Linear Vs. Logarithmic Charts And Scale – What Is Log Scale Chart (What Is The Difference?)
Last Updated on October 23, 2022
Linear vs logarithmic charts and scale is important to understand because the difference between linear and logarithmic charts might be huge – the bigger the scale the more it matters. The difference between a linear chart and a log scale grows significant as the time frame expands.
In this article, we explain what a log scale chart is. We look at linear vs. logarithmic charts and scales, what is the difference, and why it’s best and important (and correct) to use a logarithmic scale and not a linear one. A linear chart shows the points change, while a logarithmic chart shows the percentage change. Thus, they differ more the bigger the movement is.
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, often called a log 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? What is best?
We can conclude that a linear chart shows the absolute values/changes, while a logarithmic scale shows the relative changes.
What is best – linear or log scale?
Obviously, a log scale is the correct one to use instead of a linear chart. 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 difference between linear and logarithmic charts. 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 in the linear chart.
This is why you should always use logarithmic charts and not linear 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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What is the best: logarithmic or linear charts and scale?
In trading, it’s important to understand log scale vs linear scale. Logarithmic charts are better than linear charts and scales – hands down. The difference between linear and logarithmic charts grows bigger as time goes by. Thus, log scale is always better than a linear scale.
We recommend using logarithmic scales as default in your charting. Over long time horizons and after huge movement it’s the proper way to display price changes. Relative values are much more important than absolute ones!