Price scaling

Price Scaling

There are two methods for displaying the price scale along the y-axis: arithmetic and logarithmic. An arithmetic scale displays 10 points (or dollars) as the same vertical distance no matter what the price level. Each unit of measure is the same throughout the entire scale.

If a stock advances from 10 to 80 over a 6-month period, the move from 10 to 20 will appear to be the same distance as the move from 70 to 80. Even though this move is the same in absolute terms, it is not the same in percentage terms.

A logarithmic scale measures price movements in percentage terms. An advance from 10 to 20 would represent an increase of 100%. An advance from 20 to 40 would also be 100%, as would an advance from 40 to 80. All three of these advances would appear as the same vertical distance on a logarithmic scale. Most charting programs refer to the logarithmic scale as a semi-log scale, because the time axis is still displayed arithmetically.


The chart above uses the 4th-Quarter performance of VeriSign to illustrate the difference in scaling. On the semi-log scale, the distance between 50 and 100 is the same as the distance between 100 and 200. However, on the arithmetic scale, the distance between 100 and 200 is significantly greater than the distance between 50 and 100.

Key points on the benefits of arithmetic and semi-log scales:

Arithmetic scales are useful when the price range is confined within a relatively tight range.

Arithmetic scales are useful for short-term charts and trading. Price movements (particularly for stocks) are shown in absolute dollar terms and reflect movements dollar for dollar.

Semi-log scales are useful when the price has moved significantly, be it over a short or extended time frame

Trend lines tend to match lows better on semi-log scales.

Semi-log scales are useful for long-term charts to gauge the percentage movements over a long period of time. Large movements are put into perspective.

Stocks and many other securities are judged in relative terms through the use of ratios such as PE, Price/Revenues and Price/Book. With this in mind, it also makes sense to analyze price movements in percentage terms.