Price Weighted Average
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.
Notice that 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 mid 2003) at a level of about 9,000 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.