How did the Dow do today? Received (in revised form): 26th April, 2003
Paul J. Haensly is Associate Professor and Coordinator of Finance at The University of Texas of the Permian Basin, where he teaches undergraduate and graduate courses in investments, capital markets and international finance. Dr Haensly earned his PhD in finance from the University of North Texas and his Masters in mathematics from The University of Texas at Austin in the USA. Prior to attending graduate school in finance, he was a systems analyst for Dynetics, Inc., an engineering research firm in Huntsville, AL, USA. School of Business, The University of Texas of the Permian Basin, 4901 E. University Blvd, Odessa, TX 79762, USA. Tel: ⫹1 432 552 2198; Fax: ⫹1 432 552 2174; e-mail:
[email protected]
Abstract Daily change in the Dow Jones Industrial Average (DJIA) is a biased and imprecise measure of actual change in the US stock market, whether measured as capital appreciation or total return, despite high correlations with other market indexes. Because it omits cash dividends, the Dow underestimates daily market total return. This paper shows, however, that the index also understates daily market capital appreciation because it is less diversified than the market. Specifically, the Dow is a large-cap index, so it underperforms the US market over the long run owing to the small-stock risk premium. The DJIA overstates daily volatility primarily because the index is less diversified than the market and thus has a significant diversifiable component to its risk. Furthermore, large daily volatility makes the DJIA a poor tool for drawing inferences about actual daily change in either US or international stock markets. Given an observed daily change in the Dow, confidence intervals for the market return can be constructed, but these intervals may prove too wide to provide much information. Keywords: stock market indexes, Dow Jones Industrial Average, statistical estimation
Introduction The Dow Jones Industrial Average (DJIA or ‘Dow’) is the most widely followed stock market index in the USA. Most practitioners may accept that the Dow is not a good measure of market performance, but CNN is ‘always on’. So it is tempting to use the Dow’s daily change as an informal guide to how the market is doing. Editors of the Wall Street Journal argue that, while other market indexes include many more stocks than the 30 in the Dow, ‘experience indicates that over time the various popular indexes
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generally move together’ (Dow Jones, 2001). Shoven and Sialm (2000) find that correlation of monthly change in the DJIA and broad US market indexes is high over the years 1928–99. Further, they test the hypothesis that the mean returns of the DJIA and the capital appreciation of a total US stock market index are the same and show that the hypothesis cannot be rejected at any conventional level of significance. The primary purpose of this paper is to explain why the Dow is not a good measure of market performance despite the high correlation with other US stock
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market indexes. The DJIA is a biased and imprecise measure of daily change in the US stock market whether this change is measured as capital appreciation or total return. The DJIA understates daily market return and overstates daily market volatility. So practitioners should avoid using the Dow as a guide — even an informal one — to the daily performance of the US market. This paper also provides practitioners with information that may help them explain to clients, unsettled by the latest news about the Dow, why broad stock market indexes may serve as a better guide to market performance. The DJIA overstates daily market volatility primarily because the index is less diversified than the market. This paper shows that a portfolio of the 30 Dow Jones Industrials has a significant diversifiable component to its volatility. As a result, the DJIA overstates the systematic risk of the stock market. Furthermore, the magnitude of the Dow’s daily volatility is large, making it a poor tool for drawing inferences about the actual daily change in the stock market. Least squares estimates of daily market return, given daily return on the Dow, have a 95 per cent confidence bound that is at least 100 basis points wide for broad US market indexes and 200 basis points or more for broad international indexes. The bias in the daily Dow is small in absolute magnitude and sometimes escapes detection by a conventional t-test. But non-parametric tests show that this bias is statistically significant. Further, the small daily bias compounds to a large difference over long time periods. The most obvious reason why the DJIA understates total market return is that the Dow does not reflect cash dividends. The Dow, however, also understates daily capital appreciation of the US market. This paper shows that a likely
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explanation for this phenomenon is that the DJIA is less diversified than the market. Specifically, the stocks in the Dow are large-caps. So a broad stock market index that includes smaller capitalisation stocks performs better than the Dow does over the long run owing to the small-stock risk premium. The next section describes the sources of data and methods for constructing the daily return series described in this paper. The third section reports statistical differences between the daily change in the DJIA and the broad US stock market indexes and evaluates their significance. The fourth section deconstructs stock market indexes in an effort to pinpoint why the DJIA does not track the broad indexes more closely. The fifth section examines the distribution of daily US stock market returns conditional on an observed change in the DJIA. The penultimate section briefly examines what, if anything, the Dow tells us about stock markets outside the US, and the final section presents the summary and conclusions.
Data and methods Nominal returns for the US stock market series and the individual Dow Jones Industrial stocks are taken from the daily database provided by the Center for Research in Security Prices (CRSP).1 The CRSP’s daily price series start on 2nd July, 1962. The analysis in this paper covers the 9,694 consecutive trading day returns from 3rd July, 1962, to 29th December, 2000 (the last trading day in 2000). Data on the DJIA itself come from three sources. The end-of-day index values are taken from the Dow Jones Indexes website (www.djindexes.com). Information about its historical composition comes from The Dow Jones Averages 1885–1990 and the Wall Street Journal for 1991–2000.2
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Nominal returns on the DJIA are calculated from the end-of-day index values. In this paper, all indexes are scaled to $1.00 on 2nd July, 1962. This paper compares the DJIA with broad stock market indexes (which, to simplify the discussion, will be labelled as ‘market indexes’ with the understanding that the discussion applies to stock markets and not the universe of all assets). To check the robustness of the conclusions, the research design includes CRSP daily series for three US market indexes. The CRSP S&P500 Universe is the CRSP reconstruction of the S&P500 Composite Index. The other two US market indexes are the CRSP NYSE index and the CRSP NYSE/Amex/Nasdaq index. These indexes include all issues listed on the respective exchanges (from 2nd July, 1962, for NYSE and Amex, and from 14th December, 1972, for Nasdaq). Each US market index has four variations: value- and equal-weighted capital appreciation, and value- and equal-weighted total return. The Dow Jones Industrials are large-caps, so the DJIA is more likely to track the value-weighted market indexes. The equal-weighted indexes provide an objective measurement to compare how well the DJIA represents the broader market which includes small-caps. This paper analyses six variations of the DJIA in order to pinpoint why the DJIA fails to track the broad market indexes. On each trading day, every variation includes the 30 Dow Jones Industrials (DJI). The alternative DJI indexes are price-weighted capital appreciation (PWCAP) and total return (PWTOT), value-weighted capital appreciation (VWCAP) and total return (VWTOT), and equal-weighted capital appreciation (EWCAP) and total return (EWTOT).
