# 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.

# Gold seasonality

Does the price of gold exhibit a monthly seasonality?

[Here we update our previous analysis of gold seasonality.]

On 17 March 1968 the system that fixed the price of gold at USD35.00 collapsed and the price of gold was allowed to fluctuate. Let’s have a quick look at the chart to see how gold has performed since it floated in 1968.

Since 1968 when gold floated, its price has grown at a CAGR of 7.7%.

Let’s look now at its monthly seasonality.

The following chart plots the average price returns for gold by month since 1968. For example, since 1968 the average return of the gold price in January has been 1.2%.

And the following chart plots the proportion of months that have seen positive returns. For example, in 60% of years since 1968 gold has had positive returns in February.

It can be seen that since 1968 gold has on average been strong in February, September and December. The weak months for gold have been March and October.

This profile of behaviour would seem to have some persistency as the same pattern can be seen for the more recent period 2000-2017, for example the following chart plots the average month returns from 2000.

The main new features recently have been the strength of gold in the months January, August and November, and the weakness in December.

## Gold and equities

The following chart shows the ratio of the FTSE All Share Index to gold (priced in sterling) since 1968. One can regard the chart as the UK equity market priced in gold.

The ratio peaked at 18.8 in July 99 and then fell to a low of 2.3 in September 2011. Since 1968 the ratio average is 6.1

The above is an extract from the newly published UK Stock Market Almanac 2018.

# Sell in May (2017)

It’s sell in May time again!

And time for many articles appearing on whether to actually sell in May or not. So, should one sell?

The issue is a little tricky. It is certainly the case that equities over the 6-month period May to October tend to under-perform the November to April period. (We have covered this in many previous posts.)

However, just because the market under-performs May-October doesn’t necessarily mean that the market experiences negative returns over these summer months.

The following chart plots the 6-month May to October returns for the FTSE All-Share Index since 1982.

As can be seen, since 1982 the market has actually risen more often than it has fallen over the May to October period –  equities have had positive returns in 20 of the past 35 years. The market has risen in ten of the last 14 years. And last year, 2016, the FTSE All-Share increased 10.1% May to October.

So, the case is not necessarily looking strong to sell in May. Especially, if one adds in the argument that being out of the market an investor will forego any dividend payments over the May-October period (and at a time when interest rates are very low).

An argument in favour of selling might be that, although the market often sees positive returns in the period, when the market does fall, the falls tend to be quite large. So, since 2000, the average return May-Oct has been -1.1%. Admittedly, this is quite heavily influenced by the fall in 2008, which might be regarded as something of an anomaly. But over the longer periods, the average returns are negative as well (-0.1% from 1982, and -1.0% from 1972).

In conclusion, whether to sell in May should likely depend on an individual’s attitude to risk and their transaction costs.

Further articles on sell in May.

# 100 years of the FTSE All-Share Index since 1917

The following chart plots the annual returns of the FTSE All-Share Index for the 100 years from 1917 to 2016.

The final bar in the chart plots the annual return for the index in 2016 (+12.3%). The Y-axis is truncated at +/-50% for legibility. In two years the returns were outside this bound: in 1974 the index fell 55%, and in 1975 the index rose 136%.

Over the 100 years since 1917 the average annual return for the index has been +7.0%.

The standard deviation has been 21.5, which means that for 66% of the years the return was between -14.5% and +28.5%.

The index saw positive returns in 65 of the 100 years.

The following chart is similar to the above, but ranks the returns in order of size.

The return of 12.3% in 2016 ranks 35th in order of annual returns for the index in the last 100 years.

# Monthly seasonality of oil

Does the price of oil display a seasonality pattern?

[We last looked at this in 2014 in this article; time to update the figures.]

To briefly recap, the original study found that since 1986 the price of oil displayed a seasonality for two parts of the year-

• March-September when WTI is strong, and
• October- February when the WTI price has been relatively weak

Let’s see if this is still the case.

## Mean returns

The following chart plots the average month returns of the price of WTI (West Texas Intermediate) for the period 2000-2016.

A two-part pattern for the year is still observable, but the periods have shifted slightly.

As can be seen, since 2000, WTI month returns have tended to be high in the period February to June. The strongest month of the year in this period has been February with an average return in the month of 4.8%.

The weak part of the year has also shifted: to September to January. The weakest month has been November, with an average price return of 3.2%.

## Positive returns

The following chart plots the  proportion of monthly returns that were positive over the same period.

This pattern of positive returns largely supports the preceding analysis.

