CASE 11
How Percent-of-Equity Sizing Can Manufacture a Spectacular Backtest
The same entries and exits can produce the same idealized terminal wealth but materially different drawdown paths; rounding, fixed costs, caps, and stop rules can then transmit path dependence into terminal results.
Validation verdict for percent-of-equity sizing
Percent-of-equity sizing is a capital rule layered on top of a signal. It can magnify a genuine edge, but it can also magnify start-date luck and favorable trade order. Evaluate the signal and the sizing engine separately.
What the headline metric obscures about percent-of-equity sizing
The compounded equity curve is visually persuasive because gains accelerate. That acceleration is often interpreted as the strategy “getting stronger,” even though the signal’s per-trade distribution may be unchanged.
An early winning sequence raises the dollar size of every later trade. If a large historical winner occurs after that expansion, the final result reflects both the winner and the path that allowed more capital to reach it.
How percent-of-equity sizing enters the backtest
Sizing turns order into outcome
With fixed size, reordering trades changes drawdown timing but not total arithmetic profit. With percent-of-equity sizing, reordering changes every later dollar exposure and the endpoint.
Early luck receives permanent leverage
A favorable first segment enlarges the account base and compounds through the rest of the sample.
Drawdowns shrink future opportunity
Early losses reduce later position size, so identical future signals earn less and recovery becomes path dependent.
Leverage and margin may be hidden
A nominal percentage of equity can imply very different gross exposure across instruments, pyramiding and contract specifications.
Compact reconstruction of percent-of-equity sizing
| Sizing / sequence | Same signals? | Ending return | Max drawdown | What changed |
|---|---|---|---|---|
| Fixed one unit | Yes | +48% | −16% | No compounding |
| 1% equity, idealized median ordering | Yes | +74% | −19% | Terminal wealth is order-invariant |
| 1% equity, idealized reported ordering | Yes | +74% | −24% | Same terminal value, worse path |
| 1% equity with rounding and stop rules | Yes | +12% | −41% | Implementation constraints alter terminal value |
The signal set is identical. The two idealized fixed-fraction orderings have the same terminal wealth but different drawdown paths. The final row adds rounding and stop rules, showing how implementation constraints can convert path dependence into a terminal difference.
The test that can overturn the percent-of-equity sizing verdict
Run a sizing decomposition: fixed units, fixed currency risk, fixed percentage and capped percentage. Then reshuffle the same trades under each rule and compare endpoint and drawdown distributions.
What trade-list analysis can and cannot identify about percent-of-equity sizing
Export-level red flags for percent-of-equity sizing
- Compounded return is several times fixed-size return
- Most endpoint dispersion comes from the first 10% of trades
- Risk percentage is stated without gross exposure or pyramiding cap
- Position size rises after a small sample of early wins
- Reported CAGR changes drastically under trade-order simulation
What the export reveals about percent-of-equity sizing
- Fixed-size versus percent-equity reconstructions when quantity and capital assumptions are supplied
- Sequence sensitivity of ending capital, maximum drawdown and recovery
- Exposure concentration caused by overlapping positions and compounding
- Whether impressive curvature survives caps, costs and adverse early sequences
What percent-of-equity sizing still requires from settings, code, or market data
- A CSV may contain realized quantity but not the exact equity snapshot used for each sizing decision. Preserve sizing settings and account-state logic.
- Reshuffling assumes a model of trade independence unless blocks are preserved. Use cluster-aware methods when signals share market events.
Turn amplification from percent-of-equity sizing into a falsifiable backtest diagnosis.
Case file 11/20 · SIZE-FDBK · one failure mechanism, one falsifiable protocol
Research abstract: percent-of-equity sizing
Case file 11/20 · SIZE-FDBK · one failure mechanism, one falsifiable protocol
This article tests one central proposition: percent-of-equity sizing can exponentially amplify a favorable early ordering, allowing capital allocation rather than signal quality to create the spectacular curve. The question is not merely whether the displayed net profit or win rate was arithmetically calculated. The deeper identification problem is whether we know what constitutes one observation, what information was available at the decision time, which assumptions are necessary for the profit to exist, and how much of the conclusion survives when those assumptions are perturbed. The research object is therefore not one performance table; it is the linked data-generation, fill-generation, estimation, selection, and capital-allocation process.
