Volatility Drag, explained.
Volatility drag describes why a sequence's compound growth can be lower than growth calculated from its arithmetic average. Returns operate on a changing balance, not an unchanged starting amount.
Why it happens
A gain and an equal percentage loss do not cancel: the second percentage applies to a different balance. For positive growth factors, their geometric mean cannot exceed their arithmetic mean. This is arithmetic, not a claim that every risky investment is undesirable.
Volatility drag is the gap between an arithmetic average of returns and compound growth. Multiplying unequal return factors can produce less growth than repeatedly applying their average.
Read the result
Change return tiles and compare the two curves. The dashed path applies the arithmetic mean each period. Move a return earlier to change the journey while preserving the product; there are no cash flows in this board.
A worked example
A rise and fall that do not cancel
Begin with 100 teaching tokens and apply a 50% gain, taking the balance to 150.
Apply a 50% loss to 150, leaving 75 rather than the original 100.
The arithmetic mean is zero, but the compound result is a 25% loss. Reversing these two factors still ends at 75 when there are no withdrawals.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Start with 100 tokens. Four return tiles multiply wealth by 1+r. The comparison compounds the arithmetic mean of the selected returns for four periods. No deposits, withdrawals, fees, or taxes occur. Tiles can be reordered without changing the endpoint, although the path changes.
Where this idea is useful
A practical use
A +50% gain followed by −50% leaves 75 from an initial 100 despite a zero arithmetic mean.
A common misconception
“A zero average return guarantees that the balance is unchanged.”
An arithmetic mean adds returns, whereas accumulated wealth multiplies their factors. Unequal factors can leave a very different balance.
What this explanation leaves out
- The return tiles are invented. This arithmetic illustration does not imply that minimum volatility is always the best portfolio or resolve Samuelson's critique of universally maximising geometric growth.
Does the smooth line represent a safer asset I could actually buy?
No. It is a constructed comparison that repeatedly applies the same mean. Availability, uncertainty, and investment suitability are outside the demonstration.
Which report in your work summarises a changing balance with an average that hides its actual path?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.