Logarithmic Price Scale
What is a Logarithmic Price Chart and how is it different fro the Linear chart?
The Logarithmic Price Scale (also known as Log scale) is a charting technique which is used to display the prices of Stocks, Bonds, ReITs, InvITs and other tradeable securities. The chart is different from a normal price chart, as the prices in the Log chart are scaled based on the percentage change in the prices.
The scale is built in such a way that any two price differences in percentage terms on the chart, will be separated by equal distances in the chart. Example: Suppose a stock price moves from INR 50 to INR 55 in the month of January and then moves from INR 100 to INR 110 in the month of September.
In both cases, the movement in percentage terms is same (10%), but the price movement is different (INR 5 and INR 10 respectively). So, in a Logarithmic Chart, the vertical distance covered in both cases will be the same.
How is a Logarithmic Price Scale built?
Like all price charts, the Log Price Scale is also made up of an x-axis and a y-axis. The x-axis represents the time interval, and the y-axis represents the price of the security. The x-axis is equally spaced based on the time interval, but the y-axis is spaced based on the percentage change in the stock price.
This means that the price difference between INR 10 to INR 15 will be spaced equally as the price difference between INR 20 to INR 30 (and so on). Even though the amount is different, the percentage change is 50% increase in both cases. In the image below, the difference between a Log scale, and a normal Linear Price Scale can be seen.
The Linear chart has equal spaces for equal price gaps, and therefore it is easier to build and display. The log price chart on the other hand, is a bit more complicated, as the scaling of y-axis has to be adapted when the stock prices move up or down. So, usually the Logarithmic Scales are difficult to build by hand, and are mostly constructed using computer software.
The Base of log
The Logarithmic price charts might slightly differ in their displays depending on the base of the log that has been chosen. This means that if we compare two log charts, one with a base 10 and the other with base ‘𝑒‘ (Natural log), then the graphs will be slightly different.
The difference in graphs will become even more evident when the y-axis is very large. This can happen for example, if the stock price moves from INR 50 to INR 1,000 in a very short time. There is no hard-core rule defined in stock markets to follow a particular base, when building the charts.
Logarithmic Price Scale vs Linear Price Scale
In the image below, the Closing Prices of a random stock for a 1-year period from 01 April to 31 March have been plotted. The charting has been done in both Log Price Scale and the Linear Scale, to highlight the differences in the y-axis, as the stock prices move up.
At first glance, both the charts appear identical in shape and direction. The differences become more evident as we see the y-axis scales. The scale of x-axis in both cases is same.
Investors will notice in the right chart that, the scale becomes thinner as prices move up (compare the distance between INR 200 and INR 300 in both charts). Similarly, the Logarithmic Price Scale appears stretched and more detailed when the prices are low (observe the gap between INR 50 and INR 100 in both charts).
Use of Logarithmic price scale
Investors might wonder what is the need for such a complex chart when the Linear price scale is easy to build and understand. The biggest problem arises when a long price history of a stock is being charted.
Example: Suppose, the share price of a company is INR 100. If this price increases by INR 25 in 1 year, then the percentage change in the price and the Market Capitalization is 25%. Now let us assume that the company grows and the share price becomes INR 500 in 7 years’ time. A price movement of INR 25 now will translate into a percentage growth of only 5%.
If we view a linear price chart of these 7 years, the price movement of INR 25 at both time intervals will appear the same. Also, as the scale of y-axis has increased from INR 100 to INR 500, the price movement of INR 25 will appear less significant at both INR 100 and INR 500.
But for long-term investing, a 25% move has a bigger significance than a 5% move. The Logarithmic Price Scale will display a higher distance covered in the chart when the percentage movement in the price is higher.
Comparing the price movements
Investors can notice the difference in the stock prices by carefully observing the image above. In the Linear Scale, it appears that the stock made modest movement between April and August, and then made a major move between January and March. However, in the log scale, it would appear that the movement between April and August was also significant, and the move between January and March is not as big as it appears in the Linear scale.
When the whole charts are compared, the prices in the Log chart will appear to have moved consistently throughout the year. Whereas in the Linear Scale, the movement towards the end, appears more significant than the initial price movements.
Which chart is better?
The next obvious question that arises is that which chart should be used by the investors?
It is virtually impossible to determine which scale is better, because the usefulness of the chart will depend on the time interval and the price movement of the security. If the time period of the security is shorter and price movements are not big, then the Linear Chart might offer a better picture about the price movement. (Example: 1 hour data is being seen on a 5 minute chart and the prices have not moved much)
On the other hand, if for example 10 years data is being observed on a daily chart, and the prices have moved significantly, then the Log Chart will show the movement better. Therefore, investors should check and decide which scale is suitable for their analysis.
Disclaimer
- This page is for education purpose only
- Some information could be outdated / inaccurate
- Investors should always consult with certified advisors and experts before taking final decision
- Some images and screenshots on this page might not be owned by FinLib