## Dow Jones Averages

The Dow Jones Industrial Average (DJIA) of 30 large, "blue-chip" corporations has been computed since 1896. Its long history probably accounts for its preeminence in the public mind. (The average covered only 20 stocks until 1928.)

Originally, the DJIA was calculated as the simple average of the stocks included in the index. Thus, if there were 30 stocks in the index, one would add up the value of the 30 stocks and divide by 30. The percentage change in the DJIA would then be the percentage change in the average price of the 30 shares.

This procedure means that the percentage change in the DJIA measures the return on a portfolio that invests one share in each of the 30 stocks in the index. The value of such a portfolio (holding one share of each stock in the index) is the sum of the 30 prices. Because the percentage change in the average of the 30 prices is the same as the percentage change in the sum of the 30 prices, the index and the portfolio have the same percentage change each day.

To illustrate, consider the data in Table 2.3 for a hypothetical two-stock version of the Dow Jones Average. Stock ABC sells initially at \$25 a share, while XYZ sells for \$100. Therefore, the initial value of the index would be (25 + 100)/2 = 62.5. The final share prices are \$30 for stock ABC and \$90 for XYZ, so the average falls by 2.5 to (30 + 90)/2 = 60. The 2.5 point drop in the index is a 4% decrease: 2.5/62.5 = .04. Similarly, a portfolio holding one share of each stock would have an initial value of \$25 + \$100 = \$125 and a final value of \$30 + \$90 = \$120, for an identical 4% decrease.

Because the Dow measures the return on a portfolio that holds one share of each stock, it is called a price-weighted average. The amount of money invested in each company represented in the portfolio is proportional to that company's share price.

Price-weighted averages give higher-priced shares more weight in determining performance of the index. For example, although ABC increased by 20%, while XYZ fell by only 10%, the index dropped in value. This is because the 20% increase in ABC represented a smaller price gain (\$5 per share) than the 10% decrease in XYZ (\$10 per share). The "Dow portfolio" has four times as much invested in XYZ as in ABC because XYZ's price is four times that of ABC. Therefore, XYZ dominates the average.

You might wonder why the DJIA is now (in early 2001) at a level of about 10,000 if it is supposed to be the average price of the 30 stocks in the index. The DJIA no longer equals the average price of the 30 stocks because the averaging procedure is adjusted whenever a stock splits or pays a stock dividend of more than 10%, or when one company in the group of 30 industrial firms is replaced by another. When these events occur, the divisor used to compute the "average price" is adjusted so as to leave the index unaffected by the event.

 DOW JONES INDUSTRIAL AVERAGE: : CHANGES SINCE OCTOBER 1, 1928
 Oct. 1, 1928 1929 1930s 1940s 1950s 1960s 1970s 1980s 1990s Nov. 1, 1999 Wright Aeronautical Curtiss-Wright (29) Hudson Motor ('30) Coca-Cola (32) National Steel ('35) Aluminum Co. of America (59) Alcoa* ('99) Allied Chemical & Dye Allied Signal* ('85) Allied Signal North American Johns-Manville (30) Amer. Express (82) American Express Victor Talking Machine Natl Cash Register ('29) IBM (32) AT&T ('39) AT&T International Nickel Inco Ltd.* ('76) Boeing ('87) Boeing International Harvester Navistar* (86) Caterpillar ('91) Caterpillar Westinghouse Electric Travelers Group (97) Citigroup* (98) Texas Gulf Sulphur Intl. Shoe ('32) United Aircraft ('33) National Distillers ('34) Owens-Illinois ('59) Coca-Cola ('87) Coca-Cola American Sugar Borden ('30) DuPont ('35) DuPont American Tobacco (B) Eastman Kodak (30) Eastman Kodak Standard Oil (N.J.) Exxon* ('72) Exxon General Electric General Electric General Motors General Motors Texas Corp. Texaco* ('59) Hewlett-Packard (97) H^lett-Packard Sears Roebuck Home Depott Chrysler IBM (79) IBM Atlantic Refining Goodyear ('30) Intelt Paramount Publix Loew's (32) Intl. Paper (56) International Paper Bethlehem Steel Johnson & Johnson ('97) Johnson & Johnson General Railway Signal Liggett & Myers ('30) Amer. Tobacco ('32) McDonald's (85) McDonald's Mack Trucks Drug Inc. ('32) Corn Products (33) Swift & Co. ('59) Esmark* ('73) Merck (79) Merck Union Carbide Microsoftt American Smelting Anaconda ('59) Minn. Mining ('76) Minn. Mining (3M) American Can Primerica* ('87) J.P. Morgan ('91) J.P. Morgan Postum Inc. General Foods* ('29) Philip Morris (85) Philip Morris Nash Motors United Air Trans. ('30) Procter & Gamble (32) Procter & Gamble Goodrich Standard Oil (Calif) (30) Chevron* ('84) SBC Communicationst Radio Corp. Nash Motors ('32) United Aircraft ('39) United Tech.* (75) United Technologies Woolworth Wal-Mart Stores (97) Wal-Mart Stores U.S. Steel USX Corp.* (86) Walt Disney (91) Walt Disney