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Return on a DJI portfolio for trading day t is Rp,t ⫽
冘
wi,t Ri,t
(1)
i 苸 S(t)
where wi,t is the weight of stock i on trading day t, and S(t) is the set of stocks in the DJIA on trading day t. If the return Rp,t represents capital appreciation, then Ri,t represents capital appreciation on stock i. If the return Rp,t is total return, then Ri,t represents total return on stock i. Portfolio weights for each alternative DJI index are constructed for each trading day. For value-weighted indexes, the weight on stock i for trading day t is wi,t ⫽
冘
Ni,t–1 Pi,t–1 Nj,t–1Pj,t–1
(2)
j 苸 S(t)
if i 苸 S(t) and zero otherwise, where Ni,t is the number of shares of stock i outstanding on day t, and Pi,t is the closing share price of stock i on day t. For price-weighted indexes of the DJI, wi,t ⫽
冘
Pi,t–1 Pj,t–1
(3)
j 苸 S(t)
if i 苸 S(t) and zero otherwise. For equal-weighted indexes of the DJI, wi,t ⫽
1 30
(4)
if i 苸 S(t) and zero otherwise. The CRSP calculates returns for trading day t from close of markets on day t ⫺ 1 to close of markets on day t. Hence, index weights for trading day t correspond to forming a portfolio with weights wi,t at close of markets on day t ⫺ 1 and holding that portfolio for one trading day. This paper also compares the DJIA with four broad international stock market indexes from Morgan Stanley
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Table 1
DJIA daily returns vs US market index daily total returns
DJIA
S&P500 Universe
NYSE
Value-wt
Value-wt
Equal-wt
NYSE/Amex/Nasdaq Equal-wt
Value-wt
Equal-wt
Panel A. Descriptive statistics for nominal series (3rd July, 1962–29th December, 2000) Maximum (%) Upper quartile Median Lower quartile Minimum Mean (%) Standard deviation (%)
10.15 0.52 0.03 –0.45 –22.61 0.0347 0.9385
8.81 0.50 0.05 –0.40 –19.46 0.0506 0.9004
9.81 0.49 0.09 –0.36 –18.42 0.0599 0.8585
8.79 0.47 0.06 –0.36 –18.35 0.0493 0.8420
9.82 0.43 0.09 –0.27 –15.00 0.0605 0.7478
8.67 0.47 0.07 –0.35 –17.17 0.0490 0.8473
6.95 0.44 0.14 –0.21 –10.48 0.0818 0.7004
Panel B. Comparison of DJIA returns and market total returns 2 2 F = sDJIA ⫼ smarket
t-statistic for difference in means (DJIA vs market index) Proportion of trading days for which RDJIA,t – Rmrkt,t > 0 Sign test statistic
1.09 (0.000) –1.20 (0.230) 0.46
1.20 (0.000) –1.95 (0.052) 0.46
1.24 (0.000) –1.14 (0.256) 0.46
1.58 (0.000) –2.11 (0.035) 0.46
1.23 (0.000) –1.11 (0.268) 0.47
1.80 (0.000) –3.96 (0.000) 0.44
–7.98 (0.000)
–7.11 (0.000)
–7.60 (0.000)
–8.31 (0.000)
–6.70 (0.000)
–10.91 (0.000)
Notes: Each series includes 9,694 daily returns. The F-test is one-sided. The t-test for difference in means assumes variances are unequal. The sign test statistic is the standardised sample proportion and is approximately standard normal for this sample size. For each test, the p-value is in parentheses.
Capital International (MSCI): the World, EAFE (Europe, Australasia, and Far East), Europe and Pacific Indexes. The daily index values are taken from the MSCI website (www.msci.com). The earliest available index values are for 31st March, 1998, so the comparison of the daily returns on the Dow and the international market indexes is limited to the period 1st April, 1998-29th December, 2000. The four MSCI indexes are market value weighted.3
Daily change in the DJIA versus the market Daily total return
Using monthly returns, both Shoven and Sialm (2000) and Clarke and Statman (2000) show that the DJIA significantly understates US market total return over October 1928–December 1999 because the DJIA measures capital appreciation but does not reflect cash dividends. For
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the same reason, DJIA daily returns should be lower than market daily total returns on average. In addition, over sufficiently long periods of time, small-caps should outperform large-caps owing to the small stock premium first documented by Banz (1981) and confirmed in later studies, eg by Ibbotson Associates (Annin and Licato, 2001). So the DJIA, a large-cap index, should have lower daily returns than the broad market indexes which, by construction, include small-caps. Statistical analysis confirms that DJIA daily returns tend to be lower than daily total returns on the market indexes (see Table 1). For example, the DJIA mean daily return is 0.0347 per cent, while mean daily total returns on the value-weighted indexes are 0.0506 per cent for the S&P500, 0.0493 per cent for the NYSE, and 0.0490 per cent for the NYSE/Amex/Nasdaq. Mean daily total returns on the equal-weighted indexes are even higher, eg 0.0599 per cent on
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the equal-weighted S&P500. The sign test applied to pairwise differences (DJIA and market index returns paired by trading date) is significant at the 0.1 per cent level for all comparisons. The t-test for difference in mean returns between the DJIA and the market is significant at about the 5 per cent level for equal-weighted market indexes. Consistent with tests reported by Shoven and Sialm (2000), however, the t-test is not significant for value-weighted market indexes. Daily DJIA returns and market daily total returns are extremely volatile, so large standard deviations in the denominator of the t-statistic reduce its magnitude and hence its significance. The small daily bias compounds to a large difference over the 38.5-year period from 2nd July, 1962, to 29th December, 2000. Wealth indexes show that the DJIA underestimates growth in the aggregate wealth of investors in the US market.4 By the end of December 2000, the DJIA grew to $18.82. The value-weighted total return index on the S&P500 grew to $90.57, while the value-weighted NYSE/Amex/Nasdaq total return index grew to $81.07. The DJIA also understates return on portfolios that are heavily weighted toward small-cap stocks. Over the entire period, the equal-weighted total return index on the S&P500 grew to $231.17, while the NYSE/Amex/Nasdaq equal-weighted total return index grew to $2,187.51. Daily DJIA returns are more volatile than daily total returns on the US market indexes (see Table 1). For example, the standard deviation of daily DJIA returns is 0.9385 per cent, while the standard deviation of daily total returns on the value-weighted S&P500 is 0.9004 per cent. The interquartile range is 0.97 per cent for the DJIA and 0.90 per cent for the value-weighted S&P500. The difference in volatility is more pronounced when the DJIA is compared
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with the other two value-weighted market indexes. Similarly, the daily DJIA exhibits greater volatility than the equal-weighted market indexes. The F-test for the difference in variances between the DJIA and the market is significant at the 0.1 per cent level for total return on every market index. Daily capital appreciation
Shoven and Sialm (2000) claim that the long-run performance of the DJIA is similar to that of capitalisation-weighted indexes of the US stock market. They find that the DJIA is similar to a capitalisation-weighted version of itself as well as the S&P500 over October 1928–December 1999. Results in this paper based on daily data for July 1962–December 2000 lead to a different conclusion. The difference between the DJIA and each US market index narrows substantially when mean daily capital appreciation is considered rather than total return, yet a significant bias still can be detected. The t-tests for the difference between the DJIA’s mean daily return and the market index’s mean daily capital appreciation are significant only for the equal-weighted NYSE/Amex/Nasdaq index (see Table 2). The DJIA daily returns, however, are significantly lower than the market index when the sign test is applied to pairwise differences. This test is significant at the 1 per cent level for all comparisons. The most likely explanation for the difference between Shoven and Sialm’s (2000) conclusions and those in this paper is that Shoven and Sialm compared mean returns but did not report tests on differences between index returns paired by trading day. The t-tests on daily data for July 1962–December 2000 are consistent with Shoven and Sialm’s t-tests on monthly data for October
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Table 2
DJIA daily returns vs US market index daily capital appreciation
DJIA
S&P500 Universe
NYSE
Value-wt
Value-wt
Equal-wt
NYSE/Amex/Nasdaq Equal-wt
Value-wt
Equal-wt
0.0352 0.8422
0.0467 0.7482
0.0357 0.8474
0.0730 0.7008
Panel A. Descriptive statistics for nominal series (3rd July, 1962–29th December, 2000) Mean (%) Standard deviation (%)
0.0347 0.9385
0.0366 0.9006
0.0464 0.8588
Panel B. Comparison of DJIA returns and market capital appreciation 2 2 F = sDJIA ⫼ smarket
t-statistic for difference in means (DJIA vs market index) Proportion of trading days for which RDJIA,t – Rmrkt,t > 0 Sign test statistic
1.09 (0.000) –0.14 (0.889) 0.48
1.19 (0.000) –0.90 (0.368) 0.48
1.24 (0.000) –0.03 (0.972) 0.49
1.57 (0.000) –0.98 (0.326) 0.47
1.23 (0.000) –0.08 (0.938) 0.48
1.79 (0.000) –3.22 (0.001) 0.45
–3.01 (0.003)
–3.78 (0.000)
–2.76 (0.006)
–5.40 (0.000)
–3.03 (0.002)
–9.30 (0.000)
Notes: Each series includes 9,694 daily returns. The F-test is one-sided. The t-test for difference in means assumes variances are unequal. The sign test statistic is the standardised sample proportion and is approximately standard normal for this sample size. For each test, the p-value is in parentheses.