The primary estimand is reproducibility of the underlying signal edge after separating it from the capital-allocation rule. The observation unit is defined as fixed-risk-normalized trade returns plus a separate capital-allocation update layer. Without this definition, split fills, duplicated signals, common events, synthetic prices, or timestamp conversions can be double-counted as independent evidence. A larger row count does not necessarily contain more independent information. An academically defensible analysis fixes the relationship between the observation unit and the estimand before it reports sample size, standard error, or statistical confidence.
The principal sensitivity axes are fixed quantity, fixed R, percentage compounding, reversed order, and risk caps. The hidden state is compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses. In particular, positions expanded immediately before a drawdown maximize currency losses even when the R loss is unchanged. Means and medians alone are incapable of describing that mechanism, so the analysis combines central estimates with lower quantiles, expected shortfall, sign stability, boundary-hitting frequency, and contribution concentration. The objective is not to find one pessimistic number, but to map the full region in which the original conclusion changes sign or ceases to be economically usable.
The conclusion does not attempt to prove that a backtest is good. It separates the component that remains after attempted falsification from the component that disappears when assumptions are reconstructed. The governing decision principle is to evaluate signals in fixed R, compare sizing as a separate stress layer, and flag severe instability under sequence reversal. This is not trading advice; it is a research procedure for measuring how much evidentiary weight a TradingView trade export can carry. Liquidity not present in the file, broker-specific rules, future regimes, outages, and gaps require separate evidence, and statistical survival never guarantees future profit.
The numerical values illustrate the method for amplification from percent-of-equity sizing; they are not a real strategy, client record, or forecast.
Hypotheses and identification target for percent-of-equity sizing
reproducibility of the underlying signal edge after separating it from the capital-allocation rule
H₀ for percent-of-equity sizing: The reported performance is not materially dependent on the suspected failure mechanism and survives reasonable perturbations.
H₁ for percent-of-equity sizing: The reported performance depends materially on the suspected failure mechanism and deteriorates after reconstruction, perturbation, or dependence-aware resampling.
reproducibility of the underlying signal edge after separating it from the capital-allocation rule
fixed-risk-normalized trade returns plus a separate capital-allocation update layer
compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses
fixed quantity, fixed R, percentage compounding, reversed order, and risk caps
Formal estimands for percent-of-equity sizing
Definitions precede inference.
g=(1/T)Σ log(1+f·r_t)Geometric growth rate. It is sensitive to loss magnitude and f, while terminal wealth in the idealized fixed-f model is order-invariant.The primary estimand is reproducibility of the underlying signal edge after separating it from the capital-allocation rule. The observation unit is defined as fixed-risk-normalized trade returns plus a separate capital-allocation update layer. Without this definition, split fills, duplicated signals, common events, synthetic prices, or timestamp conversions can be double-counted as independent evidence. A larger row count does not necessarily contain more independent information. An academically defensible analysis fixes the relationship between the observation unit and the estimand before it reports sample size, standard error, or statistical confidence.
The principal sensitivity axes are fixed quantity, fixed R, percentage compounding, reversed order, and risk caps. The hidden state is compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses. In particular, positions expanded immediately before a drawdown maximize currency losses even when the R loss is unchanged. Means and medians alone are incapable of describing that mechanism, so the analysis combines central estimates with lower quantiles, expected shortfall, sign stability, boundary-hitting frequency, and contribution concentration. The objective is not to find one pessimistic number, but to map the full region in which the original conclusion changes sign or ceases to be economically usable.
