The Escalator and the Elevator
Why long trades and short trades require independent, asymmetric trend models, and the structural mechanism within Fractal Market Theory that explains why.
This appendix accompanies Phase 2 of The Feedback Engine series. Episode 8 introduced the escalator/elevator asymmetry as a structural consequence of long-biased agent populations and showed that asymmetric trend calibration improves portfolio performance. Episode 9 delivered the verdict on what survives and what doesn’t. But the main series was written for accessibility. It argued from the top down, from observable market behaviour to the mechanism beneath it.
This document goes the other direction. It builds the escalator/elevator thesis from the bottom up, starting with the microstructural mechanism (Bouchaud’s square-root impact law, stimulated refill, and the aggregate consequences of asymmetric agent populations) and works upward to the empirical patterns the series documented. It includes the full derivation, the literature grounding, the testable predictions, and the results of recovering square-root impact scaling directly from the daily futures data used throughout the series.
None of this is required reading. The appendix stands on its own. But for readers who want the complete structural argument (why the asymmetry exists, not just that it exists) this is where the chain closes.
Research Findings
We asked whether the conclusion in Episode 7 (that short-side alpha is extinct) might be an artifact of the symmetric trend model used in the test, and whether there is a structural reason within the Fractal Market Theory framework for treating long and short signals independently with asymmetric lookbacks. The answer to both questions, based on the literature and the logic of the framework, is yes.
This document presents the evidence in four parts: the empirical asymmetry between bull and bear dynamics, the structural mechanism within Fractal Market Theory, the literature supporting asymmetric trend models, and a proposed research plan for formal testing.
Part 1: The Empirical Asymmetry
The asymmetry between upward and downward price moves is one of the most robust findings in empirical finance, documented across more than two centuries of data.
Lunde and Timmermann (2004), in a study covering two centuries of US stock market data (1802 to 2002), found that bull markets averaged approximately 46 months in duration with a median return significantly larger in absolute terms than bear markets. Bear markets averaged approximately 14 months, roughly one-third the duration of bull markets. Critically, the median drift in bear markets was 50 to 100 percent larger in absolute terms than the median drift during bull markets. Prices rise slowly and fall quickly. The escalator and the elevator.
Gonzalez, Powell, Shi and Wilson (2005), using a hidden semi-Markov model on US stock data, identified five distinct market states: three bull states (low-volatility bull, high-volatility bull, and bubble) and two bear states (regular bear and crash/correction). The bear states were shorter in duration but more intense in their price impact.
Albuquerque, Eichenbaum and Rebelo (2015), analysing US equity data from 1869 to 2013, found annualised equity excess returns of 14.2 percent during bull markets versus negative 15.5 percent during bear markets. The asymmetry is not merely directional. The intensity per unit time is dramatically higher on the downside.
Lunde and Timmermann’s duration dependence analysis, using daily data from 1885 to 1997, found that bull market hazard rates decline with age (the longer a bull market has lasted, the less likely it is to end tomorrow), while bear market hazard rates exhibit a U-shaped pattern (rapid initial termination probability, then slower, then rapid again at extremes). This is precisely the pattern you would expect from the escalator/elevator dynamic: bull trends self-reinforce gradually, while bear trends either exhaust quickly or cascade violently.
The key empirical facts are:
Bull markets last approximately 3 to 5 times longer than bear markets. Bear markets deliver intensity per unit time that is 50 to 100 percent greater than bull markets. The volatility signature is asymmetric: downside volatility exceeds upside volatility persistently. The hazard rate functions are qualitatively different in each direction.
A symmetric trend model, using the same lookback for both long and short signals, is calibrated to a single frequency. If bull trends operate at low frequency (long duration, moderate intensity) and bear trends operate at high frequency (short duration, extreme intensity), the symmetric model is structurally misaligned with at least one side at all times.
Part 2: The Structural Mechanism Within Fractal Market Theory
The escalator/elevator asymmetry is not an anomaly within Fractal Market Theory. It is a direct, predictable consequence of the agent impact framework described in Postulate 1.