1928–December 1999. The sign test applied to returns matched by trading day, however, is sensitive to differences not detectable when the data are aggregated in the mean returns. The small daily bias compounds to a large difference over the period July 1962–December 2000. Wealth indexes show that the DJIA underestimates capital appreciation of the US market. By the end of December 2000, the DJIA grew to $18.82. The value-weighted capital appreciation index for the S&P500 grew to $23.30, while the value-weighted capital appreciation index for the NYSE/Amex/Nasdaq index grew to $22.50. The DJIA also understates capital appreciation on portfolios that are heavily weighted toward small-cap stocks. Over the entire period, the equal-weighted capital appreciation index on the S&P500 grew to $62.41, while the equal-weighted capital appreciation index on the NYSE/Amex/Nasdaq index grew to $929.82. Furthermore, the daily Dow is more volatile than the daily capital appreciation of the US market indexes. The F-test for the difference in variances between the
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DJIA daily return and capital appreciation on each US market index is significant at the 0.1 per cent level. The higher volatility yet lower return relative to the market suggests that a Dow Jones Industrials portfolio has a significant diversifiable component in its total risk. With only 30 stocks, the DJIA is far less diversified than the broad market indexes in this study. Thus, the DJIA overstates the risk of a well-diversified portfolio of US stocks. This conclusion is consistent with Campbell et al. (2001) and Newbould and Poon (1996), who show that 30 stocks in general are insufficient to diversify away all idiosyncratic risk. Furthermore, the market indexes have greater systematic risk due to their greater small-cap exposure. Hence, the differences reported in Tables 1 and 2 might understate the magnitude of the diversifiable risk in the DJIA.
Deconstructing the indexes Deconstructing the indexes shows that the DJIA has significantly greater volatility than the market indexes for one
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DJIA 1 PWCAP capital appreciation on price-weighted DJI 2 VWCAP capital appreciation on value-weighted DJI
2
2
EWCAP capital appreciation on equal-weighted DJI
3 VWMRKTCAP capital appreciation on value-weighted market
PWTOT total return on price-weighted DJI
VWTOT total return on value-weighted DJI
3
3
2 EWTOT total return on equal-weighted DJI 3
VWMRKTTOT total return on value-weighted market
4
EWMRKTCAP capital appreciation on equal-weighted market
4
EWMRKTTOT total return on equal-weighted market
Figure 1 Deconstructing the indexes: (1) index weight adjustments for stock splits and other special distributions; (2) portfolio weights; (3) diversification; (4) inclusion or omission of dividend yield
main reason: the DJIA is less diversified. Index weight adjustments, portfolio weights and omission of dividend yield play virtually no role in explaining the greater volatility of the DJIA. Deconstruction also shows why the DJIA daily return is significantly lower than the market indexes. Figure 1 outlines the discussion in this section. Index weight adjustments for stock splits and other special distributions
One possible explanation for differences between the DJIA and CRSP market indexes is that the Wall Street Journal editors and CRSP apply different rules for recognising stock splits and other special distributions. The CRSP Data Description Guide (CRSP, 2000) indicates that CRSP adjusts stock returns for a more comprehensive list of stock and other special distributions than do the Wall Street Journal editors, who apparently adjust the DJIA divisor only for large distributions. The divisor
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changes for the DJIA from October 1928 to December 1990 include only a dozen distribution events that are not stock splits (Pierce, 1991). The smallest of these non-split distributions are two 1989 Texaco special dividends that are about 7 per cent of closing share price in the ex-month. The other non-split events are 10–20 per cent stock dividends or other special distributions at least this large. The different rules for recognising distributions explain why the price-weighted DJI daily capital appreciation series constructed in this paper (PWCAP) is not identical to returns on the reported Dow. DJIA daily returns have a mean of 0.0347 per cent and a standard deviation of 0.9385 per cent, while PWCAP returns have a mean of 0.0346 per cent and a standard deviation of 0.9347 per cent. The two daily series are not significantly different, however. The F-test for difference in the variances is not significant (p-value of 0.34). Neither the t-test for difference in
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Table 3
Daily returns on alternative indexes of the 30 Dow Jones Industrials Capital appreciation indexes DJIA
Price-wt PWCAP
Value-wt VWCAP
Total return indexes Equal-wt EWCAP
Price-wt PWTOT
Value-wt VWTOT
Equal-wt EWTOT
Panel A. Descriptive statistics for nominal series (3rd July, 1962–29th December, 2000) Maximum (%) Upper quartile Median Lower quartile Minimum Mean (%) Standard deviation (%)
10.15 0.52 0.03 –0.45 –22.61 0.0347 0.9385
8.34 0.51 0.04 –0.45 –21.52 0.0346 0.9347
10.44 0.52 0.03 –0.47 –21.70 0.0320 0.9457
9.16 0.53 0.04 –0.46 –22.19 0.0377 0.9533
8.34 0.54 0.05 –0.44 –21.48 0.0498 0.9348
10.44 0.53 0.04 –0.45 –21.68 0.0483 0.9449
9.16 0.55 0.06 –0.45 –22.16 0.0533 0.9533
Panel B. PWCAP vs capital appreciation alternatives and PWTOT vs total return alternatives 2 2 F = salternative ⫼ sPW
t-statistic for difference in means (PW vs alternative) Proportion of trading days for which RPW,t – Ralternative,t>0 Sign test statistic
1.024 (0.125) 0.20 (0.842) 0.50
1.040 (0.026) –0.23 (0.819) 0.50
1.022 (0.145) 0.11 (0.909) 0.50
1.040 (0.027) –0.26 (0.795) 0.50
0.89 (0.371)
0.49 (0.626)
0.85 (0.394)
0.45 (0.655)
Notes: Each series includes 9,694 daily returns. The t-test for difference in means assumes variances are unequal. The sign test statistic is the standardised sample proportion and is approximately standard normal for this sample size. For each test, the p-value is in parentheses. For a two-sided F-test in Panel B, compare the p-values with ␣/2, where ␣=level of significance. For a 5 per cent level of significance, ␣/2=0.025, so all the F-statistics in Panel B are not significant.
