# Long-term trend of the Dow Jones Industrial Average

What can the very long term tell us about the trend of the US equity market?

## 1900-2017

The chart below plots the month-end values of the DJIA (Dow Jones Industrial Average) from 1900 to the present day.

In January 1900 the DJIA had a value of 66 points, and in December 2017 (the time of writing) a value of 24,651.

The above chart may be useful as a visual record of actual values of the DJIA, but it is not very helpful in discerning any underlying trend of the index.

Because the values of the DJIA vary so greatly over the period from 1900, it is more useful to plot them on a semi-log chart, where the Y-axis has a logarithmic scale. This is done in the following chart.

This starts to look more useful.

To this chart we can now add a trendline (as has been done in the chart below).

Regression analysis was used to fit a straight line of best fit to the values of the DJIA.

[Side note: although the trendline in the above chart is a straight line, it is useful to remember that this is an exponential line of best fit because the Y-axis is logarithmic.]

Obviously, the trendline does not perfectly match the DJIA values, but the fit is not bad. R-squared (R2) is a statistical measure of how close the data are to the fitted regression line. In this case the R2 value is 0.93. which is surprisingly high given the supposed nature of random-walk equity prices.

We can use the equation of the fitted line to calculate trendline values of the DJIA at any time, including the future. The following table gives the calculated trend values for the current day and a few arbitrary dates in the future.

The calculated trend value of the DJIA for today (15 December 2017) is 11,941. The current actual level of the DJIA is 24,651, which means the DJIA is currently trading at a 106% premium to its trend value. Or, expressing this another way, the DJIA has to fall 52% to equal it’s long-term trend value.

As already mentioned, the table also calculates future trend values for the DJIA. For example, the DJIA trend value in December 2020 will be 13,928. And by December 2030 the DJIA trend value (23,142) will still be just below the current actual level of the DJIA index.

How much faith can we have in these calculated trendline values?

Well, the above trendline was fitted to DJIA data for the period from 1900 to today. Let’s see how the calculations change if we fit a trendline to DJIA data from 1919, just after the First World War.

## 1919-2017

So, the following chart is similar to the previous chart, except this time the time range is shorter at 1919-2017.

By shortening the time range, the line of best fit now has an R2 of 0.94, a slight improvement on that for the previous chart (0.93). This means that we can have slightly more confidence that the DJIA actual values will be close the calculated  trend values.

Visually, we can see that the DJIA has been closer to this trendline in the last few years since the financial crisis in 2008, than the trendline calculated for the period from 1900..

As before, the following table shows the trend values calculated using the equation of the new line of best fit on the DJIA data from 1919.

This time the calculated trend value of the DJIA for today (15 December 2017) is 15,129. With the current actual level of the DJIA at 24,651, this means the DJIA is currently trading at a 63% premium to its trend value. Or, alternatively, the DJIA has to fall 39% to equal it’s long-term trend value.

So, first, it would seem that the trendline calculated on data from 1919 gives a closer approximation for today’s actual value of the DJIA than that calculated from 1900.

And, second, it seems that the trendline equations are quite sensitive to the exact time period analysed. In which case, let’s look at another example, this time DJIA data starting from 1946, just after the Second World War.

## 1946-2017

The following chart is as before, but this time the time range analysed is shorter: 1946-2017.

The R2 (at 0.95) has again marginally increased for this line of best fit on this shorter period. Which suggests that the calculated trendline better fits the actual DJIA data.

And, visually, we can see that the  DJIA has been even closer to the trendline in the last few years since the financial crisis in 2008 than for the previous two time periods.

Broadly, the DJIA index traded very close to the trend line in the years 1946-1954, then the index traded above the trend. But from 1965 the index traded largely in a sideways pattern, and so by 1969 it crossed over the rising trendline to trade beneath it. Although the great bull market started in 1982, it wasn’t until 1995 that the index moved definitively back above the trendline. The market fell during the dot-com crash, but despite that the DJIA bounced off the trendline and did not fall below it. The index managed to stay above the trendline until the credit crunch in 2008, when the DJIA crashed down through the trendline. By 2011, the index had recovered to the trendline and then traded close to it for a number of years until the start of 2017 when the DJIA grew strongly and diverged from the trendline.

The following table shows the trend values calculated using the equation of the new line of best fit on the DJIA data from 1946.

