Introduction
In finance it is well established that percentage returns are path dependent. When returns fluctuate, the compounded or geometric return is lower than the simple arithmetic average. This phenomenon is widely known as volatility drag or variance drain.
The most common example of return asymmetry is simple and familiar. If an asset falls 50 percent, it must rise 100 percent to return to break even. This is a direct consequence of percentage math and geometric compounding.
Most articles stop at this one move asymmetry. What is rarely discussed in trading is what happens when the same total move is broken into many smaller segments through entries, stop losses, re entries, scaling, and partial profit taking.
This article focuses entirely on that segmented behavior. I refer to this trading level expression of known compounding math as the Segmentation Asymmetry Effect, or SAE.
Arithmetic vs Geometric Returns
Arithmetic return is the simple average of percentage changes across periods.
Geometric return is the compounded result of those same percentage changes. This is the return that actually determines real capital growth or decay.
Whenever returns vary over time, the geometric return is strictly lower than the arithmetic return. The difference increases with the variance of returns.
A commonly used approximation is:
g ≈ a - (σ² / 2)
In this expression, g is geometric return, a is arithmetic return, and σ² is the variance of returns.
This relationship forms the mathematical core of volatility drag and variance drain. It is the same math that explains the behavior of segmented trading paths.
Definition of the Segmentation Asymmetry Effect
SAE describes the distortion that occurs when a continuous price move is broken into multiple percentage measured segments.
When a total price move is segmented into smaller legs, the sum of the individual percentage changes of those legs does not equal the percentage change of the full move from start to finish. This happens because each segment computes its percentage change from a different and shifting base.
The distortion is directional:
- Downward segments mathematically exaggerate the total loss when their percentages are summed.
- Upward segments mathematically understate the total gain when their percentages are summed.
SAE is independent of segment size. It applies whether segments are equal, unequal, random, intraday, generated by stop losses, or generated by scaling and partials.
Numerical Illustration
Consider a price moving from 10,000 to 13,000 or from 13,000 to 10,000. The absolute distance is the same in both cases. The move is now split into three equal absolute segments of 1,000.
Upward segmentation
10,000 to 11,000 = +10.00 percent.
11,000 to 12,000 = +9.09 percent.
12,000 to 13,000 = +8.33 percent.
Sum of segments: +27.42 percent.
Direct move result: +30.00 percent.
Segmented gains understate the true total gain.
Downward segmentation
13,000 to 12,000 = -7.69 percent.
12,000 to 11,000 = -8.33 percent.
11,000 to 10,000 = -9.09 percent.
Sum of segments: -25.11 percent.
Direct move result: -23.08 percent.
Segmented losses overstate the true total loss.
This behavior follows directly from geometric compounding. It is a mechanical property of percentage math.
Stop Losses and Re Entries
When a trader repeatedly attempts long positions with tight stop losses, each failure creates a small downward percentage segment.
Because downward segments exaggerate total loss when added together, a sequence of small long stop outs produces a larger cumulative percentage loss than a single equivalent continuous drop.
When a trader repeatedly attempts short positions with tight invalidations, each failure creates a small upward percentage segment.
Because upward segments understate total loss when added together, a sequence of failed short attempts accumulates percentage damage more slowly than a comparable continuous adverse move.
This asymmetry exists even when position size is fixed and no compounding is applied.
Buying the Dip Behavior
Buying the dip in a downtrend mechanically produces a stack of downward segments.
Even when each stop loss is small, the geometric effect amplifies cumulative loss relative to a single larger exit.
This is one of the reasons repeated dip buying in bearish conditions is structurally destructive even when risk per trade appears controlled.
Partial Profit Taking
Taking profits in pieces during an uptrend breaks the move into upward segments.
Because upward segments understate gains in percentage terms, partial profit taking systematically captures less geometric return than holding the continuous move with a single exit.
This explains why strong trends often feel under monetized when profits are taken incrementally.
Grid and High Frequency Strategies
Grid systems and high frequency execution deliberately create many micro segments.
As segmentation increases, volatility drag accumulates faster. The strategy can show positive arithmetic expectation while the geometric return decays.
This is one of the main structural risks inside grid and martingale based systems.
Directional Bias in Strategy Design
Because downward and upward segments behave asymmetrically under percentage math, long and short strategies cannot be treated as mirror images.
Risk per attempt, invalidation distance, scaling logic, and profit structure must be directionally adapted.
Ignoring this leads to persistent long side erosion in choppy or declining markets and reduced upside capture in rising markets.
Why This Matters in Practice
SAE is not a new law of mathematics. It is the direct trading level expression of volatility drag and geometric compounding.
What is new for most traders is seeing this math applied not to portfolios over years but to execution behavior over minutes and days.
It provides a structural explanation for why repeated stop outs feel worse than expected, why partial profits feel insufficient, and why symmetric long short systems often degrade over time.
Limitations
SAE does not predict market direction.
It does not guarantee profitability for shorts or unprofitability for longs.
It does not replace position sizing, execution quality, or market context.
It only describes how segmented percentage paths accumulate through geometric math.
Conclusion
The Segmentation Asymmetry Effect is the application of known geometric return and volatility drag mathematics to real trading execution.
Segmentation through stop losses, re entries, scaling, and partials distorts cumulative percentage outcomes in a direction dependent way.
Downward segmentation amplifies losses.
Upward segmentation mutes gains.
Understanding SAE allows traders to align risk management and execution logic with the actual mechanics of compounded returns instead of relying on simple arithmetic intuition.
References
Messmore, Frank (1995). Variance Drain: Is Your Return Leaking Down the Variance Drain? The Journal of Portfolio Management, Volume 21, Issue 4.
CFA Institute (2015 to 2018). Volatility Drag, Geometric vs Arithmetic Returns, and Return Path Dependence. CFA Institute Blogs.
Bogleheads Wiki. Variance Drain. https://www.bogleheads.org/wiki/Variance_drain
Kitces, Michael. Volatility Drag and the Impact on Investment Returns. https://www.kitces.com/blog/volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns/
Avellaneda, Marco and Zhang, Stanley (2009). Path Dependence of Leveraged ETF Returns. SSRN.
CSS Analytics. Volatility Drag and Return Path Dependence. https://cssanalytics.wordpress.com
Bainbridge, Stephen (1999). Path Dependent Choice in Finance. SSRN.