the means nor the sign test for pairwise differences between the daily returns is significant at the 20 per cent level. Hence, the rules applied by the Wall Street Journal editors for recognising special distributions have no material effect on the index. For all practical purposes, the PWCAP and the DJIA are the same.
and the variances are not significantly different at the 5 per cent level (see Table 3). The mean for PWCAP is not significantly different from the means for either VWCAP or EWCAP. Similarly, location and dispersion statistics for PWTOT are not significantly different from those for either VWTOT or EWTOT.
Portfolio weights
Diversification
The index weighting also makes no significant difference. As a price-weighted index, the DJIA reflects changes in stock prices but not market capitalisation, eg each time a component stock splits, its weight in the DJIA decreases. A capitalisation-weighted index overcomes this weakness, but the improvement is minimal. PWCAP has similar volatility to both VWCAP and EWCAP. The interquartile ranges are nearly the same,
Generally, each DJI index has significantly lower returns and significantly greater volatility than the corresponding US market index (see Table 4). The sign tests for pairwise differences provide significant evidence that the DJI indexes generally have lower returns than the corresponding market index. The evidence is strongest for the equal-weighted indexes (0.1 per cent level of significance) and is consistent
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with the small-cap risk premium. The sign tests for differences between the value-weighted capital appreciation indexes show that the DJI index (VWCAP) is significantly lower than the S&P500 and NYSE/Amex/Nasdaq indexes (at the 5 per cent level) and the NYSE index (at the 10 per cent level). The weakest evidence of a difference is from comparisons with value-weighted total returns, where the sign test is significant (at the 10 per cent level) only for the S&P500. The F-tests for differences between variances of each DJI index and its corresponding market index are significant at the 0.1 per cent level in all comparisons. The 30 Dow Jones Industrials are a subset of stocks in the S&P500 and NYSE/Amex/Nasdaq indexes. (They also were a subset of the NYSE index stocks until 1st November, 1999, when Microsoft and Intel became the first non-NYSE listed stocks to be included in the DJIA.) The DJI and market indexes are matched by weighting method and type of return in Table 4, so the only difference in each pair is the portfolio of securities. The composition of the Dow portfolio differs from the market index portfolios in three ways: industry representation, number of securities and market capitalisation of the component securities. Industry representation
Dow Jones claims, ‘The 30 Dow Industrials are chosen as representative of the broad market and the American industry’ (Dow Jones, 2001: 6). Dow Jones, however, segregates the transportation and utilities industries in special indexes separate from the industrials. And the broadest CRSP indexes include issues other than common stock, eg REITs. Without further analysis, however, it is unclear whether differences in industry
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representation are sufficiently important to explain any of the performance differences between the DJIA and the market indexes. Number of securities
Sample size alone may explain part of the difference in variance. Over the period of this study, the S&P500 index includes 500 stocks while the NYSE index ranges from 1,149 to 2,901 issues, and the NYSE/Amex/Nasdaq index ranges from 2,021 to 8,848 issues. From a purely statistical perspective, Newbould and Poon (1996) show that average total risk for random samples of 30 stocks includes a substantial amount of diversifiable risk. This result, however, is on average. Total risk for some portfolios of 30 stocks may be lower than the market risk. Diversifiable risk for DJI portfolios can be estimated by using the market model Rd,t ⫽ ␣dM ⫹ dMRM,t ⫹ d,t
(5)
where Rd,t is the return on a DJI index on trading day t, RM,t is the return on trading day t for a market index M with the same portfolio weights (value-weighted or equal-weighted) and the same type of return (capital appreciation or total return) as the DJI index, and d,t is the random error term. For this model, total risk can be written as
2d ⫽ 2dM 2M ⫹ 2d
(6)
where 2M is the variance of the market index return,  2dM 2M is market risk, and 2d is the diversifiable risk. The DJI indexes have greater volatility than the market indexes because the former have diversifiable risk.5 The diversifiable risk for the value-weighted DJI indexes is about 16 per cent of total risk when the NYSE/Amex/Nasdaq
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Table 4 Indexes of 30 Dow Jones Industrials (DJI) vs corresponding US market indexes (nominal series; 3rd July, 1962–29th December, 2000) Panel A. Value-weighted daily capital appreciation indexes: VWCAP vs the market VWMRKTCAP VWCAP (DJI stocks) Mean (%) Standard deviation (%) F = s2VWCAP ⫼ s2VWMRKTCAP
0.0320 0.9457
t-statistic for difference in means (VWCAP vs market) Proportion of trading days for which RVWCAP,t ⫼ RVWMRKTCAP,t > 0 Sign test statistic
S&P500 Universe
NYSE
NYSE/Amex/ Nasdaq
0.0366 0.9006 1.10 (0.000) –0.35 (0.728) 0.49
0.0352 0.8422 1.26 (0.000) –0.25 (0.802) 0.49
0.0357 0.8474 1.25 (0.000) –0.29 (0.769) 0.49
–2.30 (0.022)
–1.83 (0.068)
–2.07 (0.038)
Panel B. Equal-weighted daily capital appreciation indexes: EWCAP vs the market EWMRKTCAP EWCAP (DJI stocks) Mean (%) Standard deviation (%) F = s2EWCAP ⫼ s2EWMRKTCAP
0.0377 0.9533
t-statistic for difference in means (EWCAP vs market) Proportion of trading days for which REWCAP,t–REWMRKTCAP,t > 0 Sign test statistic
S&P500 Universe
NYSE
NYSE/Amex/ Nasdaq
0.0464 0.8588 1.23 (0.000) –0.66 (0.508) 0.48
0.0467 0.7482 1.62 (0.000) –0.73 (0.466) 0.47
0.0730 0.7008 1.85 (0.000) –2.93 (0.003) 0.46
–3.70 (0.000)
–4.98 (0.000)
–7.98 (0.000)
NYSE
NYSE/Amex/ Nasdaq
0.0506 0.9004 1.10 (0.000) –0.18 (0.861) 0.49
0.0493 0.8420 1.26 (0.000) –0.08 (0.937) 0.49
0.0490 0.8473 1.24 (0.000) –0.05 (0.956) 0.49
–1.73 (0.084)
–1.36 (0.174)
–1.54 (0.123)
Panel C. Value-weighted daily total return indexes: VWTOT vs the market VWMRKTTOT VWTOT (DJI stocks) Mean (%) Standard deviation (%) F = s2VWTOT ⫼ s2VWMRKTTOT
0.0483 0.9449
t-statistic for difference in means (VWTOT vs market) Proportion of trading days for which RVWTOT,t – RVWMRKTTOT,t > 0 Sign test statistic
index represents the market (Panel A in Table 5). Diversifiable risk for the equal-weighted DJI indexes is about 48 per cent of total risk when the NYSE/Amex/Nasdaq index represents
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S&P500 Universe
the market (Panel B in Table 5). Results for the total return indexes are almost identical to results reported in Table 5 for the corresponding capital appreciation indexes.