This time the calculated trend value of the DJIA for today (15 December 2017) is 19,396. With the current actual level of the DJIA at 24,651, this means the DJIA is currently trading at a 27% premium to its trend value. Or, alternatively, the DJIA has to fall 21% to equal it’s long-term trend value.

And now, with this new trendline, the calculated trend value will be close to the current level of DJIA by December 2020.

So, the trendline of DJIA data from 1946 is not doing a bad job at estimating the current actual value of the Index.

Finally, let’s look at what happens when we calculate a trendline for the DJIA from 1971 – a somewhat arbitrary date, but chosen as the year that the Bretton Woods system ended and the US dollar became a fiat currency.

## 1971-2017

The following chart is as before, but this time the time range analysed is shorter: 1971-2017.

As can be seen, for fairly long periods the DJIA traded close to the calculated trend values. And, for the first time in this analysis, the calculated trendline is currently above the level of the DJIA.

Again, and finally, the following table shows the trend values calculated using the equation of the new line of best fit on the DJIA data from 1971.

For this final period, the calculated trend value of the DJIA for today (15 December 2017) is 25,733. With the current actual level of the DJIA at 24,651, this means the DJIA is currently trading at a 4% discount to its trend value.

## Summary

The following table summarises the  premiums that the DJIA is currently trading at over its calculated trend value, for the four different time periods.

For example, as a reminder, at the time of writing the DJIA Index is trading at a 106% premium to its trend value as calculated for data from 1900.

So, which trendline do you choose?

That, of course, is the big question.

If you think that data from the period 1900 to today is representative of the long-term trend of the DJIA Index and, importantly, that this trend is likely to continue, then this is the trendline to choose, with its indication that the DJIA is currently 106% “over-valued”. As such, you will be concerned that the DJIA is currently at risk of a large fall to move back towards its long-term trend value.

Alternatively, if you think that the time period of 1971 to today is more representative of the long-term trend of the DJIA Index, then you will be happy with the current level of the DJIA as it close to its trend value.

# Stock Index changes (other indices) – paper review

Previously, we have reviewed the academic literature on index changes for the FTSE 100 and S&P 500 indices; here we present a brief review and listing of academic papers on other indices.

Generally, most of the papers found similar effects for companies added to or deleted from indices as has previously been reported for the S&P 500 and FTSE 100 indices. Namely, shares experience positive abnormal returns and increased trading volumes following the announcement of their addition to an index.

An exception was Beneish and Gardner (1995) who found that share prices and volumes were not affected for new DJIA companies (probably due to a lack of index funds associated with the DJIA) although shares saw big falls when deleted from the index.

Shankar and Miller (2006) found that shares experienced greater increases (declines) when companies were introduced (deleted) from the series of S&P indices, than those companies that just moved between S&P indices.

One of the greatest points of difference is whether the index change effects on shares are permanent or temporary. The papers finding the effects permanent were: Hacbedel (2007) with respect to the MSCIEM, and Liu (2011) for the Nikkei 225. While those finding the effects temporary were: Shankar and Miller (2006) for the S&P SmallCap 600 Index,  Chakrabarti, Huang, Jayaraman and Lee (2005) for the MSCI indices, and Biktimirov, Cowan and Jordan (2004) for the Russell 2000.

## INDEX (of papers listed below)

[Papers listed in reverse date order; indicates major paper.]

What Happens When a Stock is Added to the Nasdaq-100 Index? What Doesn’t Happen?
Authors [Year]: Susana Yu, Gwendolyn P. Webb, Kishore Tandon [2014]
Journal [Citations]:
Abstract: Additions to the Nasdaq-100 Index are based primarily on market capitalization rather than on judgments about a firm’s stature in its industry. We analyze abnormal returns upon announcement that a stock will be added to the Nasdaq-100 Index in a multivariate analysis that incorporates several possible alternative factors. We find that only liquidity variables are significant, but that factors representing feedback effects on the firm’s operations and level of managerial effort are not. This evidence suggests that additions to the Nasdaq-100 Index are associated with liquidity benefits but not with certification effects of the type associated with additions to the S&P indexes.
Ref: BA006

