Work it out
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Worked example
Both moves gain 10%, so both have log distance ln(1.1). Their absolute changes are 10 and 20 price units.
Linear distance counts price units
On a linear price axis, equal vertical spacing represents equal differences in price. A move from 100 to 110 and a move from 200 to 210 each cover 10 units.
The percentage moves differ because their starting prices differ. A linear distance comparison is most interpretable when the unit, currency and contract convention are held constant.
Logarithmic distance counts ratios
The logarithmic distance between two positive prices is ln(end/start). Equal price ratios therefore have equal distance: 100 to 110 and 200 to 220 both have a ratio of 1.1.
The tool multiplies that logarithm by 100 for a convenient display. The output is labelled log change ×100; it is not relabelled as the ordinary percentage return.
Read the three numbers together
Absolute change is end minus start. Simple change is 100×(end/start−1). Log change is 100×ln(end/start). They describe the same pair of prices with different mathematical measures.
For small moves simple and log changes can be close. As the move grows they diverge. An equal log distance does not imply equal dollar profit when quantities differ.
Reversing a move exposes the difference
Doubling and then halving are +100% and −50% in simple returns. Their logarithmic changes are equal in magnitude and opposite in sign, so their sum is zero.
This additive property can help compare sequential ratios, but it does not remove volatility, costs or the arithmetic constraints of a real portfolio.
Check the input basis before comparing
The logarithm requires positive prices, so zero and negative inputs are rejected. Some real instruments can have non-positive quoted prices; this tool is not suitable for those observations.
Match time periods, currency, units and any adjustment basis. A stock split, changed contract multiplier or inconsistent data source can overwhelm the meaning of a scale comparison.
What this tool does not calculate
- Endpoint comparison only; no historical chart or investment recommendation.
- Does not adjust prices for splits, currency changes, dividends or contract rolls.
Common questions
Does a log chart change my return?
No. It changes the spacing of the price axis, not the prices, quantities or cash flows.
Is log change ×100 a percentage return?
It is a scaled logarithmic return. The separately labelled simple percentage is the ordinary end/start−1 calculation.
Why reject zero or negative prices?
The real-valued logarithm used here is defined only for positive price ratios with positive endpoints.
Sources & method
An original calculation tool built with AI assistance. Its method and limits are documented here, and calculation examples are checked with automated tests.
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