Linear Vs. Logarithmic Charts And Scale – What Is Log Scale Chart (What Is The Difference? What Is Best?)

Last Updated on August 26, 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 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?

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. 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:

A linear chart shows the absolute movement, not the percentage (relative) movements.

As you can see, the movements prior to 2017 are hardly noticeable.

If we switch to a logarithmic scale the change is dramatic:

A logarithmic chart shows the relative moves – it shows the percentage movements.

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:

A linear graph shows a smooth equity curve, ie. a reliable and consistent return.

However, when we switch to log scale the equity curve differs:

A logarithmic equity curve. Most of the gains happened early in the period. The strategy is still fantastic, but not as fantastic as it was 20 years ago.

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 of logarithmic and linear charts and scale? Logarithmic charts and scale are better than linear

After reading this article, we hope you have concluded that the best option is to use a logarithmic scale in your charting. Over long time horizons and after huge movement it’s the proper way to display price changes.

We recommend setting logarithmic scale as a default all over your trading platform. In trading, relative values are much more important than absolute ones!

 

Disclosure: We are not financial advisors. Please do your own due diligence and investment research or consult a financial professional. All articles are our opinions – they are not suggestions to buy or sell any securities.