More secrets of the DJIA Index revealed

Following on from my overall summary chart of 110 years of the DJIA last week (here or here),  there are yet more secrets to be revealed from the long term DJIA series back to 1896. It all confirms the picture that in this era of the bubble factory, we are still in for a heck of a ride – whether we go up first, or down. Either way, the additional detail below should make it clear that discretion is the better part of valour for the foreseeable future.  This detailed analysis further serves to demonstrate that volatility has been reliably consistent for the past 110 years and now is no different. The fact that volatility in 2008 is the same today as it was in 1908 provides a sobering reminder of what might yet be in store.

Leading on from last weeks DJIA summary, I discovered on the 10base LOG chart that there was an approximate 16.6year bounding box with 43% depth that could be repeatedly applied throughout the entire DJIA price history – stacked vertically and added horizontally. I have since discovered this was no accident, and below shows you how it was derived, in both time and price.

Log charts are excellent for analysing long time series data which contains any signs of underlying compounding growth (CAGR). A straight line on a log chart (of any base) is a line of constant underlying annual growth. A 10base LOG chart is the most popular and has major axes at factors of 10 being 1,10,100,1000 etc configurable by design. Since the DJIA appears predisposed to a standard 10base LOG form, taking any one major axis intervals (10 to 100 say) and dividing this into quartiles or quintiles reveals more secrets about the DJIA price history. It explains the recurring and persistent range of movement in the index.

As shown below –

•  Showing a standard Log10 interval divided into equal quartiles and quintiles. Remember measured moves in LOG thinking is in multiples, not linear deltas. So Q1 = 1.778xbase for quartiles, or 1.585 for quintiles (rounded).
• This conversion means a 10x LOG range is displayed as 4 equal ranges of 1.778 (=77.8% move), or 5 equal ranges of 1.585 (+58.5% move). When displayed on a chart, there are sufficient indications of DJIA targeting both quartile and quintile levels on moves up and on pullbacks. A discerning eye with see these as price targets in the trends of the index charts.

QUARTILES & QUINTILES? WHAT THE?

Calculating the quartiles or quintiles of a 10Base LOG is easy enough, since they are 4th or 5th root of 10. For example, find the interval Y where 10xY xY xY xY = 100 reduces to Y^4 = 10, Y = 10^(1/4) for quartiles, Y=10^(1/5) for quintiles.

Remembering on a LOG chart, the ratios of vertical height of boxes and lines remains the same wherever they are placed on the chart. This then identifies measured moves as ratios (relative fixed % price movements), and not deltas. Y = 1.778 for quartiles, Y=1.585 for quintiles. So any quartile box based on 10.0, with the top at 17.78 has a volatility of 43.8% since the base value is always going to be 56.2% of the value at the top. Hence the 43% repeating box in the previous DJIA history is in fact a quartile of a major range (between major axes). Thus 4 boxes makes a 10x vertical movement from 10 to 100, 100 to 1000 etc (1.778 x 1.778 x 1.778 x 1.778 = 10). Doing the exercise was simple enough to do for both quarts and quints while I completed it, and found the DJIA price movements are more respectful for quintiles than quartiles in some situations.

It then occurred to me it would be extremely simple if Excel could base the LOG scale on either 1.778 or 1.585, but the MS designers only factored in entering whole integers to configure the LOG base in Excel charts. But using base2 go it close, and actually makes a LOG chart easier when you get used to it (try it out for yourself). To work around this you simply have to extract the linear graph by running the DJIA index values through some simple log(DJIA,1.778) or log(DJIA,1.585) maths on the raw data in Excel 2007. You can then plot the result on a linear graph. Doing it this way you cannot pick off direct readings and must convert targets back to DJIA via (1.778)^(num) = raised to the power of etc.

For simplicity, I have created separate charts of DJIA using LOG bases in quartiles and quintiles (not the standard 10base) below. You can see subtle minor differences in support/resistance levels depicting targets for ranges of movement. Compiling total linear regression charts of the 2 LOG adjusted bases for the whole of data from 1896 to Jan 2012 we get the following.

QUARTILES – every increment of 1 is a quartile of 10Base log chart (4= 10x, 8= 100x etc), fitted with LOG regression analysis

QUINTILES – every increment of 1 is a quintile of 10Base log chart (5= 10x, 10= 100x etc), fitted with LOG regression analysis

– Note, at first glance these charts appear identical, however you will notice the levels where the DJIA resists and pulls back to align with quartiles on large volatility during consolidation, and quintiles on trending upwards movements. In a 10x movement which has occurred clearly twice since 1932, a linear chart does not identify these subtleties in movements because the deltas for 1000 in 1983 to 10,000 in 2000 are 10x larger than the previous upleg into 1966 from 100.
– Again, remember that the volatility has been consistent throughout the entire history of the DJIA index. A basic law of number numbers commonly encountered in technical analysis. The underlying DJIA CAGR is 5.0% (rounded form of 4.97%).

