Why does The Motley Fool use logarithmic charts to show stock price movements? 

Spend any time looking at charts of stock price movements at Fool.com and you’ll be looking at logarithmic charts. So, why does The Motley Fool use logarithmic charts and what exactly are they?

The basics of stock charts

There are two common kinds of charts used to present things like stock price movement — one is linear and the other, logarithmic.

Think back to your high school math classes … with most such charts, the “X axis” (the horizontal measure) reflects time passed. So it might show you days, weeks, months, or years. The “Y axis” (the vertical measure) shows you how the stock price has changed over the given time period.

The difference between linear and logarithmic charts is in their treatment of the Y axis. Let’s first explain how the charts differ in structure, and then we’ll explain why we use log charts.

Linear charts

With a linear chart, the Y axis is structured in such a way that an equal distance along the axis represents an equal absolute change in stock price.

Translation: shifting up three centimeters on the vertical axis might represent a change in stock price from $10 to $13, and shifting up another three centimeters further up on the axis might represent a change in stock price from $45 to $48.

For our hypothetical chart … three centimeters = three dollars.  Every time.

linearchart

Logarithmic charts

With a logarithmic chart, however, the prices on the Y axis are not positioned equidistantly — instead, an equal distance along the Y axis represents an equal percentage change.

In other words, if you move up three centimeters on the vertical axis, that might represent an increase of 15% in the stock price — perhaps from $20 to $23. Shifting up another three centimeters further up on the axis will represent another 15% change in the stock price, but this time perhaps from $80 to $92.

In the first case, three centimeters represents an absolute price change of $3. But farther up the axis, three centimeters represents an absolute price change of $12. But it’s still the same percentage change!

For our hypothetical chart … three centimeters = 15% percentage change. Every time.

logchart

Why choose logarithmic?

The vast majority of traders use logarithmic charts to represent the movement of stock prices. Why?  Well, imagine a company with a stock increasing by 15% each year for 20 years.  Think about how you would normally draw a chart of its stock price.

Chances are, you would use a linear chart, as that’s what most of us learned to do in school. It’s just a matter of connecting the dots … literally.

But the graph you’d get from using a linear chart would be misleading, as it would show a really curved line. It would look like the stock price grew slowly in the first years, and then shot up in the last few years.

Here’s a linear chart for a stock starting at $2 and increasing by 15% for 20 years…

linear2

As you can see, the absolute changes look pretty small at the beginning, but they start looking larger later on. But in reality, there’s just a steady 15% increase from year to year. Now let’s see what the line would like if you used a logarithmic scale…

log2

See the difference? Same data, same accuracy, different price scale. Remember — with the log scale, equal distances represent equal percentage changes. But with the linear scale, equal distances represent equal price changes.

As you can tell, with a logarithmic chart, you get a more accurate representation of how the stock is growing. A straight, upward-sloping line (like the one in the graph above) indicates that the company is growing at a steady clip.

With a linear chart, a sharp curve doesn’t tell you very much — but with a logarithmic chart, a dramatic curve represents dramatic growth.

If you want to see how it all works, head over to our Quotes & Data area and look up a company’s stock  chart. Still have questions? Try asking them over on the Quotes & Data Feedback discussion board.

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