Market reactions to changes in the Nasdaq 100 Index
Authors [Year]: Ernest N. Biktimirov and Yuanbin Xu [2013]
Journal [Citations]:
Abstract: We examine stock market reactions to changes in the Nasdaq 100 index. We find asymmetric price response accompanied by a significant increase in trading volume on the effective date. Firms added to the Nasdaq 100 Index experience significant increases ininstitutional ownership, the number of market makers, and the number of shareholders. In contrast, firms removed from the index show significant decreases in the number of institutional shareholders. Additions to the Nasdaq 100 Index also show significant increases in four liquidity measures, whereas deletions demonstrate significant decreases in two liquidity measures. These changes in liquidity are related to the abnormal return on the announcement day. Taken together, the results provide support for the liquidity hypothesis.
Ref: AA723

# Super Bowl Indicator

This coming Sunday is Super Bowl XLVIII.

One of the most famous market predictors in the U.S. is the Super Bowl Indicator. This holds that if the Super Bowl is won by a team from the old National Football League the stock market will end the year higher than it began, and if a team from the old American Football League wins then the market will end lower.

Unlikely?

Well, it certainly sounds far-fetched that a game of mutant rugby could affect the economy and stock market. However, in 1990 two academics published a paper (Krueger and Kennedy, 1990) finding that the indicator was accurate 91% of the time.

And then in 2010 George Kester, a finance professor at Washington and Lee University, published a paper (Kester, 2010) with new research that found that the Super Bowl Indicator still worked (although its accuracy had fallen to 79%). Kester also calculated that a portfolio that switched between stocks and treasury bills governed by the Super Bowl Indicator would be worth twice that of a simple portfolio invested continuously in the S&P 500.

And the connection between American football and the UK stock market is…?

Seeing how closely correlated the U.S. and U.K. stock markets are, it might be interesting to see how the Super Bowl Indicator applies to the U.K. market.

The following chart shows the annual returns of the FTSE All Share index since 1967 (when the Super Bowl started). The Y-axis has been capped at +/- 50%, which truncates the bars for the years 1974 (-55%) and 1975 (+136%). The years for which the Super Bowl Indicator failed to accurately predict the direction of the market has been indicated with white bars in the chart.

As one can see, the indicator got off to a great start in the years following 1967, but recently its record has been patchy. Overall, the indicator was accurate in 72% of years (only slightly less than its accuracy rate in the US).

Unfortunately a paper (Born and Acherqui, 2013) published last year has rather spoilt the fun. The authors found that the ability of the Super Bowl Indicator to forecast the market had reduced to almost zero in the years since publication of the Krueger and Kennedy paper in 1990.

## Market around the time of the Super Bowl

The chart below shows the market behavior around the time of the Super Bowl; the bars represent the average daily returns in the FTSE All Share Index since 1967 for the three days before, and three days following, the Super Bowl (which always takes place on a Sunday).

The average daily returns in the index for all days since 1967 was 0.03%; we can see therefore that the market is abnormally weak two days before a Super Bowl and abnormally strong one day before it.

# Quantifying the relationship between news and trading volume and price

## Summary

A recent academic paper finds evidence for a relationship between the volume of news mentions of certain stocks and the volume of trading size of price change in those stocks.

## Content

There have been quite a few papers on the relationship between news or information searching and market movements. But this paper, Quantifying the Relationship Between Financial News and the Stock Market, tries to measure the relationship.

To research this the authors, Merve Alanyali, Helen Susannah Moat and Tobias Preis, studied daily issues of the Financial Times for the period 2007-2012. (As a by-product of this analysis they found that 891,171 different words appeared in the FT over this period!)

They tracked mentions of the companies in the Dow Jones Industrial Index and the corresponding movements in volume and price for these companies on the NYSE for the same day and the following day.

They found evidence for a relationship between the number of mentions of a company on a day and both the volume of trading and size of price change for a company’s stock on the same day.

The following figure from the paper shows the ranking of DJIA companies according to the correlation between FT mentions and absolute movement in the stock price.

The strongest correlation among the DJIA companies they found was for Bank of America.

The paper concludes with the qualification that their analyses do not allow them to draw strong conclusions about whether news influences the markets, or the markets influence the news; but they propose that movements in the news and movements in the markets may exert a mutual influence upon each other.

## Citation

Alanyali, Merve and Moat, Helen Susannah and Preis, Tobias, Quantifying the Relationship Between Financial News and the Stock Market. Sci. Rep. 3, 3578; DOI:10.1038/srep03578 (2013)