Last Updated on June 11, 2021 by Oddmund Groette
Don’t let the word “logarithmic” scare you away, it’s not as complicated as it sounds. But the difference between a linear chart and a log scale grows significant as the time frame expands.
In this article, we look at what linear and logarithmic scales are, why they differ, and why it’s important (and correct) to use a logarithmic scale.
What is a linear chart?
A linear chart shows the same distance between the values on the y-axis. For example, a rise from 50 to 51 shows the same distance as from 100 to 101, even though the first one rises 2% and the latter rises only 1%.
The scale below is linear and the difference between 120 to 140 is the same as 320 to 340:
What is a log scale chart?
A logarithmic scale shows the percentage (relative) change. If an asset rises from 50 to 60, a rise of 20%, it’s presented in the same way as a change from 10 000 to 12 000 (also a 20% rise).
If we change the linear scale from the pic above to log scale (logarithmic scale), the scale changes significantly:
The distance between the lower numbers is higher than the upper numbers.
Why does it change? Because the log scale shows the percentage changes (relative changes) – not absolute changes. A rise from 120 to 140 is much bigger relatively than a rise from 320 to 340, even though both rise 20 points.
What is the difference between a linear and logarithmic chart?
We can conclude that a linear chart shows the absolute values/changes, while a logarithmic scale shows the relative changes.
What is best?
Obviously, a log scale is the correct one. The importance of using logarithmic scales grows as the time frame gets bigger.
What is the benefit of logarithmic charting?
The main benefit is that you get a correct visualization of percentage moves, not absolute moves. For example, if you show a linear chart of bitcoin from 2015 until 2021, the chart gives an improper view of the “real” changes in the asset.
A picture describes the differences much better:
A visualization of linear vs. logarithmic charting
Let’s look at the differences. The first chart is bitcoin (in USD) using a linear chart:
As you can see, the movements prior to 2017 are hardly noticeable.
If we switch to a logarithmic scale the change is dramatic:
Both charts show the exact same data, but the display is significantly different. For example, the rise in 2017 is more significant than in 2020/21, but this is not shown on the linear chart.
This is why you should always use logarithmic charts! By using log scale you respond to skewness towards large values.
It’s when the differences from the beginning and the end of the period are large, that you need to use a log scale. This applies to equity curves as well:
Logarithmic vs. linear scale on equity curves:
If you test a strategy from 1990 until 2021, for example, you might get a 12% CAGR over the whole period.
However, the performance might be different from the first and last data: the strategy might have been fantastic in the 1990s, but have performed worse in the last 5-6 years, let’s say from 2015. If you’re using a linear equity curve, this difference might not be noticeable and “hide” a deterioration of the strategy.
Let’s show this by using an example of how the equity curve of a strategy might differ by changing from linear to a logarithmic scale. We start by showing the performance of the strategy linearly:
However, when we switch to log scale the equity curve differs:
The strategy above is tested on Nasdaq/QQQ and has an average gain of 3.21% per trade from 1999 until the end of 2005. From 2006 until 2021 the average gain is “only” 1.16%. The strategy is still firing on all cylinders, but it worked better during the crazy volatility during the dot-com crash (despite being a long-only strategy).
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Conclusion about linear and logarithmic charting:
We recommend setting logarithmic scale as default all over your trading platform. In trading, relative values are much more important than absolute ones!