- Thousands of printable math worksheets for teachers, home schooling or general study!
Math Worksheets

Worksheet News

Math Riff: Why the Dow Jones Industrial Average is Almost Entirely Meaningless

Oooh boy. It’s been a wild week in the stock market. With the Dow Jones Industrial Average (the DJIA or the “Dow”) swinging madly up and down several hundred points at a day, 100 year old companies biting the dust and comparisons to 1929 in the wind, a number of family and friends around here grew a healthy crop of gray hair. So while everyone had the daily change in the Dow right on the tip of their tongue, it turns out almost nobody could actually describe what a change in that number really means.

People associate up moves on the Dow with healthy markets, a strong economy, sunny days, bumper farm crops, and who knows what else. Investors assume the Dow is a reliable market indicator, but in reality, the Dow is poorly constructed, tells little and should never be used as a benchmark. I haven’t used the Dow in decades […]. My advice to you is you will see markets better if you train yourself to ignore the Dow for the rest of your life as well.

- Ken Fisher, #271 on the Forbes 400, from his book "The Only Three Questions That Count"

As you might guess from Ken's opinion, the Dow itself isn’t exactly a straightforward number, and even the components from which the big number is derived don’t match measure value the way people generally expect. To find out what a change in the Dow means in real dollar terms, you need to understand how it is calculated... And that will lead you directly to Ken Fisher's conclusion that the Dow is pretty much useless. In a nutshell, the DJIA is computed by adding up per-share price of a basket of 30 companies and dividing by a special magic number that gets reset periodically. The stocks are picked by the editors of the Wall Street Journal when the need arises, and while these aren’t necessarily the largest traded companies, they tend to come from that select circle. To compute the Dow, we just add up the share prices of the thirty components, then divide by the secret number and out pops the current index value. That all sounds reasonable enough until you realize what a share price actually represents. A share of stock is a deed to a small chunk of ownership in a company, but it doesn’t tell you how much. It’s like saying milk is $2.00 but not saying if you’re buying a pint, a quart or a gallon. It all depends on how much you get for your dollar. In the case of a company like GE, which today has almost 10 billion shares of stock outstanding, buying one share for $25 gets you one ten-billionth of the company. You’re going to have to empty all your piggy banks to get a seat on the board there. With that in mind, it’s pretty clear that share price alone doesn’t tell you much about how much a company is worth. If a stock is $25 and has a thousand shares outstanding, $25 buys you a much bigger chunk than if the stock is $25 and there’s a billion shares outstanding. The share price by itself is meaningless, but the DJIA is constructed entirely based on share price. Whoops. So what does a single tick in the DJIA mean today? Well, here’s the statistics for the 30 companies that made up the Dow on Friday, September 19, 2008: Company Name Symbol Last Sale Market Cap ($ Billions) Shares (Millions) Alcoa Inc. AA $26.79 $21.8 813 American International Group Inc. AIG $3.85 $10.4 2,688 American Express Co. AXP $40.40 $46.8 1,159 Boeing Co. BA $59.76 $44.2 740 Bank of America Corp. BAC $37.48 $170.9 4,560 Citigroup Inc. C $20.65 $112.5 5,446 Caterpillar Inc. CAT $66.49 $40.5 609 Chevron Corp. CVX $87.80 $180.4 2,054 E.I. DuPont de Nemours & Co. DD $48.04 $43.3 902 Walt Disney Co. DIS $34.39 $64.5 1,876 General Electric Co. GE $26.62 $264.5 9,937 General Motors Corp. GM $13.08 $7.4 567 Home Depot Inc. HD $27.37 $46.5 1,699 Hewlett-Packard Co. HPQ $48.26 $118.2 2,449 International Business Machines IBM $118.85 $161.0 1,355 Intel Corp. INTC $19.23 $108.1 5,622 Johnson & Johnson JNJ $69.99 $195.6 2,795 JPMorgan Chase & Co. JPM $47.05 $161.7 3,437 Coca-Cola Co. KO $52.72 $121.9 2,311 McDonald's Corp. MCD $63.98 $72.0 1,125 3M Co. MMM $72.68 $50.8 699 Merck & Co. Inc. MRK $31.84 $68.2 2,143 Microsoft Corp. MSFT $25.16 $229.7 9,130 Pfizer Inc. PFE $18.55 $125.1 6,741 Procter & Gamble Co. PG $70.36 $213.5 3,034 AT&T Inc. T $30.43 $179.3 5,893 United Technologies Corp. UTX $64.30 $62.0 964 Verizon Communications Inc. VZ $33.30 $94.8 2,848 Wal-Mart Stores Inc. WMT $59.70 $234.9 3,934 Exxon Mobil Corp. XOM $79.61 $413.5 5,194 Totals $1,398.73 $3,664.0 92,725 The Dow