Intro to Stock Charts (5 lessons)
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# 5 Key Differences between Semi-Log versus Linear Scaling

Price scaling is the concept of determining how to show or display price along the y-axis of the price chart. Every stock chart, as one might know comprises of two axes, the x-axis which is typically used to plot time and the y-axis which is used to plot the price values.

Simple as it may sound, price scaling deals with how to plot the price on the y-axis. There are basically two ways to plot price, which is the arithmetic and the logarithmic versions. It goes by different names such as semi-log scale and linear scale.

The term semi-log is used interchangeably with a logarithmic price scale. The reason why the term semi-log is used is because on a price chart, while the y-axis can be logarithmically scaled, the x-axis is linear. Meaning that the x-axis represents equal units of time (60 minutes, 1 day, 1 week or 1 month which is linear) while the y-axis can be logarithmic.

While most traders don't typically pay much attention to the way the price scale is set, there are some aspects that every trader should know. What's important to understand is that there is nothing mystical about the type of price scale one chooses except in some circumstances where one type of price scale surely trumps the other.

In this article we will look at the five key differences between the semi-log and the linear scale in the price charts.

## 1. Linear and log-scale measures price changes differently

The way the linear price scale chart and the logarithmic price scale chart shows the values on the y-axis is greatly different. Most commonly, one expects to see a uniform distribution of the values on the y-axis. This is made possible using a linear chart.

On the other hand, the logarithmic chart displays the values differently, making both these types of price scaling rather unique to each other.

When using a linear price chart, the values on the y-axis are structured in a way that the distances between the units are equal in distance. This means that with a linear scale, if the distance was 5 units, then the values on the y-axis would be 0, 5, 10 and 15 and so on.

The chart below shows an example of the linear scale chart for AAPL stock chart. Here, you can see that the price chart has a y-axis divided at 0.20. Therefore, you will find values such as 114.00 and 114.20, where the units are distanced by \$0.20.

The linear price scale chart therefore shows equal values, where price moves from \$100 to \$100.20 or even \$114.80 to \$115.00.

Example of linear scale chart with distance of \$0.20

With a logarithmic chart, the y-axis is structured such that the distances between the units represent a percentage change that is spread across equally. For example, this percentage difference can be 5%, 10% or 15%.

The main difference being that while the linear price chart shows values that are equally distributed in absolute dollar terms, with the logarithmic chart, the y-axis values are distributed in equal percentage terms.

The next chart below shows the same AAPL stock chart but with logarithmic scale enabled.

Example of log scale chart with distance of 0.30% approximately

In the above chart you can easily notice how the values on the y-axis are distributed. While prices look rather congested at the bottom, such as 140.40, 140.70 and so on, the distribution becomes spread out further apart as price values progresses.

Thus, near the top end of the chart, the distribution of values (in absolute dollar terms) is more dispersed and we see values such as 142.70, 143.10 (a distance of \$0.40) and 144.00 and 144.50 (a distance of \$0.50) and so on.

## 2. A logarithmic stock chart plots percentage changes more clearly

One of the big differences between a logarithmic chart and the semi-log or linear scale chart is evident from the name itself.

If price of a security moved in a linear fashion in absolute dollar terms, a linear chart will no doubt make sense. To put it differently, this is akin to saying that a linear chart works best when you have a stock or a security that moves \$10 every month or over a regular period of time.

We know that the markets rarely exhibit such tendencies.

On the other hand, it is common to expect a stock or a security move 10% or 20% over a certain period of time regularly. In this instance, using the logarithmic price chart makes more sense as it captures the price movement of the stock or security in question more clearly.

The next chart below shows a comparison of the Intel stock chart (INTC). On the left side is a linear price scale and the right side represents a logarithmic price scale.

Comparison of the linear and logarithmic scales for INTC price chart

Although both the linear and the log-scale charts might look the same in terms of representing the information, the differences stand out when you closely look at the distribution of the price values on the y-axis.

Comparing this to the price movement on the two types of charts it is evident that the linear price chart shows a more curved line in prices. You can also notice the linear chart somewhat depicts the idea that price moved rather slowly in the initial periods before price started to move more rapidly in the latter parts.

This distortion occurs because the values are distanced in absolute dollar terms. On the other hand the logarithmic chart shows a steady 1% approximate percentage change in the values and shows a more uniform scale of price change over the period of time.

