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When To Use Logarithmic Scaling

It is important to know the difference between linear and logarithmic scaling and the impact that switching between the two has on chart analysis.

Changing between linear and logarithmic price scaling will create inconsistencies in any geometrically constructed technical overlay. This includes trendlines, channels, triangles, wedges, flags and any other chart pattern. For instance, observe the rising trendline drawn on the linear chart of gold in figure 1.

Figure 1

The trendline is constructed by connecting two peaks from 2006 and 2008 and projecting forwards. The trendline is used as minor resistance in 2011 before price breaks above the trendline for a few volatile months but falls back below. Then, in 2012, price returns up to the trendline and reverses from it, using it once again as a strong resistance.

Now, look at the chart in figure 2. This is the same chart of gold over the same time frame. The difference here is that the price axis is plotted in a logarithmic fashion.

Figure 2

The same trendline is drawn by connecting the same two peaks. As you can see, on the logarithmically scaled chart price never reaches the trendline again. When using any geometrically constructed indicator, it’s important to maintain consistency in the type of scaling. A geometrically constructed indicator is any one which refers to angles of ascent or descent (has a diagonal component). These angles are distorted when switching between logarithmic and linear charts.

Numerically constructed indicators, however, will remain consistent across both scaling types. Figure 3 shows the same chart of gold, returned to the linear scale. A moving average is shown with a period of 50 months in blue, and a set of Fibonacci retracement levels in red.

Figure 3

The current moving average value is shown as $1256.70. The value of each Fibonacci level is also shown in brackets. Notice how price respects the 0.618 level by retracing from it twice in 2016 and 2018.

Now see in figure 4 how the moving average and Fibonacci levels are impacted when the scaling is switched to logarithmic.

Figure 4

The shape of the moving average seems to be distorted as it looks flatter. However, it is distorted in exactly the same way as price, meaning each moving average value is the same. The same goes for the Fibonacci levels. They appear to have moved upwards, but that is in accordance with the logarithmic scale which compresses upper-end price action. All levels are the same. Notice how the green arrows point to the market rebounding from the 0.618 level just as they did on the linear chart. Any numerical indicator is valid across both linear and logarithmic charts. A numerical indicator is one that is the result of a calculation such as determining a rolling mean or dividing a range into ratios. All horizontal levels are consistent on all types of scaling, be they derived from Fibonacci, prior support or resistance levels or Gann Analysis.

When should logarithmic scaling be used instead of linear scaling? Well, logarithmic scaling helps to improve the definition of price action at lower prices by expanding lower-end prices while compressing upper-end prices. This makes logarithmic scaling useful for analysing charts of a longer time frame, or assets with a large price range. If for example, you’re looking at a chart of 10 years or more, or equities priced at $100 or more, logarithmic scaling may be more appropriate.

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