through March 2009, it remained well below the 14,200 high achieved during 2007. To regain that level, the Dow would have had to rebound over 100 percent. (Once again, comparing negative and positive percentage changes is misleading. A decline from 14,200 to 6,440 is a 55 percent loss but would require a gain of 120 percent to recoup the loss.)
There may be an interesting parallel between the recent performance of the stock market and its performance during the 1970s. In 1972 the Dow Jones Industrial Av- erage broke 1,000, and it reached 1,052 in 1973. Then it fell to 578 in 1974 for a 45 percent decline and did not pass its previous high until 1982. In 2007, the Dow rose to 14,280 and then fell, bottoming out in March 2009 at 6,440, a decline in excess of 55 percent. If history repeats itself, the Dow will not pass its previous high until 2017!
Graphical Illustrations
While a picture may be worth 1,000 words, pictures can be misleading. So, before pro- ceeding to the discussion of other indexes of stock prices, it is desirable to consider the composition of graphs (i.e., the pictures) used to illustrate indexes of stock prices. The choice of the scale affects the graph. This choice can influence the reader’s perception of the index and, hence, the performance of the stock market.
This impact may be illustrated by the following monthly range of stock prices and percentage increases:
Month Price of Stock
Percentage Change in Monthly Highs
January $5210 —
February 10215 50
March 15220 33
April 20225 25
Even though the monthly price increases are equal ($5), the percentage increments de- cline. The investor who bought the stock at $10 and sold it for $15 made $5 and earned
a return of 50 percent. The investor who bought it at $20 and sold for $25 also made
$5, but the return was only 25 percent.
These monthly prices may be plotted on graph paper that uses absolute dollar units for the vertical axis. This is done on the left-hand side of Figure 10.2. Such a graph gives the appearance that equal price movements yield equal percentage changes. However, this is not so, as the preceding illustration demonstrates.
To avoid this problem, a different scale can be used, as illustrated in the right-hand side of Figure 10.2. Here, equal units on the vertical axis represent percentage change.
Thus, a price movement from $10 to $15 appears to be greater than one from $20 to
$25, because in percentage terms it is greater.
The impact of using the percentage scale may be seen by comparing Figures 10.1 and 10.3. Both present the annual price range of the Dow Jones Industrial Average, but Figure 10.1 uses an absolute scale while Figure 10.3 expresses prices in relative terms. The general shape is the same in both cases, but the large absolute increase in the Dow Jones Industrial Average during the late 1990s is considerably less impressive in Figure 10.3.
Because absolute price changes are reduced to relative price changes, graphs like Figure 10.3 are better indicators of securities price movements and the returns investors earn.