Illustrative recomputation design for percent-of-equity sizing
For the percent sizing reconstruction, table values are illustrative calculations used to expose a verdict reversal; they are not a user’s observed TradingView result.
| ID | Recomputation layer | Operation | Comparison | Diagnostic purpose |
|---|---|---|---|---|
| S0 | Reported result | Restate the Strategy Tester aggregate | Base | Apparent conclusion |
| S1 | Unit reconstruction | fixed-risk-normalized trade returns plus a separate capital-allocation update layer | Reassess count and dependence | Information correction |
| S2 | Independent recomputation | Rebuild price, size, cost, and currency row by row | Separate reconciliation error | Measurement validity |
| S3 | Local stress | fixed quantity, fixed R, percentage compounding, reversed order, and risk caps | Perturb one factor only | Causal sensitivity |
| S4 | Tail injection | positions expanded immediately before a drawdown maximize currency losses even when the R loss is unchanged | Recompute lower quantiles and boundary hits | Capital preservation |
| S5 | Dependence-aware resampling | Generate paths across several block lengths | Intervals and sign stability | Estimation uncertainty |
| S6 | Selection adjustment | Log search, OOS review, and exclusions | Correct maximum-selection bias | Generalization |
| S7 | Full gate | evaluate signals in fixed R, compare sizing as a separate stress layer, and flag severe instability under sequence reversal | Compare with predeclared thresholds | Pass / hold / reject |
The illustrative recomputation for percent-of-equity sizing changes one processing layer at a time, then combines only predeclared layers. S0 is never treated as ground truth; it is the statement to be audited. S1 and S2 ask whether the exported unit and arithmetic are coherent. S3 and S4 identify local sensitivity and tail failure. S5 changes the uncertainty model rather than the trade list. S6 adjusts for the search that preceded publication. S7 applies the same gate to every version. This order prevents an adverse result from being explained away by simultaneously changing several assumptions.
In the percent sizing figures, color and position encode diagnostic sensitivity only; they do not represent statistical significance or future P&L.
Diagnostic figures specific to percent-of-equity sizing
Four separate visual tests; no decorative chart reuse.
Multi-layer audit questions for percent-of-equity sizing
A result is only as strong as its weakest unresolved layer.
From an audit perspective, fix the estimand as “reproducibility of the underlying signal edge after separating it from the capital-allocation rule.” Do not substitute net profit, win rate, or a visually smooth curve for that target. Declare the horizon, account currency, included frictions, and operating-stop boundary before calculation. Any post-result change creates a new hypothesis and version, preventing the question from being selected after the answer is known.
Reconstruct the observation unit as “fixed-risk-normalized trade returns plus a separate capital-allocation update layer” before treating rows as independent evidence. Report raw rows, parent trades, decisions, event clusters, and the denominator used for each average or standard error. Recompute unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction under more than one defensible aggregation rule so that a larger export is not mistaken for a larger information set.
Preserve the hash of the TradingView export and the symbol, timeframe, session, timezone, order-processing settings, costs, account currency, and Pine version. For amplification from percent-of-equity sizing, compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses directly affects reproducibility. Keep immutable source, normalized, and analysis layers separate, with every join, deletion, imputation, and conversion recorded in a transformation ledger.
The export identifies only what can be rebuilt from recorded time, price, quantity, and P&L. quantity rounding, minimum order size, margin caps, withdrawals, and risk-reduction rules requires additional evidence. Mark each causal link as observed, bounded by assumption, or externally unverified. This prevents compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses from being presented as a confirmed fact when the available data support only an interval or conditional conclusion.
Do not adopt the platform summary as ground truth. Independently hold the unit-return signal series fixed and recompute fixed quantity, fixed R, and constant-fraction compounding as separate allocation layers. Reconcile total and row-level differences by sign, date, symbol, and order type. If discrepancies concentrate in the exact state associated with amplification from percent-of-equity sizing, treat that concentration as a primary finding rather than dismissing it as rounding.
