Linear Vs. Logarithmic Charts And Scale – What Is Log Scale Chart (What Is The Difference?)
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.
Let’s get going:
Key takeaways
- Definition and Representation:
- Linear Charts: Display equal spacing between values on the y-axis, representing absolute changes. For instance, an increase from 50 to 51 is depicted the same as from 100 to 101, despite the former being a 2% increase and the latter only 1%.
- Logarithmic (Log) Charts: Depict percentage (relative) changes, with spacing on the y-axis corresponding to equal percentage moves. A rise from 50 to 60 (20% increase) is shown similarly to a rise from 10,000 to 12,000 (also a 20% increase).
- Visualization Differences:
- Linear charts can misrepresent data over large time frames or significant value changes, making early movements appear insignificant.
- Logarithmic charts provide a more accurate visualization of percentage moves, ensuring that equal percentage changes are represented equally, regardless of the absolute values.
- Application in Financial Analysis:
- Logarithmic scales are particularly beneficial for analyzing long-term data or assets with large value ranges, as they offer a clearer view of relative performance over time.
- When evaluating investment strategies or equity curves, log scales can reveal performance patterns that might be obscured in linear representations.
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 it has 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 a 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 massive movement, it’s the proper way to display price changes. Relative values are much more critical than absolute ones!
FAQ:
How does a linear chart differ from a logarithmic chart?
A linear chart shows the same distance between values on the y-axis, representing absolute changes. In contrast, a logarithmic chart, or log scale, depicts percentage changes, giving a more accurate view of relative movements.
Why is it best to use a logarithmic scale rather than a linear one in trading?
A logarithmic scale accurately represents percentage changes, providing a correct visualization of market movements. The importance of using logarithmic scales increases with the duration of the time frame.
What does a linear chart display, and how does it differ from a logarithmic chart?
A linear chart shows absolute movements, where the distance between values remains consistent. In contrast, a logarithmic chart illustrates relative changes, emphasizing percentage movements, especially noticeable in larger market shifts.
Can logarithmic scales distort data?
Logarithmic scales do not distort data but present it differently to highlight relative changes instead of absolute changes. However, they can confuse viewers unfamiliar with their interpretation. It’s essential to label axes clearly and explain why a logarithmic scale is being used to avoid misinterpretation.
Are logarithmic scales commonly used in financial analysis?
Yes, logarithmic scales are widely used in financial analysis, especially for long-term stock charts or when analyzing assets with exponential growth. They allow investors to better understand percentage gains or losses over time and compare price movements across assets with vastly different price ranges.
When should I use a logarithmic scale instead of a linear scale?
Use a logarithmic scale when you want to analyze data that spans several orders of magnitude, such as stock prices, population growth, or sound intensity. Logarithmic scales are helpful in identifying percentage changes or growth rates, as they emphasize proportional differences. Use a linear scale when the data changes at a constant rate or to emphasize absolute differences.
How does the interpretation of trends differ on linear and logarithmic scales?
On a linear scale, equal vertical movements correspond to equal absolute changes in value. On a logarithmic scale, equal vertical movements correspond to equal percentage changes. For example, a move from 10 to 20 on a linear scale shows a 10-unit increase, but on a logarithmic scale, the same vertical distance might represent a doubling (e.g., 10 to 20 or 100 to 200).