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Table 4
Continued
Panel D. Equal-weighted daily total return indexes: EWTOT vs the market EWMRKTTOT EWTOT (DJI stocks) Mean (%) Standard deviation (%) F = s2EWTOT ⫼ s2EWMRKTTOT
S&P500 Universe
0.0533 0.9533
t-statistic for difference in means (EWTOT vs market) Proportion of trading days for which REWTOT,t – REWMRKTTOT,t > 0 Sign test statistic
NYSE
NYSE/Amex/ Nasdaq
0.0599 0.8585 1.23 (0.000) –0.50 (0.615) 0.48
0.0605 0.7478 1.63 (0.000) –0.58 (0.562) 0.48
0.0818 0.7004 1.85 (0.000) –2.37 (0.018) 0.46
–3.35 (0.001)
–4.90 (0.000)
–7.19 (0.000)
Notes: Each series includes 9,694 daily returns. The F-test is one–sided. The t-test for difference in means assumes variances are unequal. The sign test statistic is the standardised sample proportion and is approximately standard normal for this sample size. For each test, the p-value is in parentheses.
Market capitalisation of components
The difference in market capitalisation of the component stocks may best explain why the DJI indexes exhibit significantly lower returns than the market indexes. Stocks in the broad indexes are much smaller, on average, than those in the Dow. For example, at the end of 2000, the median market cap was $68,915m for the DJI stocks versus $110m for the NYSE/Amex/Nasdaq index stocks. The smallest market cap for the DJI stocks was $12,123m, while 97 per cent of the stocks in the NYSE/Amex/Nasdaq index had a lower market capitalisation. If large-caps are defined as stocks with market capitalisation of $10,000m at the end of 2000, then only 72 per cent of the capitalisation of the NYSE/Amex/Nasdaq index was in large-caps. Hence, the small-firm effect would explain why the DJI indexes have lower returns than the broad market indexes. Dividend yield
Omission of cash dividends partly explains why the DJIA’s mean daily
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return is lower than the market’s mean daily total return but does not explain why daily volatility on the Dow exceeds market volatility. As expected, each market capital appreciation index has significantly lower return than the corresponding total return index. Sign tests for pairwise differences between value-weighted capital appreciation (VWMRKTCAP) and value-weighted total return (VWMRKTTOT) and between equal-weighted capital appreciation (EWMRKTCAP) and equal-weighted total return (EWMRKTTOT) are significant at the 0.1 per cent level. Corresponding capital appreciation and total return series, however, have almost identical volatility. Standard deviation, interquartile range, and other measures of dispersion are almost the same for VWMRKTCAP versus VWMRKTTOT and for EWMRKTCAP versus EWMRKTTOT. See Table 6 for the NYSE/Amex/Nasdaq index. Results for the S&P500 and NYSE indexes are similar to those reported in Table 6. In summary, dividend yield has no significant effect on index volatility.
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How did the Dow do today?
Table 5 Diversifiable risk of indexes of 30 Dow Jones Industrials (DJI) measured with respect to corresponding US market indexes (3rd July, 1962–29th December, 2000) Panel A. Value–weighted daily capital appreciation indexes: VWCAP vs the market VWMRKTCAP VWCAP (DJI stocks) Standard deviation (%) 0.9457 Beta coefficient estimate Diversifiable to total risk (market model)
S&P500 Universe
NYSE
NYSE/Amex/ Nasdaq
0.9006 0.9995 0.0940
0.8422 1.0537 0.1194
0.8474 1.0223 0.1607
Panel B. Equal–weighted daily capital appreciation indexes: EWCAP vs the market EWMRKTCAP EWCAP (DJI stocks) Standard deviation (%) 0.9533 Beta coefficient estimate Diversifiable to total risk (market model)
S&P500 Universe
NYSE
NYSE/Amex/ Nasdaq
0.8588 1.0274 0.1433
0.7482 1.0790 0.2828
0.7008 0.9764 0.4848
Notes: Each series includes 9,694 daily returns. The market model includes one independent variable, the contemporaneous market return. Diversifiable risk equals total risk minus market risk and is expressed as a variance. The ratio, ‘diversifiable to total risk’, equals diversifiable risk divided by variance on the DJIA return.
A bias decomposition The above deconstruction of the indexes shows that the DJIA daily return is significantly lower than the market indexes for two reasons. First, the DJIA is a capital appreciation index, not a total return index. Secondly, the DJIA is less diversified than the market. In particular, the DJIA is a large-cap index. Thus, over the long run, broad market indexes have greater capital appreciation than the DJIA owing to the small-stock risk premium. A bias decomposition quantifies the relative magnitude of the sources of bias in the DJIA daily return. Potential sources of bias discussed in this paper fall into four categories. The effect of index weight adjustments for stock splits and other distributions can be measured by comparing daily DJIA returns with capital appreciation on a price-weighted DJI index (PWCAP). The effect of the index weighting method can be measured by comparing PWCAP to daily
䉷 Henry Stewart Publications 1479-179X (2003)
capital appreciation on a value-weighted DJI index (VWCAP). The effect of diversification can be measured by comparing VWCAP to daily capital appreciation on a value-weighted market index (VWMRKTCAP). Finally, the effect of dividend yield on return can be measured by comparing daily capital appreciation (VWMRKTCAP) with total return (VWMRKTTOT) on the same value-weighted market index. Most of the bias in the daily Dow is due to the omission of cash dividends. Diversification is a secondary source (see Table 7). For example, when the stock market is represented by the NYSE/Amex/Nasdaq index, bias measured as difference in daily mean returns is –0.0143 per cent. Most is due to omission of dividends (–0.0133 per cent). Insufficient diversification (in the sense that the DJIA includes large-caps but not small-caps) accounts for the remainder (–0.0037 per cent). These sources are partially offset by a positive
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Table 6 Market capital appreciation vs market total return for CRSP NYSE/Amex/Nasdaq index (nominal series; 3rd July, 1962–29th December, 2000) Value–weighted
Equal–weighted
Capital appreciation VWMRKTCAP Mean (%) Standard deviation (%) F = s2CAP ⫼ s2TOT
Total return VWMKRTTOT
0.0357 0.8474
0.0490 0.8473 1.00 (0.492) –1.09 (0.277) 0.00 –98.46 (0.000)
t-statistic for difference in means (capital appreciation vs total return) Proportion of RCAP,t – RTOT,t > 0 Sign test statistic
Capital appreciation Total return EWMRKTCAP EWMKRTTOT 0.0730 0.7008
0.0818 0.7004 1.00 (0.475) –0.88 (0.380) 0.00 –98.44 (0.000)
Notes: Each series includes 9,694 daily returns. The F-test is one-sided. The t-test for difference in means assumes variances are unequal. The sign test statistic is the standardised sample proportion and is approximately standard normal for this sample size. For each test, the p-value is in parentheses.
