Stock Market Indexes
The daily performance of the Dow Jones Industrial Average is a staple portion of the evening news report. While the Dow is the best-known measure of the performance of the stock market, it is only one of several indicators. Other more broadly based indexes are computed and published daily. In addition, several indexes of bond market performance are widely available.

The ever-increasing role of international trade and investments has made indexes of foreign financial markets part of the general news. Thus, foreign stock exchange indexes such as the Nikkei Average of Tokyo and the Financial Times index of London have become household names.

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. 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. You might wonder why the DJIA is now (in mid-2002) at a level of about 8,500 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, 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 the average unchanged by the substitution. By now, the divisor for the Dow Jones Industrial Average has fallen to a value of about .145.

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.

Standard & Poor’s Indexes
The Standard & Poor’s Composite 500 (S&P 500) stock index represents an improvement over the Dow Jones averages in two ways. First, it is a more broadly based index of 500 firms. Second, it is a market value-weighted index. In the case of the firms XYZ and ABC in Example 2.2, the S&P 500 would give ABC five times the weight given to XYZ because the market value of its outstanding equity is five times larger, $500 million versus $100 million.

The S&P 500 is computed by calculating the total market value of the 500 firms in the index and the total market value of those firms on the previous day of trading. The percentage increase in the total market value from one day to the next represents the increase in the index. The rate of return of the index equals the rate of return that would be earned by an investor holding a portfolio of all 500 firms in the index in proportion to their market value, except that the index does not reflect cash dividends paid by those firms.

A nice feature of both market value-weighted and price-weighted indexes is that they reflect the returns to straightforward portfolio strategies. If one were to buy each share in the index in proportion to its outstanding market value, the value-weighted index would perfectly track capital gains on the underlying portfolio. Similarly, a price-weighted index tracks the returns on a portfolio comprised of equal shares of each firm.

Investors today can purchase shares in mutual funds that hold shares in proportion to their representation in the S&P 500 as well as other stock indexes. These index funds yield a return equal to that of the particular index and so provide a low-cost passive investment strategy for equity investors. Standard & Poor’s also publishes a 400-stock Industrial Index, a 20-stock Transportation Index, a 40-stock Utility Index, and a 40-stock Financial Index.

Other U.S. Market Value Indexes
The New York Stock Exchange publishes a market value-weighted composite index of all NYSE-listed stocks, in addition to subindexes for industrial, utility, transportation, and financial stocks. These indexes are even more broadly based than the S&P 500. The National Association of Securities Dealers publishes an index of 4,000 over-the-counter firms using the National Association of Securities Dealers Automatic Quotations (Nasdaq) service.

The ultimate U.S. equity index so far computed is the Wilshire 5000 Index of the market value of all NYSE and American Stock Exchange (Amex) stocks plus actively traded Nasdaq stocks. Despite its name, the index actually includes about 7,000 stocks.

Equally Weighted Indexes
Market performance is sometimes measured by an equally weighted average of the returns of each stock in an index. Such an averaging technique, by placing equal weight on each return, corresponds to a portfolio strategy that places equal dollar values in each stock. This is in contrast to both price weighting, which requires equal numbers of shares of each stock, and market value weighting, which requires investments in proportion to outstanding value.

Unlike price- or market value-weighted indexes, equally weighted indexes do not correspond to buy-and-hold portfolio strategies. Suppose you start with equal dollar investments in the two stocks of Table 2.4, ABC and XYZ. Because ABC increases in value by 20% over the year, while XYZ decreases by 10%, your portfolio is no longer equally weighted but is now more heavily invested in ABC. To reset the portfolio to equal weights, you would need to rebalance:
Either sell some ABC stock and/or purchase more XYZ stock. Such rebalancing would be necessary to align the return on your portfolio with that on the equally weighted index.

Foreign and International Stock Market Indexes
Development in financial markets worldwide includes the construction of indexes for these markets. The most important are the Nikkei, FTSE (pronounced “footsie”), and DAX. The Nikkei 225 is a price-weighted average of the largest Tokyo Stock Exchange (TSE) stocks. The Nikkei 300 is a value-weighted index. FTSE is published by the Financial Times of London and is a value-weighted index of 100 of the largest London Stock Exchange corporations. The DAX index is the premier German stock index.
More recently, market value-weighted indexes of other non-U.S. stock markets have proliferated. A leader in this field has been MSCI (Morgan Stanley Capital International), which computes over 50 country indexes and several regional indexes.

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