Note: Year of change shown in (); * denotes name change, in some cases following a takeover or merger; t denotes new entry as of Nov. 1, 1999. To track changes in the components, begin in the column for 1928 and work across. For instance, American Sugar was replaced by Borden in 1930, which in turn was replaced by Du Pont in 1935. Unlike past changes, each of the four new stocks being added doesn't specifically replace any of the departing stocks; it's simply a four-for-four switch. Home

Depot has been grouped as replacing Sears because of their shared industry, but the other three incoming stocks are designated alphabetically next to a departing stock.

Source: From The Wall Street Journal, October 27, 1999. Reprinted by permission of Dow Jones & Company, Inc. via Copyright Clearance Center, Inc. © 1999. Dow Jones & Company, Inc. All Rights Reserved Worldwide.

 Initial Value of Final Value of Initial Final Shares Outstanding Stock Outstanding Stock Stock Price Price (Million) (\$ Million) (\$ Million) ABC \$ 25 \$30 20 \$500 \$600 XYZ 50 45 2 100 90 TOTAL \$600 \$690

For example, if XYZ were to split two for one and its share price to fall to \$50, we would not want the average to fall, as that would incorrectly indicate a fall in the general level of market prices. Following a split, the divisor must be reduced to a value that leaves the average unaffected by the split. Table 2.4 illustrates this point. The initial share price of XYZ, which was \$100 in Table 2.3, falls to \$50 if the stock splits at the beginning of the period. Notice that the number of shares outstanding doubles, leaving the market value of the total shares unaffected. The divisor, d, which originally was 2.0 when the two-stock average was initiated, must be reset to a value that leaves the "average" unchanged. Because the sum of the postsplit stock prices is 75, while the presplit average price was 62.5, we calculate the new value of d by solving 75/d = 62.5. The value of d, therefore, falls from its original value of 2.0 to 75/62.5 = 1.20, and the initial value of the average is unaffected by the split: 75/1.20 = 62.5.

At period-end, ABC will sell for \$30, while XYZ will sell for \$45, representing the same negative 10% return it was assumed to earn in Table 2.3. The new value of the price-weighted average is (30 + 45)/1.20 = 62.5. The index is unchanged, so the rate of return is zero, rather than the -4% return that would be calculated in the absence of a split.

This return is greater than that calculated in the absence of a split. The relative weight of XYZ, which is the poorer-performing stock, is reduced by a split because its initial price is lower; hence the performance of the average is higher. This example illustrates that the implicit weighting scheme of a price-weighted average is somewhat arbitrary, being determined by the prices rather than by the outstanding market values (price per share times number of shares) of the shares in the average.

Because the Dow Jones Averages are based on small numbers of firms, care must be taken to ensure that they are representative of the broad market. As a result, the composition of the average is changed every so often to reflect changes in the economy. The last change took place on November 1, 1999, when Microsoft, Intel, Home Depot, and SBC Communications were added to the index and Chevron, Goodyear Tire & Rubber, Sears Roebuck, and Union Carbide were dropped. The nearby box presents the history of the firms in the index since 1928. The fate of many companies once considered "the bluest of the blue chips" is striking evidence of the changes in the U.S. economy in the last 70 years.

In the same way that the divisor is updated for stock splits, if one firm is dropped from the average and another firm with a different price is added, the divisor has to be updated to leave the average unchanged by the substitution. By now, the divisor for the Dow Jones Industrial Average has fallen to a value of about .1706.

CONCEPT CHECK ^ QUESTION 5

Suppose XYZ in Table 2.3 increases in price to \$110, while ABC falls to \$20. Find the percentage change in the price-weighted average of these two stocks. Compare that to the percentage return of a portfolio that holds one share in each company.

Dow Jones & Company also computes a Transportation Average of 20 airline, trucking, and railroad stocks; a Public Utility Average of 15 electric and natural gas utilities; and a Composite Average combining the 65 firms of the three separate averages. Each is a price-weighted average, and thus overweights the performance of high-priced stocks.

CHAPTER 2 Markets and Instruments 51

THE DOW JONES AVERAGES

Figure 2.11 The Dow Jones Industrial

Source: The Wall Street Journal, August 1, 2000. Reprinted by permission of The Wall Street Journal, © 2000 Dow Jones & Company, Inc. All Rights Reserved Worldwide.

Figure 2.11 reproduces some of the data reported on the Dow Jones Averages from The Wall Street Journal (which is owned by Dow Jones & Company). The bars show the range of values assumed by the average on each day. The crosshatch indicates the closing value of the average.

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