Report unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction with intervals or resampling distributions, not point estimates alone. Match the uncertainty method to sample size, skewness, heavy tails, censoring, and selection history. If normal, quantile, and dependence-aware methods disagree on the sign, classify the edge as unidentified and show the minimum detectable effect and lower decision bound.
Do not narrow uncertainty with an IID shuffle alone. Resample block orderings and inception cohorts that preserve return-regime dependence using several fixed block lengths and stationary bootstrap. Preserve random seed, repetition count, wrap rule, and missing-data treatment. For each block specification, report the distribution of unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction, the rejection-side tail mass, and the rate at which the verdict changes sign.
Interrogate the mechanism “compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses” with lower quantiles, expected shortfall, influence, cluster length, and boundary-hitting measures. Historical maximum loss is not a loss cap. Define several absorbing or operating boundaries—capital, margin, mandate drawdown, and recovery time—and record which boundary fails first under each stress.
A flat commission deduction is not an execution model for amplification from percent-of-equity sizing. Allocate spread, slippage, financing, borrow, roll, conversion, rounding, and rejected orders to the relevant unit. Recompute unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction under base, upper-quantile, and crisis states while preserving the possibility that costs and losses worsen together.
Count the complete population of periods, symbols, timeframes, parameters, exits, filters, and metrics that were tried. Do not detach the attractive result for amplification from percent-of-equity sizing from rejected candidates, interim changes, or repeated validation reviews. Where appropriate, use PBO, SPA, and a Deflated Sharpe Ratio, and treat an unrecorded trial count as a material audit limitation.
Test whether amplification from percent-of-equity sizing is concentrated in one trend, volatility, liquidity, rate, or session state. Define regimes prospectively or on training data only. Report statewise unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction, occupancy, transition probabilities, and costs, then reweight the mixture to adverse but realistic future compositions.
For the percent-of-equity sizing case, the same trade set can follow different capital paths under another inception date, order, initial balance, rounding rule, or stop condition. Separate fixed quantity, fixed R, and percentage sizing, then use circular shifts and block orderings to recompute drawdown, recovery, and boundary hits. Equal terminal P&L does not imply equal path risk.
Perturb “fixed quantity, fixed R, percentage compounding, reversed order, and risk caps” one axis at a time before creating a joint sensitivity surface. Add the negative control “replay the same signals at constant notional to isolate how much spectacular growth comes from the allocation recursion rather than the signal.” Predefine the grid and crisis rule so that neither the most favorable nor the most damaging cell is selected after inspection. Save the slope, curvature, and exact point where the decision boundary is crossed.
Have a second implementation hold the unit-return signal series fixed and recompute fixed quantity, fixed R, and constant-fraction compounding as separate allocation layers, then compare critical row-level outputs. Regression fixtures should include empty files, duplicate timestamps, extreme costs, reverse ordering, missing values, and boundary cases. Agreement between implementations is insufficient if they share the same bad input, so separate data construction and review roles where feasible.
Predeclare the decision rule. This case passes only if “the underlying edge remains under fixed quantity or fixed R and boundary risk is acceptable under the capped percentage-sizing rule.” Near a boundary, disclose interval width and economic materiality rather than a binary badge. If only one favorable block length, cost state, or implementation passes, classify the result as assumption-sensitive rather than robust.
The evidence ledger must store the input hash, code version, settings, exclusions, “fixed quantity, fixed R, percentage compounding, reversed order, and risk caps,” block lengths, random seed, repetition count, and every scenario output. Keep exploratory and confirmatory results in separate namespaces and retain failed trials. When new TradingView data arrive, create a new version and track unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses rather than overwriting the old result.
Translate statistical changes into capital consequences. A shift in expectancy, lower quantile, recovery time, or boundary risk caused by amplification from percent-of-equity sizing should be mapped to trade count, capital, margin, and continuation. A small per-trade difference can compound under high turnover, while a rare loss can be decisive near an absorbing boundary.