The other lovely discovery was finding the 4181 trading day cycle period (the red vertical lines on the charts) – which was extracted from the DJIA trend, is a Fibonacci number. This is the 16.6year width of the blue box from last week. This cycle period lines up perfectly with alternating periods of no growth and real growth as indicated by the yellow amber sideways arrows, and growth periods indicated by green arrows.

Each rise of unit on the quartile chart is a move +77.83% of the previous level (x1.7783). This means a fall of 1 quartile is a retrace of 43.7%, back to a level 56.2% per quartile of move down. It shows the magnitude of the 1929 market crash being very nearly 4 quartiles – a factor of 10x reduction in the market index from 1929 to 1932.

The completed annotated DJIA chart – (using LOG based quartiles)

• Graph notated showing alternating periods, highlighted volatility, and amount of growth in quartile boxes (in blue). Similar can be done using the quintile LOG chart, but the repeating range is predominantly in quartiles.

Consolidation is easy to explain via the distribution and redistribution of gains achieved from the preceding real growth period. The slope of each growth period is clearly in excess of the fundamental growth in underlying value and the equity market outperforms to a point where further upside price extension is not possible (seen as too risky by comparison of risk/reward). Profit taking and a reduction in risk taking sees the market indexes pull back, consolidating for a period until average growth regresses back closer to underlying fundamentals. The length of the consolidation period would be proportional to the excess rate of return of the index during the growth phase. Further supporting that we are in for an extended period of no real index growth.

Explicit confirmation of the DJIA moves to 100,1000,10000 comingling with the 4181 trading day cycle is this. I extracted the cycle based around the 1000 level, the next projected full growth cycle following the 1966-1982 consolidation ended to the day it broke 10,000 for the first time in March 1999. The 1982-1999 growth into the first bubble of the bubble era was start to finish nothing but upwards trend. The so called ‘crash’ of 1987 is insignificant in magnitude to what we are living through today. If people had realised at the time, it was nothing but a blip on the radar and simply a pullback in any other previous era. The machinery sure works in mysterious ways doesn’t it?

It is then possible run your DJIA daily or hourly data through a LOG filter on a continuous basis for entry into any linear charting package. Easy peasy.

CUT TO THE CHASE! WHERE ARE WE?
It should be obvious by now that it becomes simple to identify several tag points from the above. We must be in a sideways consolidation period, about 75% the way along. For those with no clue or interest in any of the above, as best I can estimate we are as per the chart below.

– 100 years later, do we find ourselves back in the same spot?

The current 4181 trading day cycle is a consolidation period following the rise into DJIA 10,000 that is due to cycle end in October 2015 for what might be the start of an upwards cycle. That is, if history is anything to go by.

Where do I think we are? As of Jan2000, we have just completed another 10 fold increase in the DJIA index, as a result of a clear upleg with excess rate of growth that was almost 3% steeper that the growth out of the 1932 low. This has ended in what appears to be a failed top similar to 1900-1910. So it stands to reason we are in another sideways consolidation period. Using the 4181 cycle lines, the current cycle period expires approximately Oct2015. The rise that has occurred during the previous cycle is the steepest sustained move in the DJIA history analysed.

Being one century after the 1900’s, and heading back into the equivalent of 1930, it now seems obvious. The 20th century completed a large expansionary phase of historic technological advance on the back of the industrial revolution of the 19th century. We are now in the strong hold of rampant monetary stupidity feeding banks with mindless public capital to be simply blowing bubbles. Just as the early 1900’s were to the 1800’s, so too is this phase of the 21st century. Nothing has changed. We are in the 21st century version of 1910 in my opinion, heading into 2030 déjà vu all over again.

It poses a question for the bullish case of the DOW into 14700 – is this going to coincide with celebrations of 100 years of the US Federal Reserve in Dec2013 to mark the magnificence of a century of monetary genius and stability? It fits within the projected range and timing very neatly. It wouldn’t look good to backdrop the celebrations in Dec2013 with the DOW tanking now would it? You can imagine entire departments competing for the catch-phrase for the event now.

CONFIRMATION
As confirmation, I then extracted the current upleg from Dec1974 low to Jan2012 (current) for comparison of the linear regression analysis to the previous completed upleg from 1932 to 1982. I picked an approximate similar period of the 1966-1982 consolidation cycle of Jan1973 for the side by side comparison of the 2 uplegs, shown below.

