Logarithmic vs. Linear Charts: Why the Same Rise Looks Different
Compare equal price intervals on linear charts with equal percentage intervals on logarithmic charts. Learn why scale settings matter for long-term trendlines and stock comparisons, and avoid common misunderstandings.
A linear price scale displays equal monetary changes at equal distances, while a logarithmic scale displays equal price ratios at equal distances. Neither changes the underlying prices, but they make long-term slopes and trendlines look different. Choose the scale that fits your question: absolute profit and loss or proportional price changes.
The same 10,000-won rise can mean different things
A rise from 10,000 won to 20,000 won and one from 100,000 won to 110,000 won have the same monetary size. On a linear scale, their vertical distances are equal, but their returns are 100% and 10%, respectively. A logarithmic scale makes that proportional difference visible, which is useful for comparing large price changes over long periods. Conversely, a linear scale may make won-denominated profit and loss more intuitive when the number of shares held is fixed. Neither scale is always correct; they emphasize different quantities.
Distinguish a logarithmic scale from a rebased return display
Comparison charts that set a starting date to 0% or 100 also use relative changes, but this is not the same function as a logarithmic scale. A rebased return display helps align the starting points of stocks with different price levels. A logarithmic scale shows equal multiplicative moves within a price series at equal distances. Do not assume a scale is logarithmic simply because it displays percentages; check the actual mode name. Changing the comparison start date can also change the ranking of relative performance, so display the date alongside the comparison.
Copy the scale settings along with a trendline
After connecting two points, the price indicated by the line at the midpoint in time depends on the scale. Asking only for the anchor points when assessing someone else's trendline may therefore be insufficient to reproduce it. Standard logarithmic scales assume positive prices; also check how the service handles zero or negative values. Changing the scale of a price chart does not change financial value or cumulative returns. Before using an on-screen slope to claim that growth has accelerated, calculate the actual percentage changes for each period.
Worked example
Hypothetical example: If prices move from 10,000 won→20,000 won→40,000 won at equal time intervals, both increases are 100%. The two moves have equal vertical distances on a logarithmic scale, but the second is twice the size of the first on a linear scale. A straight line connecting the first and last prices gives a midpoint in time of 25,000 won on a linear scale and 20,000 won on a logarithmic scale. This is why the meaning of a trendline changes even with the same data.
What to check
- Decide whether the analysis concerns monetary differences or proportional differences.
- Distinguish logarithmic mode from a comparison mode rebased to 100 on a starting date.
- Save the scale settings along with the trendline.
- Calculate actual returns over equal periods instead of relying on screen angles.
Sources and primary materials
This is educational material about research methods. For an actual company decision, verify the filings and primary sources for the relevant period.