DJIA
Forecast
Signal 1900-1925
Signal 1926-1950
Signal 1951-1975
Signal 1976-2000
Signal 2001-2005
Historical Prices


S&P 500
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Signal 1976-2000
Signal 2001-2005
Historical Prices


NASDAQ
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Signal 1950-1975
Signal 1976-2000
Signal 2001-2005
Historical Prices


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7/14/06
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A 15% decline is likely this year.
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This issue of Investment Tips
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Arithmetic or Logarithmic Scale?
Proprietary Graphs, Tables and Analyses - All Rights Reserved
Our Market Timing...  Your Triple Gain !                             Backtested 100 Years !
SignalTrend
1921                                             1929             1932
1921                                             1929           1932
A
A
B
Arithmetic: Both graphs above portray the Dow Jones Industrial Average for the same time period
(1921-1932). Both graphs are accurate. However, they use different scales. Arithmetic scale (left chart) shows
an equal distance for each unit of price change. Notice that each point on the vertical scale represents a vertical
distance of 40 points, and each point  is equidistant.  However, each point represents a different percentage
movement. (A 40 point movement from 320 represents a 12.5% increase. But, a 40 point movement from 40
represents a 100% increase.) To further clarify the issue, observe the gray and green lines on the Arithmetic (left)
graph.  The gray lines portray a vertical distance on the chart for a movement in the Dow from 120 to 160. That's
a rise of 40 points (33% increase from 120). The green lines portray a vertical distance on the chart for a
movement from 240 to 320. That's a rise of 80 points (33% increase from 240). The movement illustrated in
green appears to be far stronger than the movement illustrated in gray. In fact, however, they each represent a 33
% movement.

Logarithmic: Logarithmic scale (right chart) shows an equal distance for equal percentage movements. For
example, a movement from 80 to 160 (100% increase) would be the same vertical distance on the Logarithmic
chart as a movement from 160 to  320 (also a 100 % increase but twice as many points).

Analysis: The arithmetic scale graph can be deceiving, especially on long term graphs. A quick glance at the
arithmetic (left) graph would lead one to believe that the market rose much faster from point B to point C than it
did from point A to point B. In fact, from B to C, the market appears to move nearly straight up (left graph).
However, a review of the Log graph (right), reveals that the rate of appreciation during period AB was very
similar to that which occurred during period BC.  Long term arithmetic graphs can subtly exaggerate the strength
of certain time periods over others.

How can I use this information?
View graphs in logarithmic scale to get a proper historical perspective of the percentage gains and losses of the
market. Investors viewing the pre-crash period in arithmetic scale would receive the mistaken impression that
the market crashed because it escalated in a dramatically accelerating upward curve that was obviously
unsustainable. To the contrary, the log scale chart indicates that the pre-crash Dow rose steadily for nine years
without a single major correction. Investors were trained by uninterrupted prosperity to place faith in the market
that it did not deserve. Nine years without a gut wrenching bear market left them unseasoned. When the bear
appeared, too many panicked and the market lost 90% of it's value.

More:
Look below to send us feedback or to see previous issues of Investment Tips.
Observations:
Arithmetic scale graphs may create a false appearance of acceleration.
● Logarithmic scale represents market movements in percentage terms.
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33%
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33%
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B
Arithmetic Scale: DJIA (1921-1932)
Logarithmic Scale: DJIA (1921-1932)