## Info

\$600

\$690

splits, 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.

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 2.5 illustrates this point. The initial share price of XYZ, which was \$100 in Table 2.4, 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 2.4. 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, greater than the -4% return that would be 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 price is lower; so 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 75 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

Bodie-Kane-Marcus: Essentials of Investments, Fifth Edition

I. Elements of Investments

2. Global Financial Instruments