The agent population is not symmetric. The global capital base is overwhelmingly long-biased. Consider the composition:
Passive index funds now represent approximately 45 percent of all US equity assets, and their proportion has grown from less than 1 percent in 1993 to roughly 16 percent of the US stock market by AUM in 2021. These are structurally long-only. They do not short. Pension funds, sovereign wealth funds, endowments, and insurance companies collectively represent trillions of dollars of structurally long-only capital. Long-only active mutual funds, despite losing market share to passive, still manage enormous assets on a long-only mandate. Corporate buybacks provide a persistent bid for equities. Retail investors, through 401(k) plans, brokerage accounts, and robo-advisors, are overwhelmingly long.
Natural short capital (dedicated short sellers, some hedge fund strategies, options market makers delta-hedging) represents a small fraction of total market capitalisation. Estimates vary, but the ratio of structurally long capital to structurally short capital in equity markets is on the order of 20:1 or higher.
This asymmetry in the agent population produces asymmetry in the feedback dynamics through a specific mechanism that maps directly onto Postulate 2 of Fractal Market Theory.
During uptrends, divergent impact (trend-followers buying, passive inflows allocating, momentum capital chasing) pushes prices higher. But convergent impact builds gradually against it. Value investors trim overweight positions. Rebalancers sell winners. Profit-takers exit. The two forces are roughly balanced in magnitude because the long-biased population is comfortable holding. Selling pressure builds slowly. Convergent agents are active but not panicked. The aggregate impact function produces slow, persistent positive feedback. The escalator.
During downtrends, the entire long-biased population becomes a potential source of divergent impact simultaneously. This is the critical insight. Margin calls force leveraged longs to sell. Stop-losses trigger across systematic strategies. Redemptions from mutual funds and ETFs force portfolio managers to liquidate. Risk management systems across thousands of institutions hit their drawdown limits at roughly the same time. Passive outflows, while shown to be somewhat less reactive to poor returns than active fund outflows, still represent forced selling at the margin. Corporate buybacks cease during uncertainty. Retail investors panic.
Meanwhile, the convergent force (bargain hunters, contrarians, value buyers) is tiny relative to the wall of forced selling. There are simply far fewer agents with mandates, capital, and willingness to buy during a violent decline than there are agents being forced to sell.
Divergent impact overwhelms convergent impact almost instantly. The aggregate impact function produces fast, violent positive feedback in the downward direction. The elevator.
In Bouchaud’s terms, the square-root impact law (price moves proportional to the square root of order size) operates differently in each direction because the aggregate order flow is asymmetric. Going up, the flow of divergent orders (buying) is persistent but moderate, met by a steady stream of convergent orders (selling/profit-taking). Going down, the flow of divergent orders (forced selling) is sudden and overwhelming, met by minimal convergent flow (bargain hunting). The impact per unit time is structurally higher on the downside.
Bouchaud’s own work on asymmetric liquidity is directly relevant here. He showed that the impact of a buy following a buy should be less than the impact of a sell following a buy, due to “stimulated refill” of the limit order book. Buy market orders trigger an opposing flow of sell limit orders. This dampening mechanism (convergent response to divergent impact) is what prevents trends from building up endlessly. But the mechanism operates asymmetrically: the convergent response to buying (profit-taking, rebalancing, value selling) is robust and well-capitalised. The convergent response to selling (bargain hunting, contrarian buying) is thin and under-capitalised, especially during crises when the very institutions that might provide convergent liquidity are themselves facing redemptions and margin calls.
This gives us a formal refinement of Postulate 2 in Fractal Market Theory:
Refined Postulate 2: The spectral state is the aggregate of agent impact, but the frequency at which positive feedback operates is direction-dependent. Due to the asymmetric composition of the agent population, positive feedback during uptrends operates at low frequency (long duration, moderate amplitude), while positive feedback during downtrends operates at high frequency (short duration, extreme amplitude). A single lookback window cannot be optimally aligned with both frequencies. The spectrum itself is asymmetric.
