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Building Better Trendlines with Logs

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Market guru Martin J. Pring suggests using logarithmic charts for long-term charts or those that encompass big market movements. What are logarithmic charts and how do they differ from the standard arithmetic chart?

Most charting services use arithmetic charts as the default setup. Unless you've changed your setup, the charts you study each day are probably arithmetic charts. On an arithmetic chart, the distance between 50 and 100 is five times the distance between 10 and 20. The chart plots each 10-point increment on the same scale.

Logarithmic--or more properly in most cases, semi-log--charts plot prices on a ratio scale. The ratio of 10 to 20 is the same as the ratio of 50 to 100. In each pair, the first number is half the value of the second. On a log chart, the distance from 10 to 20 would be the same as the distance from 50 to 100. The ratio is the same. As prices move higher on a semi-log chart, the distances between each 10-point range decrease. These charts are deemed semi-log charts because only the prices are plotted proportionately. The time scale along the bottom of the chart continues to use an arithmetic scale.

The easiest way to understand the difference is to look at a couple of charts. First is a traditional arithmetic chart, followed by the same chart employing a semi-log scale.

Annotated Weekly Chart of CSCO, Arithmetic Scale


Annotated Weekly Chart of CSCO, Log Scale


Why bother to use log charts? Pring feels that market moves tend to happen proportionately. He uses the example of a rectangular consolidation pattern that forms between 50 and 100. It's possible to set targets with breakouts from a rectangular pattern. The breakout predicts a move that travels the same distance as the width of the rectangle. Obviously, though, a downside break would be unlikely to result in a drop to zero, a 50-point move from the breakdown point. A decline to 25 might be possible, however, with 25 being half of 50, just as 50 is half of 100. The proportionate move would be the same.

This becomes clear when looking at big rallies. Movements that seem exaggerated and overdone, sometimes even parabolic, look less so on a log chart.

Annotated Weekly Chart of the TRAN, Arithmetic Scale


Annotated Weekly Chart of the TRAN, Log Scale


The disparity in behavior near trendlines is even more apparent in a monthly chart of the DJUSHB, the Dow Jones US Home Builders.

Annotated Monthly Chart of the DJUSHB, Arithmetic Scale


Annotated Monthly Chart of the DJUSHB, Log Scale


Many traders have watched that almost parabolic climb on the $DJUSHB's arithmetic chart, attempting to pick tops in the housing stocks, when the climb looked much healthier and less parabolic on a log chart. Some individual homebuilders boasted similar charts. A bull might have felt more comfortable buying on trendline tests with the log chart if studying a semi-log chart, and a bear might have been less likely to start trying to pick a top quite so soon.

Annotated Monthly Chart of TOL, Arithmetic Scale


Annotated Monthly Chart of TOL, Log Scale


Would a log chart have kept traders from shorting the homebuilders quite so readily? You bet. Although even the semi-log charts now show parabolic moves that begin to scary, those semi-log charts might have convinced a few traders to participate in gains made after homebuilders as a group and individually appeared to go parabolic in mid-2003 on arithmetic charts.

For a balanced long-term look at trends, both ascending and descending, take a look at charts on a log scale. You might like what you see a little better.

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