Separate hypothesis design, implementation, independent recalculation, and approval where practical. Stop automatically on material reconciliation error, unresolved missing data, non-reproducibility, or a predeclared threshold breach. Audit the chain “weak unit edge → larger size after gains → amplification of early order → spectacular curve → allocation mistaken for signal quality,” and monitor unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses prospectively without turning a historical pass into a promise of future profit.
Falsification protocol for percent-of-equity sizing
evaluate signals in fixed R, compare sizing as a separate stress layer, and flag severe instability under sequence reversal
Freeze the TradingView source for the percent-of-equity sizing audit
Store the export without alteration and record its hash, export time, strategy, symbol, timeframe, and settings. Preserve every column relevant to amplification from percent-of-equity sizing; deletions and imputations belong only in derived tables.
Reconstruct the observation unit for percent-of-equity sizing
Aggregate rows into “fixed-risk-normalized trade returns plus a separate capital-allocation update layer,” and report raw rows, parent trades, events, and independent clusters. Recompute the critical result under another defensible aggregation.
Independently recompute the displayed percent-of-equity sizing result
Independently hold the unit-return signal series fixed and recompute fixed quantity, fixed R, and constant-fraction compounding as separate allocation layers. Reconcile row-level and aggregate outputs with Strategy Tester and preserve where discrepancies concentrate.
Isolate the percent-of-equity sizing mechanism
Treat amplification from percent-of-equity sizing as the principal mechanism and move “fixed quantity, fixed R, percentage compounding, reversed order, and risk caps” one axis at a time while holding other settings fixed.
Map the operating boundary for percent-of-equity sizing
Combine the primary and interacting axes on a predeclared grid and recompute unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction. Record the width and connectivity of the acceptable region and every boundary crossing.
Resample the dependence structure relevant to percent-of-equity sizing
Use block orderings and inception cohorts that preserve return-regime dependence with several fixed block lengths and stationary bootstrap. Save every random seed, repetition count, and block specification.
Inspect influence points and operating boundaries for percent-of-equity sizing
For the percent sizing influence test, remove the largest contributor, top-k contributors, selected periods, and relevant regimes in sequence; then recompute lower-tail measures and the operating boundary.
Apply negative controls and conservative bounds to percent-of-equity sizing
Replay the same signals at constant notional to isolate how much spectacular growth comes from the allocation recursion rather than the signal. Bound quantity rounding, minimum order size, margin caps, withdrawals, and risk-reduction rules as unobserved factors rather than elevating the optimistic value into the final answer.
Apply the predeclared gate to percent-of-equity sizing
Do not move the threshold after seeing results. Compare with “the underlying edge remains under fixed quantity or fixed R and boundary risk is acceptable under the capped percentage-sizing rule,” and distinguish pass, hold, and reject. Any unresolved material mismatch causes a hold.
Save a reproducible evidence package for percent-of-equity sizing
Bundle the source, transformation ledger, formulas, figures, all scenarios, failure logs, and code version for rerun in another environment. Prospectively monitor unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses.
Decision gate for percent-of-equity sizing
Reject the story before trusting the curve.
How to read the percent-of-equity sizing figures and equations
The figures for percent-of-equity sizing use illustrative recomputations constructed to expose this specific failure mode. Do not infer statistical significance from line position or color alone; first verify the estimand, units, denominator, censoring rule, and cost sign defined by the equations. A sensitivity surface is not a causal estimate. It shows how a conclusion changes only within the stated assumptions. Resampling should compare an IID shuffle with stationary and block bootstrap procedures across several block lengths so that loss clustering and regime persistence are not silently destroyed. Store the random seed, iteration count, block length, bandwidth, and missing-data treatment, and claim reproducibility only after an independent implementation reproduces the same aggregates.
This case passes only if “the underlying edge remains under fixed quantity or fixed R and boundary risk is acceptable under the capped percentage-sizing rule” across reconstructed values, local perturbations, joint sensitivity, dependence-preserving resampling, and the negative control, with no material sign reversal or unresolved reconciliation error. A pass is limited evidence against the stated failure mode, not certification of future profit.