This asymmetry should vary by asset class in proportion to the long-bias of the agent population:
Equities should show the strongest asymmetry (most long-biased agent population due to passive flows, pension mandates, corporate buybacks, retail 401(k)s). This is consistent with Episode 6, where equities showed the most anomalous spectral fingerprint (both spectral states producing VR below 1.0, duration ratio of 1.0x, and an inverted VR gap of −0.495).
Commodities with commercial hedgers on both sides (grains, energy) should show less asymmetry, because the convergent response to price declines (commercial buyers locking in low input costs) is well-capitalised and structurally motivated. This is consistent with livestock showing the cleanest spectral separation (duration ratio 2.2x, largest positive VR gap of +0.376).
Part 3: Literature Supporting Asymmetric Trend Models
Several independent sources confirm that treating long and short signals asymmetrically improves trend-following performance.
Agerback, Gudmundsen-Sinclair and Peltomaki (2017), in “The Long and Short of Trend Followers,” presented direct evidence for the asymmetric profitability of long and short trend-following strategies. They found that the long side is more profitable than the short side, and that CTA exposures have become increasingly biased toward long positions over time. Their core conclusion: the long and short sides should be differentiated in the analysis of dynamic investment strategies.
CSS Analytics (2020), in an analysis of adaptive momentum, identified the oscillation period asymmetry as a key driver of trend-following performance degradation. They noted that if it takes longer to go up than down, the oscillation period is asymmetric, and a fixed lookback will be structurally misaligned with one direction. They cited Garg et al., whose state-dependent analysis concluded that slower-speed momentum should follow correction months and faster-speed momentum should follow rebound months. This is precisely the asymmetric lookback logic.
The crypto literature has independently converged on asymmetric allocation. Recent work on adaptive trend-following in cryptocurrency markets uses a 70/30 long-short allocation scheme explicitly grounded in the empirical positive drift of the markets. While crypto markets differ from futures, the structural logic is identical: the positive drift creates an asymmetric opportunity set that a symmetric model cannot capture.
The options literature provides theoretical support. Fung and Hsieh (2001) showed that trend-following returns resemble lookback straddle payoffs. A lookback straddle’s payoff is the difference between the maximum and minimum price during the option’s life. If up-moves and down-moves operate at different frequencies, the optimal straddle maturity for capturing each direction differs. A single maturity (analogous to a single lookback) is suboptimal by construction.
Part 4: Implications for Episode 7 and Proposed Research
The conclusion in Episode 7 that short-side alpha has collapsed (ninety-three percent of post-2020 returns from the long side) may be partially an artifact of the symmetric model design. The symmetric 200-day lookback is well-matched to the slow escalator of bull trends but far too slow to capture the fast elevator of bear moves. By the time a 200-day signal triggers short, the most violent phase of the decline may already be over.
This does not mean the conclusion is wrong. It means it may be incomplete. Short-side alpha may not be dead. It may be invisible to a symmetric model operating at the wrong frequency.
The research plan to test this should address five specific questions:
Question 1: Does separating long and short signals with independent, asymmetric lookbacks recover short-side alpha that the symmetric model declared dead?
Test: Run the same 68-market trend strategy from Episodes 4 through 7, but with independent lookbacks for long and short signals. Long lookback: 200 to 500 days (calibrated to the slow escalator). Short lookback: 20 to 100 days (calibrated to the fast elevator). Compare the asymmetric model’s short-side contribution to the symmetric model’s.
Question 2: What is the optimal lookback ratio between long and short?
Test: Grid search across lookback combinations (long: 100 to 500 days in 50-day steps; short: 10 to 100 days in 10-day steps). Map the surface of MAR ratio as a function of long lookback and short lookback. If the escalator/elevator asymmetry is structural, the optimal ratio should be significantly different from 1:1.
Question 3: Is the asymmetry stable over time, or has it intensified?
Test: Run the optimal lookback ratio analysis separately by decade. The growth of passive investing (from less than 1% of equities in 1993 to approximately 45% today) should have made the agent population more long-biased, predicting that the optimal lookback ratio should have widened over time.