is computed by adding up all the share prices and dividing by the magic number (the DJIA divisor) computed by Dow Jones, which today is 0.12282011. Combined with $1,398.73 from the chart above this gives us the Dow’s close at 11,388.44. The divisor gets recomputed periodically, like whenever there’s a stock split or change in a component stock. The divisor is useful if you want to see exactly how much a change in a particular stock contributed to movement in the Dow. If you need it, you can get the divisor from the Dow Jones web site, but it requires navigating to a fairly obscure location and downloading a daily report... I did it, but if you are playing with the Dow components anyway it's easier to just sum the share prices and divide by the current index to compute it. What you’ll notice about these stocks is that they’re all monsters with billions of dollars in market capitalization, and hundreds-of-millions of outstanding shares. It’s really only because these stocks happen to be roughly of equivalent size that the DJIA actually means anything, but even there you’ll see enormous variations. The smallest and largest Dow components, GM and GE, are right next to each other on today’s graph. In terms of market capitalization, there is an almost 37x difference between the two companies. However, GM’s stock is half the price of GE’s… Right there is an immediate example of why stock price alone doesn’t tell you anything. In terms of the DJIA, because the index is based on stock prices, a $1 change in GE’s stock price is going to have exactly the same effect as a $1 change in GM’s stock. However, because GE has vastly more shares of stock outstanding, a $1 change in GM’s stock means a lot more to the economy and the world at large. A $1 change in GE translates into $10 billion worth of something happening in the world. A $1 change in GM is only about $500 million dollars, or 20 times less. The Dow doesn’t care. Another way to look at it is to look at the largest and smallest share prices. IBM is the current leader at almost $119 per share, and AIG is on the other end of the scale with just under $4 per share. You can see that a $1 change in IBM amounts to a less than 1% change, whereas a $1 change in AIG would be a 25% increase. This is illustrative more than anything… If you’ve been tuned into CNBC at all this week, you know AIG is basically gone and will be removed from the Dow on Monday (being replace by Kraft Foods, and triggering a new divisor), but the point remains apt. This means a big swing in the Dow doesn’t tell you much of anything unless you look at what stocks accounted for the change and why. Or, if you’re lazy like me, you might consider the averages. The average Dow component’s market capitalization is $122 billion, and the average number of shares outstanding is 3 billion. In other words, each $1 change in value of an average Dow stock translates into $3 billion in equity ($1 x 3 billion shares) out in the wild either being created or destroyed. Using our current Dow divisor, 0.12282011, that $1 change translates into about 8 points in the DJIA number. Or, conversely, $3 billion x 0.1222720 equals approximately $368 million dollars. So in other words, every time the Dow moves up or down by one point, it corresponds to about $368 million dollars of business value being created or destroyed. In the context of last week’s roller coaster ride, that amounts to some pretty big numbers… Date Previous Close Close Change Value ($ Billion) 9/19/2008 11019.69 11388.44 368.75 $136 9/18/2008 10609.66 11019.69 410.03 $151 9/17/2008 11059.02 10609.66 -449.36 -$165 9/16/2008 10917.51 11059.02 141.51 $52 9/15/2008 11421.99 10917.51 -504.48 -$186 Swinging $150 billion around is scary, but also keep in mind the Dow components have a combined market capitalization of $3.6 trillion dollars, and the total market capitalization of public companies around the world is over $50 trillion. Given the shaky way the Dow is constructed, big swings in the Dow don’t necessarily translate into big changes in the whole universe of stocks. There's room in IBM's stock price alone to create the kind of Dow swings we saw last week, and with the Dow loaded up with financial stocks (AIG, BAC, C, JPM and the finance division in GE), the real story is how the Dow came out just about even for the week even after AIG imploded. Don’t sweat the Dow. Pay attention to market cap weighted indexes like the NASDAQ or the S&P (or, if you think Ken’s done okay, the MSCI World). They’re actually useful. But, still Ken... I’ll take that 778.78 point gain from the last two days even if it is completely meaningless.