Therefore, a logarithmic chart is more suited in the above example as it depicts the growth of the stock price on a steady note with a fairly straight trajectory. When the pace of growth starts to change, the logarithmic chart also adjusts accordingly and depicts the change accordingly, which isn't the case with a linear chart because the values remain the same, regardless of whether price moved  just \$0.50 or 5%.

## 3. Logarithmic scales are useful for long term perspective

We have learned so far that with the linear scale, the price values are equally distributed and in absolute dollar terms. This means that a move from \$100 to \$150, which represents a 40% move is the same as a move from \$200 to \$250.

You can see that the distribution here is of \$50 per unit, but in percentage terms, you have a 40% move initially (from \$100 to \$150) and a 22% approximate move from \$200 to \$250.

What this tells us is that a logarithmic price scale is more applicable in determining the long term duration of the chart. In such cases, the large price movements are better depicted using a logarithmic chart which focuses on the percentage move.

On the other hand, a linear price scale is more applicable for analyze the security that is moving in a tight range or within a short time frame such as intraday trading sessions.

Obviously, it makes more sense to focus on the absolute dollar moves on an intraday basis rather than focus on the percentage move in the price of underlying security.

Linear scale is ideal for intraday charts or short term charts

The above chart example shows a 10-minute price chart for AAPL using a linear price scale. Here the units are distributed at an equal distance of \$0.20. You can also see an example of a simple breakout method relatively easy to spot and trade.

Because of the equal distribution in absolute dollar terms, the \$0.20 price range that was established in the sideways market gives the upside and the downside target at a distance of \$0.20 making it relatively easy to trade the short term price charts using the linear price scale.

Even if you would use a logarithmic scale on the intraday charts, because the price movements are typically confined, you will get the same results as using the linear scale chart.

Likewise, the linear scale charts are practically useless when it comes to depicting the long term price movements on the charts. Here, the logarithmic scale chart is more applicable and useful in conveying information such as ensuring that the price movement is relative to the percentage change rather than the absolute values.

## 4. It is the stock or security that will eventually determine what price scale to use

When it comes to analyzing stocks, the price of the security is usually analyzed in relative terms. Metrics such as price earnings ratio, price book values and so on are used. Thus, when depicting the price of the security in question, it makes more sense to represent or analyze the security's stock movement in percentage terms rather than in absolute values.

Although this might miss most traders' eyes, using the correct chart type plays an important role in one's analysis. In most cases, the current technology now a days allows for the charting platform to automatically adjust between linear and logarithmic scale automatically.

Therefore, chances are that traders are automatically shown the appropriate price scale without even knowing the difference between the two types of price scales.

At the end of the day, the security that one is analyzing typically dictates whether you should choose a linear price scale or a semi-log chart or a logarithmic scale chart.

Even within stocks, not all securities behave similarly. While on one hand there are stocks that have explosive price movements, there are also stocks that are typically confined to a range, at times over years.

Therefore, despite looking at a long term price chart and if the security in question has been range bound, a linear chart is more ideal to use than a logarithmic price chart.

## 5. Trends are better judged with a log-scale chart

Price action can be judged quite differently depending on the type of price scale one uses. Let's start with a simple example of drawing trend lines for the same security and compare how the trend lines evolve between a linear or a semi-log scale chart and a logarithmic chart.

Trend lines plotted on a linear and a logarithmic chart

The above chart shows the Intel Corp (INTC) chart where on the left we have a linear price chart while on the right is the logarithmic price chart.

The trend lines plotted on both the charts are exactly the same. If you spare a few minutes looking at the trend lines it is not that difficult to spot the differences.

As you can see price action can also greatly differ depending on the type of price scale one is using.

This brings us to the question of which of the above two charts types is showing the right information? It is the logarithmic price scale chart on the right side which shows the trend lines much better as compared to the trend lines from the left.

## Is linear or a logarithmic scale better?

The answer to this question depends on a number of factors such as the security in question and how price behaves and of course the time frame as well. However, the log scale or the semi-logarithmic price scale is broadly preferred to the linear scale.

Chances are that one might not have really noticed the difference as the logarithmic price scale fits perfectly well. With most charting platforms now being more advanced, the trader doesn’t really have to bother much as to which of these two price scales to use, unless one switches to this option manually.

Nearly all charting platforms default to the logarithmic scale as the units are equally spaced in percentage terms, making it easier to use the log scale as a base chart across any security that a trader wants to analyze.

As illustrated above in some of the differences, there are clearly certain scenarios where using one type of price scale is definitely better. At the end of the day it is all about the security that is being analyzed and the security’s price behavior that will eventually determine what type of a price scale one should choose.