Current upleg from Dec1974 to Jan2012 – linear regression of Log quintile DJIA

Compared to similar status of Jul1932 to Jan1973 upleg – linear regression of Log quintile DJIA format

Note: the different CAGR’s calculated, on the average DJIA growth rate over the period 1932-1973 was 6.9% p.a. Presently the most recent upleg from 1974 is running at 9.5% p.a., an extra 2.6% per annum higher! Without sustained and underlying organic growth in tangible asset values, we were a long way overvalued by comparison.

For clarity, the same linear regression performed on standard linear (raw) data (not LOG) looks like this –

– for information only, but generally for any linear regression, backtesting the underside of the linear regression average is a low risk sell signal. Note the LOG regression analysis picks up the failure of the trend much earlier.

Since we know what happened after Jan1973, it needs little imagination to what might lay in store for the DJIA from Jan2012 in light of the ongoing maelstrom of financial incompetence. If we do go up here, the previously identified upside target of 14700 would be obvious. However, DJIA 12300 area remains the major local pivot for upside continuation, or downside pullback.

One tipping factor within the current weak climate would be the financial sector galvanising together to provide the good ship US with a successful 100 year celebration of the Federal Reserve in Dec2013. While there is absolutely nothing that suggests to me sanity is prevailing with profligate financial self-interest elsewhere, timing a market drop before or during the celebrations would not bode well for cynics of an independent Federal Reserve. In any event, more downside seems assured at some future point in time however limited it might be.

BUT WAIT, THERE’S MORE
In this analysis, I’ll even throw in a set of steak knives. Doing a bit of photoshop pasting with an overlay of Doug Shorts Q Ratio analysis (sourced here), we get this interesting result –

The above shows that the previous growth cycles have all commenced on a Q Ratio low, as it did in 1983, and would also be timed similarly for lows in other market value ratios such as P/E etc. It further confirms the current level of the Q Ratio after the growth period into 2000 is yet to reach anywhere near the low levels of the 3 previous consolidation periods. Interestingly, it shows the bubble factory commenced prior to 1996, since the Q ratio was already at all time highs going higher, which coincides with the unprecedented CAGR in the DJIA at the time. Historically, the underlying growth in tangible value was probably growing at an unprecedented rate also, but was obviously not sustainable and likely at a lesser and divergent rate. Easy enough to see looking back from the lofty perch of 2012 with perfect 20/20 hindsight.

Just in case the markets have magically offset the Q Ratio low into a higher level, it would indicate the recent low at the arithmetic mean of 0.71 as the last remaining positive consideration for a bull trend continuation. A Q Ratio below this arithmetic mean again and it signals the continuation of the sideways consolidation into – which is what the rest of this analysis indicates.

IT’S TIME TO GO …
The last two charts indicate how all this analysis also relates to the S&P500 index (same equal consideration). Using only the data to 1950 on a quintile LOG base with linear regression analysis, we get –

•  which shows the similar 100 fold increase (2x major blocks of 5 quintiles) in the index aligning with the DJIA move during the same timeframe. Interestingly, the form of the S&P500 history differs slightly, in that the 100 fold increase into 1585 as a quintile 16.0 level.
•  Also unsurprisingly is the much referenced crash of ’87 is likewise just another blip on the radar for the S&P500. Underlying S&P500 CAGR of 7.2% over the period 1950-2012.

Taking the difference (delta) of 2 Logs shows the difference in growth rates over time, which is what I did with the chart below expecting to see more or less a constant (flat) relationship. The delta of two quintile Log charts using DJIA less S&P500 since 1950 (same time frames, below), shows the DJIA underperformed the S&P500 in the 33 year period 1950 to 1983 tech era bubble, whereas since 1983 the DJIA has outperformed the S&P500.

The squggly area just prior to the bursting of the 2000 tech bubble would probably make for interesting analysis further down the track. This area is not just noise and indicates a decoupling of the DJIA and S&P500 indexes. That’s for another day.

I will end (hooray, finally!) with this consideration regarding the current batch of financial wizards desperately grabbing for the public purse in 2008/2009 and continuing now in Europe still. When (and not if) there is another avalanche of now Too-Big-To-Bail failures due to more bubble popping prices on the back of evaporating liquidity propagated by the lack of effective regulation. If history repeats, nothing is being avoided by current the profligate monetary actions.

Remember to ride the waves created by the largest trend momentum, whether up or down. Hopefully the information above serves as a large enough signpost for others. The next time a gun gets metaphorically held to the collective head of the public, dig out this post. I figure it will be a timeless reference for the next so-called ‘crash’, at least for me anyhow.

Regards,