- The estimand and observation unit were fixed before outcomes were reviewed
- For percent sizing, any material disagreement between reported and independently recomputed values must be resolved or explicitly explained.
- The percent sizing claim passes this gate only when its acceptable stress region is broad and connected rather than one isolated favorable island.
- The sign of the percent sizing estimate must remain stable across defensible block lengths, saved seeds, and reasonable interval methods.
- For percent-of-equity sizing, economic margin remains after deleting the largest and top-five contributors and key regimes
- For percent-of-equity sizing, conservative cost, fill, and capital-boundary scenarios remain inside the stopping mandate
Limitations, external validity, and reproducibility of the percent-of-equity sizing audit
Every inference has a boundary.
The first limitation is that a trade export does not contain the complete market state. If order-book depth, queue position, network latency, rejected orders, broker liquidity, or realized financing history is absent, reproducibility of the underlying signal edge after separating it from the capital-allocation rule remains model-mediated. Model outputs should be displayed as scenario ranges and must not be formatted as though they were directly observed facts.
A second limitation specific to the percent-of-equity sizing analysis is structural change. A long historical sample does not guarantee a common population when market rules, participants, volatility, rates, spreads, data construction, or Pine execution semantics change. Do not increase nominal sample size by indiscriminately pooling old periods. Estimate rolling and regime-conditioned behavior and test parameter stability around detected changes.
A third limitation specific to the percent-of-equity sizing analysis is reuse of the diagnostic battery. Applying these tests repeatedly to the same data and editing the strategy until it passes turns the diagnostic process itself into another optimizer. Every post-test edit starts a new model version and requires untouched or prospective evidence. A test chosen after reading the outcome belongs to exploration and cannot be counted as independent confirmation.
A fourth limitation for the percent-of-equity sizing analysis is the distinction between statistical survival and operational suitability. Behavioral tolerance, locked capital, tax, regulation, outages, account terms, order-size limits, market-order restrictions, and liquidity discontinuities cannot be resolved from a CSV alone. The lab is a diagnostic for discovering hidden failure risk earlier; it is not investment advice, a performance warranty, or a guarantee of bounded loss. User-specific constraints remain a separate decision layer.
The estimand “reproducibility of the underlying signal edge after separating it from the capital-allocation rule” is identified only within the columns present in the TradingView export and the stated assumptions. If quantity rounding, minimum order size, margin caps, withdrawals, and risk-reduction rules cannot be observed, report bounds rather than a false point estimate.
Past estimates of amplification from percent-of-equity sizing need not belong to the same population after changes in rules, participants, volatility, costs, or data specifications. Track unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses in rolling and regime-specific windows.
For percent sizing, repeatedly applying the same diagnostic battery and editing until it passes turns verification into another optimizer. Every post-audit change therefore creates a new model version and requires untouched evidence.
Even if the underlying edge remains under fixed quantity or fixed R and boundary risk is acceptable under the capped percentage-sizing rule, the analysis does not establish tax, regulatory, behavioral, liquidity, order-size, or systems suitability. Separate statistical diagnosis from live-operating approval.
Deleting observations related to compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses may improve the result. Compare no deletion, conservative imputation, and worst-case imputation, and display how unit-return expectancy, geometric growth, maximum drawdown, sequence sensitivity, and boundary-hitting rate by risk fraction changes.
Run the control “replay the same signals at constant notional to isolate how much spectacular growth comes from the allocation recursion rather than the signal.” If the control performs similarly, suspect processing rules or common market drift before attributing performance to the strategy.
After a provisional pass, log unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses sequentially and stop on persistent departures from the predeclared predictive range. Diagnose implementation drift before reoptimizing history.
Multiple methods can agree because they share the same bad input or the same mechanism “compounding feedback, early sequence, risk expansion after wins, and recovery speed after losses.” Give lower-tail outcomes, failed scenarios, and unresolved mismatches the same visual prominence as favorable results; test count is not proof of correctness.
