## Check

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.

market value-weighted index

Computed by calculating a weighted average of the returns of each security in the index, with weights proportional to outstanding market value.

To illustrate how value-weighted indexes are computed, look again at Table 2.4. The final value of all outstanding stock in our two-stock universe is \$690 million. The initial value was \$600 million. Therefore, if the initial level of a market value-weighted index of stocks ABC and XYZ were set equal to an arbitrarily chosen starting value such as 100, the index value at year-end would be 100 X (690/600) = 115. The increase in the index would reflect the 15% return earned on a portfolio consisting of those two stocks held in proportion to outstanding market values.

Unlike the price-weighted index, the value-weighted index gives more weight to ABC. Whereas the price-weighted index fell because it was dominated by higher-price XYZ, the value-weighted index rose because it gave more weight to ABC, the stock with the higher total market value.

Note also from Tables 2.4 and 2.5 that market value-weighted indexes are unaffected by stock splits. The total market value of the outstanding XYZ stock increases from \$100 million to \$110 million regardless of the stock split, thereby rendering the split irrelevant to the performance of the index.

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.

5. Reconsider companies XYZ and ABC from Concept Check Question 4. Calculate the percentage change in the market value-weighted index. Compare that to the rate of return of a portfolio that holds \$500 of ABC stock for every \$100 of XYZ stock (i.e., an index portfolio).

### 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. Figure 2.10 reproduces a listing of stock index performance that appears daily in The Wall Street Journal. Vanguard offers mutual funds to small investors, which enables them to match the performance of the Wilshire 5000 Index, the S&P 500, or the Russell 2000 index of small firms.

### 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

Concept

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