Table 7 Bias decomposition of daily returns on the DJIA relative to US market indexes (nominal series; 3rd July, 1962–29th December, 2000)
Sources of bias
Arithmetic mean daily Incremental return (%) bias (%)
Fraction of total bias
DJIA PWCAP
0.0347 0.0346
0.0001 (0.84) [0.97]
–0.0063
VWCAP VWMRKTCAP VWMRKTTOT
0.0320 0.0366 0.0506
0.0026 (0.84) [0.37] –0.0046 (0.73) [0.02] –0.0140 (0.28) [0.00]
–0.1635 0.2893 0.8805
Index
Panel A. Bias relative to the CRSP S&P500 Universe Index weight adjustments for stock splits & special distributions Portfolio weighting Level of diversification Inclusion/exclusion of cash dividends
Panel B. Bias relative to the CRSP NYSE/Amex/Nasdaq Index Index weight adjustments for stock splits & special distributions Portfolio weighting Level of diversification Inclusion/exclusion of cash dividends
DJIA PWCAP
0.0347 0.0346
0.0001 (0.84) [0.97]
–0.0070
VWCAP VWMRKTCAP VWMRKTTOT
0.0320 0.0357 0.0490
0.0026 (0.84) [0.37] –0.0037 (0.77) [0.04] –0.0133 (0.28) [0.00]
–0.1818 0.2587 0.9301
Notes: Each series includes 9,694 daily returns. PWCAP is capital appreciation on the price-weighted DJI index. VWCAP is capital appreciation on the value-weighted DJI index. VWMRKTCAP is capital appreciation on the market index. VWMRKTTOT is total return on the market index. The p-value for the t-statistic for difference in mean returns is listed in parentheses in the column for incremental bias, while the p-value for the sign test statistic for pairwise differences is listed in square brackets.
bias contribution from price weighting (⫹0.0026 per cent).
about the meaning and role of the DJIA. For example, John Prestbo, Markets Editor, wrote (Prestbo, 1991):
Estimating daily market returns conditional on DJIA daily return In recent years, the Wall Street Journal editors have become a bit defensive
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Nonetheless, critics of the average propose splitting it or making other radical changes to bring it into compliance with their conceptions of statistical orthodoxy. Such
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How did the Dow do today?
Table 8 OLS regression of the daily market return on daily DJIA return (nominal series; 3rd July, 1962–29th December, 2000) Dependent variable (market return) OLS statistics
VWMRKTCAP
VWMRKTTOT EWMRKTCAP EWMRKTTOT
Panel A. Market is CRSP S&P500 Universe R2 0.91 Constant coefficient estimate b0 0.000048 Standard error of b0 0.000027 (0.082) p-value of t-test that b0 = 0 0.915470 Slope coefficient estimate b1 Standard error of b1 0.002923 p-value of t-test that b1 = 1 (0.000) 0.9202 Predicted market return at rDJIA = 1% (%) Standard error of prediction at rDJIA = 1% (%) 0.2701
0.91 0.000188 0.000028 (0.000) 0.915018 0.002931 (0.000) 0.9338 0.2709
0.86 0.000170 0.000033 (0.000) 0.846289 0.003535 (0.000) 0.8633 0.3267
0.86 0.000305 0.000033 (0.000) 0.845979 0.003534 (0.000) 0.8765 0.3266
0.86 0.000198 0.000032 (0.000) 0.839266 0.003379 (0.000) 0.8591 0.3123
0.50 0.000546 0.000050 (0.000) 0.529664 0.005347 (0.000) 0.5843 0.4941
0.50 0.000634 0.000050 (0.000) 0.529565 0.005341 (0.000) 0.5930 0.4935
Panel B. Market is NYSE/Amex/Nasdaq R2 0.86 0.000066 Constant coefficient estimate b0 Standard error of b0 0.000032 (0.038) p-value of t-test that b0 = 0 Slope coefficient estimate b1 0.839587 0.003376 Standard error of b1 p-value of t-test that b1 = 1 (0.000) Predicted market return at rDJIA = 1% (%) 0.8462 Standard error of prediction at rDJIA = 1% (%) 0.3120
Note: The term 'prediction' in the above panels refers to statistical estimation, not forecasting. For each market index, the corresponding standard error of prediction is approximately the same for daily DJIA returns ranging from –1.39% (the 5th percentile in the sample) to 1.47% (the 95th percentile).
tinkering would dilute, if not eliminate, the value of a century-plus of market tracking, and still wouldn’t achieve perfection. A single market measure, no matter how it is calculated, isn’t equally useful to all investors all the time; their needs are too diverse and are always changing. The Dow average, as it is, provides a constant beacon for investors hoping to successfully navigate the market’s rough seas.
This paper, however, has shown that the Dow understates daily return and overstates daily volatility of the stock market during the period July 1962–December 2000. In this section, statistical orthodoxy is used to explore the distribution of daily market returns conditional on the daily DJIA return in an effort to determine what the Dow really does reveal about the US stock market.
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Correlation between the daily DJIA and each daily market index is high. The correlation with the value-weighted S&P500 is 0.95 and with the equal-weighted S&P500 is 0.92. The correlation with the value-weighted NYSE/Amex/Nasdaq index is 0.93 and with the equal-weighted version is 0.73. The high correlations between the daily DJIA and the daily market indexes indicate that an ordinary least squares (OLS) regression of the market return on the DJIA return will have a high coefficient of determination (R2). Hence, a simple linear model explains a large part of the variability of the market return. Table 8 summarises the OLS results.6 By applying one of these regression models to an observed value of today’s DJIA return, the uncertainty of the estimate of the corresponding market
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return can be quantified. The standard error of prediction, however, is relatively large for all US market indexes and a wide range of DJIA daily returns. Roughly speaking, the 68 per cent confidence bound on the estimated daily market return is at least 50 basis points wide, and the 95 per cent confidence bound is at least 100 basis points wide. For example, if today’s return on the DJIA is 1 per cent, then today’s value-weighted total return on the NYSE/Amex/Nasdaq market has a 95 per cent probability of falling between 0.23 per cent and 1.48 per cent, about two standard errors of prediction on either side of the estimated market return of 0.85 per cent.