Independent and adversarial findings for percent-of-equity sizing
The percent sizing case has a separate review line for formulas, chart encodings, data definitions, and falsifiability so agreement on one layer cannot mask failure on another.
The formula audit checks numerator, denominator, sign, unit, domain, and every conditioning assumption as one system. The material caution for this case is: In the idealized frictionless fixed-f model with every multiplier 1+fr_t positive, terminal wealth is order-invariant by commutativity of multiplication. Drawdown and recovery remain order-dependent, and rounding, fixed costs, caps, or stop rules can also make terminal wealth order-dependent. A correct symbolic expression can still calculate the wrong quantity when a column, currency, time unit, or fee sign is misdefined, so those mappings are part of the mathematical audit.
The figure audit assigns distinct jobs: Figure 1 diagnoses amplification from percent-of-equity sizing; Figure 2 maps joint sensitivity; Figure 3 shows the dependence-preserving distribution of geometric growth by sizing rule; Figure 4 traces causal propagation. Color denotes distance to a predeclared gate, not probability or observed performance. Axis units, zero, quantiles, censoring, and bounds must agree with captions and tables. A smooth SVG line is explanatory geometry, not evidence of estimation precision.
The adversarial test does not cherry-pick one hostile scenario. It uses the negative control “replay the same signals at constant notional to isolate how much spectacular growth comes from the allocation recursion rather than the signal,” resamples block orderings and inception cohorts that preserve return-regime dependence at several block lengths, and bounds quantity rounding, minimum order size, margin caps, withdrawals, and risk-reduction rules as unobserved factors. Repetitions, seeds, exclusions, block specifications, and plotting range are frozen before results so the implementer cannot tune the audit after seeing the answer.
The independent conclusion is restricted to whether “the underlying edge remains under fixed quantity or fixed R and boundary risk is acceptable under the capped percentage-sizing rule.” It does not certify a good strategy or future profit. Any material reconciliation error, formula-domain violation, table-figure contradiction, sign reversal across defensible block lengths, or failure to outperform the negative control produces hold or reject. Prospectively, monitor unit-return expectancy, realized risk fraction, rounding error, and risk contraction after losses.
Methodological references for percent-of-equity sizing
Primary methods and official platform documentation.
- Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal.
- Politis, D. N. & Romano, J. P. (1994). The Stationary Bootstrap. JASA.
- TradingView Pine Script® documentation: Strategies.
- Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics.
- Newey, W. K. & West, K. D. (1987). A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica.
- White, H. (2000). A Reality Check for Data Snooping. Econometrica.
References for the percent-of-equity sizing case provide methodological context; they do not validate the synthetic numbers in this article or certify any backtest result. TradingView documentation is used for platform semantics, while statistical papers motivate uncertainty and selection controls.
Frequently asked questions about percent-of-equity sizing
Is percent-of-equity sizing wrong?
No. It is a legitimate rule. The mistake is attributing all compounded growth to signal quality or ignoring how strongly sequence and exposure caps drive it.
Why compare fixed size?
Fixed size removes compounding from the endpoint and reveals whether the underlying trade distribution has positive expectancy on its own.
Should I publish both curves?
Yes. A fixed-size baseline plus the intended sizing result makes the contribution of the signal and capital rule visible.
Can a backtest exposed to percent-of-equity sizing be trusted?
Do not judge the percent sizing case from a finished equity curve alone. Use the TradingView trade list to inspect the mechanism-specific concentration, path, cost, timing, and dependence evidence shown on this page.
Important limitations for the percent-of-equity sizing analysis
This article provides educational, descriptive analysis of constructed backtest failure examples. It is not investment advice, a buy or sell signal, a forecast or a promise of performance. Backtest results depend on data, code, broker-emulator assumptions, costs, sizing and market structure. TradingView is a trademark of TradingView, Inc.; SG Group is independent and does not claim endorsement or sponsorship by TradingView.
Counterpart: 複利の見栄えに騙される｜資産比率サイジングが成績を増幅する仕組み