## Dow Jones Averages

price-weighted average

An average computed by adding the prices of the stocks and dividing by a "divisor."

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. So, 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 (excluding any dividends paid) 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.

The Dow measures the return (excluding dividends) on a portfolio that holds one share of each stock, so 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.

Consider the data in Table 2.4 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.

Notice that price-weighted averages give higher-priced shares more weight in determining the 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.

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