SCALES: ARITHMETIC VS LOGARITHMIC

The purpose of a price chart is to show how the price of an asset changes over time. The typical price chart—whether it represents a stock, commodity, currency-pair, or index—has time on its x-axis and price on its y-axis. Time plods forward at a predictable and linear rate, so the x-axis is always the same—it is divided into equal time intervals or periods. Price, however, is not so predictable and linear. Some asset’s prices stay stable for long periods of time, but others jump around wildly, and sometimes even increase or decrease exponentially. It is for this reason that some price charts use an arithmetic scale and some use a logarithmic scale.

An arithmetic scale is the most common type of scaling on graphs. When price is scaled arithmetically on a chart, each increment of price is given the same space on the axis. For example, an arithmetic chart might have ten tick-marks spaced evenly along the price axis, with each tick-mark representing an increase of 1 USD over the last. This type of scaling is best for charting asset prices that stay in a fairly small range and do not tend to make huge jumps between time intervals.

An arithmetic scale cannot be used in all cases. Imagine a stock that trades between 10 and 20 USD for six months, then leaps to the 500 USD to 600 USD range for the next six months. Using an arithmetic scale to chart that whole year would squish the data from the first six months—when it traded between 10 and 20 USD—into an unreadably small vertical space. Either that, or the y-axis would have to be so tall to accommodate both ranges equally that the chart would have an impractical size. This is where a logarithmic scale comes into play.

A logarithmic scale is used on the price axis when asset’s price has experienced an enormous variation, from tens of dollars to hundreds of dollars to thousands of dollars. On a logarithmic price axis, each evenly spaced tick-mark represents the next multiple of ten. For instance, imagine a logarithmic chart with five tick-marks spaced one inch apart up the whole axis. The first tick-mark would be the 1 USD mark, the next one would be the 10 USD mark, then the 100 USD mark, then 1,000 USD, and finally 10,000 USD. The smaller sections between tick-marks are spaced unevenly, with the lower values given larger vertical space. The overall design of the logarithmic price axis means that asset prices over a large period can be comfortably shown on one chart no matter how extreme their range.