Question 4: Does the asymmetry vary by asset class as the agent population predicts?
Test: Compute the optimal lookback ratio separately for each of the eight asset classes. Equities (most long-biased) should show the strongest asymmetry (largest ratio between optimal long and short lookbacks). Grains and energy (commercial hedgers on both sides) should show less asymmetry. This test connects the lookback ratio directly to the spectral fingerprint from Episode 6.
Question 5: Does the MAR ratio for the asymmetric model exceed the symmetric model’s MAR?
Test: Compare full-sample and sub-period MAR ratios for symmetric (200-day) versus asymmetric (optimal long/short pair) models across the full universe. This is the definitive test. If the asymmetric model recovers meaningful short-side alpha, the MAR should improve materially, and the improvement should be concentrated in post-2008 data (when passive dominance and central bank backstops intensified the agent population asymmetry).
Part 5: What This Means for Fractal Market Theory
The escalator/elevator asymmetry has been tested empirically and constitutes a sixth postulate of Fractal Market Theory:
Postulate 6: The frequency of positive feedback is direction-dependent. Due to the asymmetric composition of the agent population (structurally long-biased), uptrends operate at low frequency (long duration, moderate amplitude) and downtrends operate at high frequency (short duration, extreme amplitude). A single lookback window is structurally suboptimal. Divergent strategies must treat the two directions as independent signal processes with independent calibration.
This postulate generates three additional predictions:
Prediction 9 (confirmed): The optimal short-side lookback is shorter than the optimal long-side lookback. The best single pair in the grid search is 250-day long and 10-day short, a ratio of 25:1. Shorter short lookbacks (10 to 30 days) dominate across virtually all long lookback pairings. The MAR surface shows the highest values concentrated in the bottom rows of the grid, confirming that faster short signals consistently outperform slower ones.
Prediction 10 (not tested): Whether the ratio has widened monotonically over time remains an open question for future research. The prediction is that the growth of passive investing should have intensified the long-bias asymmetry, producing a wider optimal ratio in recent decades.
Prediction 11 (partially confirmed): Asymmetric calibration recovers meaningful portfolio-level improvement in most asset classes. Grains show the largest improvement (+153%), followed by metals (+42%), energy (+32%), and fixed income (+28%). Equities improve by 17%. FX and livestock show slight deterioration under this specific asymmetric pair, consistent with FX having two-sided institutional flow. Standalone short-side alpha remains negligible post-2020. The improvement comes primarily from better long-side alignment and reduced short-side bleeding, not from resurrecting short-side edge.
The empirical results confirm two of three predictions and leave the third for future research. Episode 7’s original conclusion has been revised: the short side is structurally impaired but operates at a different frequency, and a symmetric model overstates the damage. Asymmetric calibration reduces the cost of maintaining the short side’s portfolio utility. The edge was partly obscured by a symmetric lens.
Summary
The escalator/elevator asymmetry is not an observation looking for an explanation. It is a structural consequence of Fractal Market Theory’s core mechanism (agent impact) combined with the empirical fact that the global capital base is overwhelmingly long-biased.
The mechanism is clean: asymmetric agent population produces asymmetric aggregate impact, which produces asymmetric feedback frequency, which requires asymmetric signal calibration. Every link in the chain is either established in the literature (Bouchaud’s agent impact, passive fund dominance, bull/bear duration asymmetry) or confirmed in the empirical tests. The recovery of square-root impact scaling from daily data, and its directional asymmetry in equities, closes the loop from microstructure to macro behaviour.
This investigation became Episode 8 of the series. It strengthens Fractal Market Theory by demonstrating that the framework generates predictions that lead to measurable improvements in strategy design, which is precisely what a good theory should do.
Part 6: Recovering Square-Root Impact from Daily Data
The series argues top-down: agent impact aggregates across a population to produce the spectral structure. Bouchaud’s square-root impact law provides the microstructural foundation for this argument, but it was established using tick-by-tick order flow data. The question is whether the square-root law leaves measurable traces in daily futures data, and whether those traces are directionally asymmetric in the way the escalator/elevator thesis predicts.
