The trading community is relentless in its pursuit to find out how
and why the market turns. Bull and bear markets surge relentlessly along
their path until one day they reverse course and set sail in an
entirely new direction, never looking back. Markets march to their own
drummer with a language all their own.

Certainly, fundamental valuations play their part in determining
where we might be in the cycle. A price/earnings ratio can tell us
whether the market, or particular stock, is cheap or expensive at a
specific point in time, but it has zero capability of telling us when
the turn will come.

To solve this riddle, many turn to technical analysis. Technical
analysis is the study of price patterns and the visual representation of
emotion in the market. Examples of key technical tools are moving
averages, trendlines and Andrew’s pitchfork. While these are important
indicators, markets can and will overshoot their technical target, and
the study of patterns can give us only a rough idea of when and where a
market might turn.

So if fundamental and traditional technical analysis can’t nail the turn consistently, what can?

One class of analysis methods that works over time involves the
studies of W.D. Gann. These techniques have proven instrumental in
pinpointing and explaining market tops and bottoms. While it’s not
always clear why a time and price symmetry identified a market turn,
such symmetries do indeed exist. Gann, a well-known analyst from the
first half of the 20th century, considered the squaring of price and
time his most important discovery. He called it range and time squared.

In short, when the duration of a move squares with the extent of a
move, price trends tend to change. On that high level, it’s simple.
However, the proper application can be tricky. In “W.D. Gann’s master
forecasting methods,” (February 2011) we examined several aspects of
Gann analysis. Here, we’ll delve deeper into time and price studies.

**Discovering detail**

Markets are enigmas, and this attribute demands a great deal of
flexibility when working with price and time studies. For example, a
common manipulation is the decimal point — a Dow range of 7,728 points
can square with a rally 77 weeks down the road. A 21-year, 1,108-point
range in a market could identify a turn 1,108 weeks later — as it did
with the 1987 stock market crash. However, as complex as this appears,
markets can get even more complicated. But as it is with the study of
pivots, the Gann calculations themselves are decidedly simple.

Take, for instance, the 2011 bear market in the BTK Biotech Index
(see “Tech crunch,” below). The peak of this market was on May 13, 2011,
with a price of 1514.60. The bottom came in on Nov. 25, at 1,001.33.
The exact range is 513.27 points. What was the date of the high? It was
May 13, or 5-13. The market had a range that was equal to the date of
the origin of the pattern. This is just another example of how Gann’s
principle of time and price balance out.

What should be understood about this mystery is it does not
materialize every day. However, when it does, it usually leads to a
powerful trend, as it did in the case of BTK. Going back to our ’87
crash example, consider the stock index price rise that followed the
bottom.

Another progression in the study of price and time work is the square
root. In the case of the BTK, the first important pullback in the bull
move off the Nov. 25 low came at 1,427.26. On the surface, that means
absolutely nothing. However, when we take the square root of that
figure, we get 37.77, which Fibonacci enthusiasts will recognize as the
derivative of 377.

The simple square root, which we all learned in grade school, is an
integral hinge on which the markets turn, but because it’s hidden just
under the surface, it’s not immediately apparent. Consider the Dow
sequence from the March 2009 bottom to the May 2011 high. The high on
May 2 was 12,876, after a bottom on March 6, 2009. The 12,876 numeral
doesn’t seem so important by itself until we take the square root,
113.47, and discover the market peaked in the 113th week of the rally.
That May high also was the day after the United States military killed
Osama Bin Laden. The media was expecting a nice rally off the news;
however, that was the day markets peaked for the year. Other markets had
their own calculations, but this was how the Dow contributed to the
peak and led to a grinding 108-day correction, which ended in October.

The all-important BKX also bottomed in early October, and the dog of
2011 has been one of the outstanding market leaders of 2012 (see
“Banking on it,” below). How did this happen? One assumption might be
that time heals all wounds and that enough time had elapsed from the
financial crisis so the investing community finally became interested.

However, the banks peaked at 58.81 in their 59th week of the rally.
The square root of 58.81 is 7.66. The peak on April 21, 2010, to the low
of Oct. 4, 2011, is exactly 75.85 weeks, and by the plus-or-minus-one
rule of market timing, it is close enough to 76. Once again, Gann came
through as investors and traders have enjoyed the best rally since the
move off the bottom — even if they aren’t exactly sure why it happened.
Notice that 76 also is a Lucas time series number and how several
interim tops and bottoms match other Lucas numbers.

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