The DJIA and the international market The Wall Street Journal editors do not claim that the DJIA represents performance of the global stock market. Nonetheless, this paper briefly examines daily international stock market returns conditional on the DJIA daily return in order to determine what, if anything, the DJIA tells investors about stock markets outside the USA. In this section, the DJIA is compared with four value-weighted MSCI indexes: Europe, Pacific, EAFE and World. The index values are taken from the MSCI website (www.msci.com). The DJIA is a capital appreciation index, so this section focuses on the capital appreciation of the MSCI indexes. The regional MSCI indexes, Europe and Pacific, are subsets of the other two indexes. Morgan Stanley Capital International constructs the Europe index from country indexes for 21 developed markets. The UK is the largest component of the Europe Index, accounting for almost one third of the market capitalisation. France, Germany and Switzerland are the next
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largest, together accounting for about one-third of the market capitalisation. The remaining countries in the index make up the balance. The Pacific Index consists of five developed countries’ market indexes. Japan is the largest, accounting for over three-quarters of the market capitalisation of the index. Australia, Hong Kong, Singapore and New Zealand make up the balance. The EAFE Index is composed of the Europe and Pacific Indexes. The World Index adds Canada and the USA to the EAFE Index. Roll (1992) analyses the relation between industrial structure and international stock price behaviour using daily data from 1988–91. His results show that asynchronous world market trading introduces cross correlation in daily return series for markets in different time zones on the same calendar day. In particular, he reports that daily return series for the different markets generally exhibit significant autocorrelation coefficients at leads and lags of one trading day but do not exhibit dependence at longer lags. Least squares regression is used here to analyse the relation between international market index returns and DJIA returns, testing two types of models: those with only a contemporaneous (same calendar day) DJIA return, and those that also include one daily lead and one daily lag in the DJIA returns. For the latter case, the basic time series regression model is RM,t ⫽ ␣dM ⫹ +dM Rd,t+1 ⫹ dM Rd,t – ⫹  dM Rd,t–1 ⫹ M,t, t ⫽ 1, 2, . . ., T
(7)
where RM,t is the market index return on trading day t, Rd,t is the contemporaneous DJIA return on trading day t, Rd,t+1 is the DJIA return leading by one trading day, Rd,t–1 is the DJIA return lagging by one trading day, and T is the
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Table 9 Least squares regression of daily international market index return on daily DJIA return (nominal series; 2nd April, 1998–28th December, 2000) Dependent variable (daily market index return) OLS Statistics
CRSP Total US
MSCI World
MSCI EAFE
MSCI Europe
MSCI Pacific
0.11 0.0001 0.18 0.2860 9.31 0.2927 0.9880
0.14 0.0000 0.06 0.3678 10.78 0.3703 1.0977
0.01 0.0003 0.47 0.0971 2.13 0.1233 1.4627
Panel A. Independent variable is contemporaneous daily DJIA return Adjusted R2 0.71 Intercept 0.0000 t-statistic –0.08 Contemporaneous DJIA return coefficient 0.9179 t-statistic 41.30 Predicted market return at RDJIA = 1% (%) 0.9159 Standard error of prediction at RDJIA = 1% (%) 0.7150
0.64 0.0000 0.01 0.6359 34.76 0.6362 0.5886
Panel B. Independent variables are the contemporaneous, one day lagged, and one day leading daily DJIA returns Adjusted R2 Intercept t-statistic Contemporaneous DJIA return coefficient t-statistic Lagged DJIA return coefficient t-statistic Leading DJIA return coefficient t-statistic
0.71 0.0000 –0.07 0.9180 41.31 0.0203 0.91 –0.0274 –1.23
0.66 0.0000 –0.22 0.6342 35.79 0.1225 6.90 0.0166 0.94
0.21 –0.0001 –0.15 0.2819 9.76 0.2752 9.51 0.0546 1.89
0.21 –0.0001 –0.22 0.3639 11.11 0.2540 7.74 0.0577 1.76
0.07 0.0001 0.24 0.0924 2.11 0.3200 7.28 0.0484 1.10
Notes: All daily market indexes are market–value weighted capitalisation indexes. The CRSP Total US index is the NYSE/Amex/Nasdaq index. For comparability between Panels A and B, the contemporaneous returns in both panels are for trading days in the period 2nd April, 1998–28th December, 2000.
total number of trading days in the sample. The primary hypothesis, based on Roll’s (1992) results, is that the coefficient for one daily lag will be significant for each model in which an MSCI index is the dependent variable. The US is among the most westerly markets open on a given calendar day. Thus each international index should reflect news that affected the DJIA on the previous calendar day. Further, there should be a significant contemporaneous effect but not a significant daily lead in models with the World, EAFE and Europe Indexes. Each includes the US market or European markets whose operating hours overlap with those in the US, so each should reflect contemporaneous news affecting the DJIA. Finally, there is no a priori reason to expect significant coefficients for
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either contemporaneous or leading DJIA returns in a model with the Pacific Index. The markets in the Pacific Index are open earliest in the calendar day, while the US market is open latest; the Pacific and US markets are not open simultaneously. The regression analysis supports these hypotheses, and the results — whether calculated with the DJIA, as reported in Table 9, or with VWCAP — are consistent with Roll’s (1992) results. The coefficient estimate for one daily lag is significant in the model for each MSCI international index, while the coefficient for one daily lead is not significant in any model. The coefficient estimate for the contemporaneous DJIA return exhibits stronger significance than the daily lagged return in all models except the Pacific Index model, where the lagged return coefficient has a t-statistic
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of 7.28 versus 2.11 for the contemporaneous return coefficient. Contemporaneous, lagged, and leading daily DJIA returns explain about as much of the variability of the daily World Index return (adjusted R2 of 66 per cent) as they do of the daily US market return (adjusted R2 of 71 per cent). The US market dominates the capitalisation of the World Index, so this result is neither surprising nor informative, but the DJIA returns explain only a small part of the variability for international indexes that do not include the US market. The adjusted R2 statistic is only 21 per cent when the market is either EAFE or Europe and is about 7 per cent when the market is the Pacific. The lagged daily DJIA return improves the explanatory power of a model with only the contemporaneous DJIA return. This improvement is modest, however. Ordinary least squares enables an unbiased estimate of the daily market return to be made given the daily return on the DJIA. The standard error of prediction, however, is relatively large for the four MSCI stock market indexes. For the EAFE, Europe and Pacific Indexes, the standard error of prediction is about 1 per cent or more. Roughly speaking, the 68 per cent confidence bound on the estimated daily market index return is at least 100 basis points wide, and the 95 per cent confidence bound is at least 200 basis points wide.
Conclusion Daily change in the DJIA is a biased measure that systematically underestimates not only daily total return but also daily capital appreciation of the US stock market. The bias is greatest for total return because the DJIA is a capital appreciation index and not a total return index. Nonetheless, the bias is significant even for capital appreciation.
