Tracking Error in the Dow Jones Industrial Average versus Alternative Market Indices: New Evidence

Article excerpt

Introduction

The Dow Jones Industrial Average (DJIA) is the most widely followed stock market index in the United States. Many people intuitively use the DJIA as an indicator for performance in the broad market. But does the DJIA track the market accurately?

The editors of The Wall Street Journal construct the DJIA by selecting a subset of 30 stocks to represent the entire U.S. stock market and then computing a price-weighted index of the subset. This approach to measuring the market has four potential flaws. First, a price-weighted index reflects changes in stock prices but not changes in market capitalization. In particular, each time a component stock splits, its weight in the DJIA decreases. A value-weighted (i.e., capitalization-weighted) index would overcome this potential weakness. (1) Second, the DJIA may include too few stocks to adequately represent the U.S. stock market. Over 8,000 common stocks actively trade in the U.S. today. The 30 stocks in the DJIA may be too small a sample. Third, the editors of The Wall Street Journal follow an informal and subjective approach to select the Dow Jones Industrials that may not yield the most representative sample. Finally, changes in the DJIA do not reflect the contribution that cash dividends make to total return.

The S&P 500 index addresses the first three potential flaws in the DJIA. The S&P 500 is a value-weighted index of 500 common stocks traded on U.S. markets and includes the 30 Dow Jones Industrials. In addition, the S&P 500 stocks currently make up roughly 80 percent of the total market capitalization in U.S. markets, while the Dow Jones Industrials account for about 27 percent as of the end of 1999. Thus, the specific details of the selection criteria applied by Standard & Poor are unlikely to have a significant effect on how well the index represents the market. For these reasons, we use the S&P 500 in our paper as a proxy for the U.S. stock market.

Recent studies show that the DJIA performs similarly to value-weighted indexes over the long run. Shoven and Sialm (2000) find that the DJIA is similar to a value-weighted version of the index as well as the S&P 500 over the period October 1928--December 1999. Both Shoven and Sialm (2000) and Clarke and Statman (2000) show that the chief flaw in the DJIA over the long run is that the index measures only capital appreciation, not total returns. (The DJIA shares this weakness with other widely reported indexes, e.g., the S&P 500, the Russell 3000, and the Wilshire 5000.)

We take a different approach. Our objective is to determine whether changes in the DJIA adequately track concurrent changes in the U.S. stock market. In other words, if the DJIA goes up or down one percent in a given time period, what does this tell us about change in the stock market for the same period? Do the returns of the DJIA and value-weighted market indices correlate? Do the returns distributions have similar variances and symmetry? Does the DJIA accurately track change in alternative value-weighted market portfolios? Is the DJIA an accurate measure of market performance?

Earlier studies report that the DJIA is an unbiased predictor of change in capitalization of value-weighted portfolios of the DJI and S&P 500. In this paper, we observe that the Dow's tracking error, as a measure of market performance, is both significant and systematic. We find the DJIA exhibits a systematic tendency to overstate and understate changes in market capitalization versus DJI and S&P value-weighted portfolios. When the market declines, the DJIA is more likely than not to exhibit a greater percentage decline; when the market rises, the DJIA is more likely than not to exhibit a greater percentage rise. We also find that the magnitude of the corresponding change in value-weighted portfolios may differ from change in the DJIA as much as two to three percentage points. For example, if the DJIA decreases one percent, then capitalization of the market might actually have decreased as much as three or four percent (or--somewhat less likely--increased as much as one or two percent). …