We tested this across all sixty-eight contracts using daily volume as a proxy for aggregate order flow and absolute daily returns as a proxy for impact. The core test measures how multi-day absolute returns scale with multi-day cumulative volume across 5, 10, and 20-day horizons. If impact scales linearly with volume, the exponent should be 1.0. If Bouchaud’s square-root law holds, it should be 0.5.
The result: the median exponent is 0.56 at the 5-day horizon, 0.55 at 10 days, and 0.61 at 20 days. This is remarkably close to the theoretical 0.5 of the square-root law and unambiguously sub-linear. Impact grows with volume, but much more slowly than linearly. The slight upward drift at longer horizons is consistent with impact correlation building cumulative directional moves, exactly the mechanism that produces the trending state.
The directional decomposition provides the strongest confirmation of the escalator/elevator mechanism. When we split the volume-impact exponent by direction, equities show a gap of 0.28 between down days (exponent 0.76) and up days (exponent 0.48). This is by far the largest directional asymmetry of any asset class. A given surge in volume moves equity prices substantially more on down days than up days. The elevator does not just move faster. It hits harder per unit of volume. Currencies show essentially zero directional difference, consistent with two-sided institutional flow. Energies show a moderate elevator effect. The ordering maps directly onto the agent population long-bias predicted by the framework.
We also confirmed impact persistence: volume on day t predicts absolute return magnitude on days t+1 through t+10, with correlations of 0.070 decaying slowly to 0.042. This is the footprint of Bouchaud’s metaorder execution in daily data. Impact does not vanish overnight. It decays over days, and this slow decay is what creates the trending state: if today’s impact persists into tomorrow, and tomorrow’s trading adds to it, the cumulative effect is a trend.
This provides a bottom-up confirmation of the framework. The square-root impact law that Bouchaud measured at the microstructural level leaves measurable traces in daily futures data, and those traces are directionally asymmetric in exactly the way the agent population framework predicts. The chain is now complete from both ends: microstructure upward through the square-root law and impact persistence, and macro behaviour downward through the spectral structure, the variance ratio, and the escalator/elevator asymmetry. Both paths converge on the same mechanism: agent impact, scaled across a long-biased population, producing direction-dependent feedback at direction-dependent frequencies.
Key References
Agerback, J., Gudmundsen-Sinclair, T. and Peltomaki, J. (2017). “The Long and Short of Trend Followers.” Available at SSRN: 2836389.
Albuquerque, R., Eichenbaum, M. and Rebelo, S. (2015). “Long-run Bulls and Bears.” Kellogg School Working Paper.
Bouchaud, J-P. (2009). “Price Impact.” arXiv:0903.2428.
Bouchaud, J-P. (2010). “The Endogenous Dynamics of Markets: Price Impact and Feedback Loops.” Panel Statement, Banque de France.
Bouchaud, J-P. (2024). “The Square-Root Law of Market Impact.” Substack.
Bouchaud, J-P., Farmer, J.D. and Lillo, F. (2008). “How Markets Slowly Digest Changes in Supply and Demand.” arXiv:0809.0822.
Fung, W. and Hsieh, D. (2001). “The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers.” Review of Financial Studies.
Goldman Sachs (2025). “Bear Market Anatomy.” Global Investment Research.
Lunde, A. and Timmermann, A. (2004). “Duration Dependence in Stock Prices.” Journal of Business and Economic Statistics.
Pagan, A. and Sossounov, K. (2003). “A Simple Framework for Analysing Bull and Bear Markets.” Journal of Applied Econometrics.
Zakamulin, V. (2024). “Stock Price Overreaction: Evidence from Bull and Bear Markets.” Review of Behavioural Finance.
This research series is drawn from The Fractals of Finance: Determinism, Adaptation and the Geometry of Markets
The book explores the full architecture of feedback, fat tails, and fractal structure in financial markets, and what it means for how we trade, invest, and understand risk.
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