Log versus Linear

A logarithmic scale is a scale of measurement that displays values using intervals corresponding to orders of magnitude, rather than a standard linear scale.

A simple example is a chart whose vertical or horizontal axis has equally spaced increments that are labeled 1, 10, 100, 1000, instead of what you’d find on a linear scale – i.e. 0, 1, 2, 3. When using a logarithmic scale, the distance between the prices in the scale will be equal when the percent change between the values is the same.

Despite the fact that the logarithmic scale is a foreign concept for most investors, we’ve made it the default on the growth chart because it’s a fairer representation of investors’ experience. Percentage gains/losses are the same in magnitude, no matter where they are on the chart. In other words, a 10% annual return on the bottom left is the same visually as a 10% gain on the upper right. On the linear version, the 10% gain doesn’t even register on the left and is a significant move on the right.

Another way to illustrate the difference is to look at it in dollar terms. On a linear scale, an increase in price from $10 to $15 (+50%) is the same as an increase from $20 to $25 (25%). When using a logarithmic scale, however, the distance between the prices will only be the same when the percent change is equal. Using the above example, the distance between $10 and $15 would be equal to the distance between $20 and $30 because both represent a price increase of 50%.

We encourage you to play around with the two charts and see what we mean.