Since 2002 WTI has seen negative returns in February in only 3 years.

By contrast, September has seen positive returns in only 6 years since 2000.

The new seasonality pattern can thus be summarised as-

1. February-June when WTI is strong, and
2. September-January when the WTI price has been relatively weak

## Cumulative performance

The following chart plots the cumulative performance of WTI for two portfolios:

1. WTI (Strong Months) – this holds WTI in just the strong months identified above (February-June), and is in cash for the rest of the year
2. WTI (Weak Months) – this holds WTI in just the weak months (September-January), and is in cash for the rest of the year

For benchmarking purposes WTI (continuous holding) and the S&P 500 Index are also plotted. All series are re-based to start at 100.

Starting at 100 in 2000, the WTI (Weak Months) portfolio would have fallen to a value of 16 by 2016. The S&P 500 would have a value of 145, and a continuous holding in WTI a value of 182. But the WTI (Strong Months) portfolio would today have a value of 1047.

Further articles on oil.

# US Democrat/Republican president portfolios

## Market performance by president

The chart below shows the performance of the UK market (FT All-Share index) over the periods the respective US presidents were in office.

From the point of view of the UK market the best president was Jimmy Carter – the market rose 145% during his 4 years as president. The worst spell was the second term Richard Nixon when the market fell 42%.

## Market performance by party of the president

The chart below plots the values of two simulated portfolios both starting with a value of 100 at the 1948 US presidential election:

• Democrat portfolio: only invests in the UK stock market when there is a Democrat in the White House, and is in cash when the president is a Republican.
• Republican portfolio: reverse of the above.

The two portfolios have largely tracked each other closely until the 2008 election of Barack Obama. From this period, the Democrat portfolio performed strongly, such that by 2016 this portfolio had a value of 1344 compared with a value of 639 for the Republican portfolio.

# UK equities and the US presidential election cycle

The chart below shows the 4-year US presidential election cycle (PEC) superimposed on the FT All-Share index from 1956. The vertical bars indicate the timing of the November elections every four years.

It can be seen that on occasions the US presidential election has (approximately) coincided with significant turning points in the UK market; notably those elections in 1960, 1968, 1972, 1976,2000, and 2008.

## Returns in each year of the PEC

The following chart shows the average annual returns for the FT All-Share Index for each of the four years in the US presidential election cycle. PEC(1) is the first full year after a presidential election, PEC(4) is the election year.

Typically, presidents have primed the economy in the year before elections [PEC(3)] – or, at least, stock markets have expected them to do so.

And the following chart plots the proportion of years that saw positive returns in each of the four years in the PEC.

For the 15 presidential cycles from 1948 to 2008, the FT All-Share Index saw positive returns in every third year of the cycle. But in the two cycles since 2008, the Index has had negative returns in PEC(3).

## US presidential election data

For reference below is data on the US presidential elections since 1948.

 Election date Elected President Party Popular vote(%) Electoral vote 02 Nov 1948 Harry Truman Dem 49.6 303 04 Nov 1952 Dwight Eisenhower Rep 55.2 442 06 Nov 1956 Dwight Eisenhower Rep 57.4 457 08 Nov 1960 John Kennedy Dem 49.7 303 03 Nov 1964 Lyndon Johnson Dem 61.1 486 05 Nov 1968 Richard Nixon Rep 43.4 301 07 Nov 1972 Richard Nixon Rep 60.7 520 02 Nov 1976 Jimmy Carter Dem 50.1 297 04 Nov 1980 Ronald Reagan Rep 50.7 489 06 Nov 1984 Ronald Reagan Rep 58.8 525 08 Nov 1988 George H. W. Bush Rep 53.4 426 03 Nov 1992 Bill Clinton Dem 43.0 370 05 Nov 1996 Bill Clinton Dem 49.2 379 07 Nov 2000 George W. Bush Rep 47.9 271 02 Nov 2004 George W. Bush Rep 50.7 286 04 Nov 2008 Barack Obama Dem 46.2 365 06 Nov 2012 Barack Obama Dem 48.1 332

# Equities in US presidential election years

The 14 charts below show the performance of the FTSE All-Share index over the 12 months of a US presidential election year. For example, the first chart shows the January-December performance of the UK market in 1960, the year John Kennedy was elected President of the United States. The dashed line in each chart indicates the date of the election.

Historically, the UK market tends to rise in the few weeks leading up to the election.

The following chart plots the annual returns of the FT All-Share Index in years of US presidential elections.