More interesting math and projections

In the previous essay price time areas were developed for the most recent bear and bull (ongoing) markets.  This follow up will look back to further bulls and bears to see how the QQQs and SPX behaved relative to the natural geometric growth measurements.

According to closing highs and lows, QQQs show striking growth patterns relative to the square root of 2 (1.414) and the square of the square of two or 2. 

The yellow highlighted number is the 2000-02 bear's area divided by that of the 1999-2000 bull.  Nearly exactly 2.  But the green highlighted periods did not show growth strictly according to the sqrt(2) or its multiples.  Very close, but not exact. 

Added to that table are projections for QQQs that would drive price to the next logical geometric milestones.  There are three projections that demonstrate how later dates will result in a lower projected closing price on each successive date.  Those projections started with what Frost and Prechter considered a debatable formation, an expanding ending diagonal triangle in QQQs (the black lines are the boundaries).

Aside from the well formed boundaries, there are 3 prominent Gann angles that are converging.  The dark grey downward sloping 1 cent X 2 angle is from the all time high.  The purple upward sloping angle is the zero line 2.236 cent X 1  (2.236 is the sqrt(5) up from the all time low in 2002.  And the yellow upward sloping angle is the zero line 5 cent X 1 from the 2009 low.  They converge at near the projections shown in orange in the table above. I believe these are powerful angles that will provide extreme resistance should the market choose to attempt these levels.  Yesterday QQQs closed at 86.60 so the projections are very unlikely to occur in the coming week.  But that's the math.

Now SPX.  Same table.

Similar to QQQs, the ratios in green are not perfect.  The 2002-07 bull is slightly more than the perfect doubling of the 1X1 square; we'd expect 2.000 not 2.06.  And I can't make heads or tails out of the .319 for 2007-09 bear.  However, if you relate 2007-09 bear to 2000-02 bear (697400 / 459427) you get 1.51.  Very close to the geometric and harmonic 1.5. 

Again, projections for dates next week in the high closing area of 1907 (Monday) to 1904 (Friday).   And again, these levels comport with a conventional ending diagonal triangle that was first posted about a month ago:

The red zero line $1 X 1 angle near perfectly bisects the triangle and, on Monday May 12, that angle is at 1890.  Projected closings in the area of 1907 (Monday) to 1902 (Friday) are just above that Gann angle and about 10 points below the upper boundary of the triangle.  Since we'd expect the intraday high to be higher than the high close (it certainly can't be lower), one might expect the all time high to be in the 1920 area.

Finally, the above tables can be replicated for extreme prices as opposed to closing prices and I've done that.  The projections would be 94.70-94.80 for QQQs highest intraday high and 1910 to 1912 for SPX.

And one more, one more thing.  Remember the green boxes in the tables?  Those prior years did not work out exactly right.  If I fudged in the prices that would force those statistics to exact geometric ratios in QQQs and then based projections on those base years, I'd all of a sudden have much higher projections in the 98.50 area.  That would delight me for a host of geometry reasons.  But I do not remotely consider that result because of those 3 Gann angles in the QQQs chart....and the fact that QQQs closed at 86.80 on Friday. 

Sheesh, just to get to 94.80s you need a 9% rally in 5 trading days....there (much less 98s) would be comparable to the last 4 days of the run-up to the dot.com bubble top (16% in 4 trading days).  Rotsa ruck.

Jim