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Deconstruction of the indexes indicates that lower capital appreciation on the DJIA relative to the market is linked to level of diversification. The most plausible explanation is that the market includes a large number of stocks with smaller capitalisation than the Dow Jones Industrials. So the higher capital appreciation on the market indexes reflects a small-stock risk premium over 1962-2000. Barber and Odean (2000) provide evidence that individual investors who directly hold common stocks tend to tilt their portfolios toward small-caps. Thus, a broad equal-weighted market index is a more suitable guide for these investors than the Dow is. The DJIA overstates the risk of a well-diversified portfolio of US stocks. Daily change in the DJIA is significantly more volatile than either capital appreciation or total return on the market. Deconstruction of the indexes shows that the DJIA has significantly greater volatility than the market, primarily because it is less diversified than the market. Direct estimates based on the market model and the broadest US market index show that the Dow’s diversifiable risk is about 16 per cent of total risk. Thus, a broad value-weighted market index is a more suitable guide for investors in well-diversified mutual funds than the Dow is. With OLS models, the uncertainty for a market return estimate calculated from the observed daily return on the Dow can be quantified. Unfortunately, the standard error of prediction is relatively large for all versions of the market index and for a wide range of daily returns on the DJIA. Roughly speaking, the 95 per cent confidence bound on the estimated daily market return is at least 100 basis points wide for all US market indexes and is about 200 basis points wide or greater for the broad international market indexes covered in this paper. Thus, as
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an informal guide to daily market performance, the Dow is too noisy to be informative. Wealth indexes show that the Dow significantly underestimates growth in capitalisation of the US stock market as well as nominal total wealth over 1962–2000. The Dow also understates the real return on the market and exaggerates the effects of inflation on an investor’s portfolio over long inflationary periods. If the Dow Jones Industrial Average provides a constant beacon for investors, then it is a misleading beacon that has more in common with the Sirens of Greek mythology than a modern lighthouse. Notes 1 Analysis of real returns and equity risk premiums leads to the same general conclusions as the nominal returns. The only important difference is that the location statistics for the real and risk premium series are shifted down relative to their respective nominal returns. Both the DJIA and the US market indexes, however, are adjusted in the same way for inflation or the risk-free rate. Thus, t-tests on means, sign tests on pairwise differences and F-tests on variances yield nearly the same results as reported in this paper for the nominal series. 2 The Dow Jones Averages 1885–1990 lists all composition changes in the Dow to 1990. Composition changed three times in 1991–2000. Caterpillar, Walt Disney and JP Morgan replaced Navistar International, USX Corp. and Primerica on 6th May, 1991 (Wall Street Journal, 28th May, 1996: R30). Hewlett-Packard, Johnson & Johnson, Travelers Group and Wal-Mart Stores replaced Texaco, Bethlehem Steel, Westinghouse Electric and Woolworth on 12th March, 1997 (Wall Street Journal, 13th March, 1997: C1). SBC Communications, Microsoft, Home Depot and Intel replaced Chevron, Goodyear Tire, Sears Roebuck and Union Carbide on 1st November, 1999 (Wall Street Journal Interactive Edition, 27th October, 1999). 3 On most US holidays (currently, about eight holidays per year), many non-US markets are open. In order to compare MSCI index returns with the DJIA trading day returns, index returns are calculated using only index values from calendar days on which the US markets are open. This approach increases the number of MSCI index returns that represent multiple calendar days. The result is a slight increase in the daily standard deviation for the period in this study, eg from 0.009474 to 0.009726 for the MSCI World Index. As a result, the t-statistics will be biased slightly
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downwards, and the hypothesis tests based on those statistics will be conservative. 4 The DJIA also understates the real return measured by US market indexes. Because the DJIA is a capital appreciation index, it fails to reflect the importance of cash dividends in offsetting the effects of inflation on investor wealth. For example, the DJIA grew to $3.27 in real dollars over July 1962–December 2000, but the value-weighted total return index on the S&P500 grew to $15.74 in real dollars. Thus, the real DJIA exaggerated the effects of inflation on an investor’s portfolio. Over the inflationary decade in the US from about 1973 to 1982, the real DJIA was substantially lower than its value on July 1962 and did not return to that level until 1987. Over the same period, real total return indexes on the market were substantially higher than the real DJIA. An investor watching the Dow might have been misled and believed that stocks were a poor investment for outpacing inflation over the long run. The real total return indexes, however, tell a different story. 5 To correct for possible autocorrelation in daily index returns due to asynchronous closing prices used to construct the market indexes, diversifiable risk is also estimated with a market model that includes leading and lagged market returns: Rd,t ⫽ ␣dM ⫹ +dM RM,t+1 ⫹ dM Rm,t ⫹ –dM RM,t–1 ⫹ d,t For this model (with conventional assumptions about the random error term), total risk can be written as
2d ⫽ (+2dM ⫹ 2dM ⫹ –2dM) 2M ⫹ 2dM+dM covar{RM,t, RM,t+1} ⫹ 2dM –dM covar{Rm,t, RM,t–1} ⫹ 2+dM –dM covar{RM,t,–1, RM,t–1} ⫹ 2d where market risk is the sum of the first four terms and 2d is the diversifiable risk for the DJI index. For each pair of DJI and market indexes, the estimate of unique risk is about the same whether the market model includes leading and lagging market returns or only includes contemporaneous returns as reported in Table 5. 6 The daily DJIA return has two outliers: ⫺22.61 per cent return on 19th October, 1987, and 10.15 per cent return on 21st October, 1987. Removing the returns for these trading days has almost no effect on the OLS results.
References Annin, M. and Licato, J. (eds) (2001) Stocks, Bonds, Bills and Inflation威 2001 Yearbook, Ibbotson Associates, Chicago, IL. Banz, R. (1981) ‘The Relationship Between Return and Market Value of Common Stocks’, Journal of Financial Economics, 9, 3–18. Barber, B. and Odean, T. (2000) ‘Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors’, Journal of Finance, 55, 773–806.
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Campbell, J., Lettau, M., Malkiel, B. and Xu, Y. (2001) ‘Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk’, Journal of Finance, 56, 1–43. Center for Research in Security Prices (2000) CRSP Data Description Guide for the CRSP US Stock Database and CRSP US Indices Database, The University of Chicago School of Business, Chicago, IL. Clarke, R. and Statman, M. (2000) ‘The DJIA Crossed 652,230’, Journal of Portfolio Management, 26, 89–93. Dow Jones (2001) The Wall Street Journal Guide to Stock Markets (an educational brochure distributed by Dow Jones), Dow Jones, New York City.
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Newbould, G. and Poon, S. (1996) ‘Portfolio Risk, Portfolio Performance, and the Individual Investor’, Journal of Investing, 5, 72–8. Pierce, P. (ed.) (1991) The Dow Jones Averages娀 1885–1990, Business One Irwin, Homewood, IL. Prestbo, J. (1991) ‘Introduction: Market volatility and the Dow’, in P. Pierce (ed.) The Dow Jones Averages娀 1885–1990, Business One Irwin, Homewood, IL. Roll, R. (1992) ‘Industrial Structure and the Comparative Behavior of International Stock Market Indexes’, Journal of Finance, 47, 3–41. Shoven, J. and Sialm, C. (2000) ‘The Dow Jones Industrial Average: The Impact of Fixing its Flaws’, Journal of Wealth Management, 3, 9–18.
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