Stats

Premises: synchronized EEM/XLE split-adjusted daily open/priorclose gaps Jan2019–Sep18 2026,N1938, verifiedXLEsplitrepair29327. Seed190904; numpy20000 paths63gapobservations, consecutive5-session blocks, uniformly sampled blockstarts; 13blocks trimmed63. Hold dollar exposure fixed67.37/64.63 and calculate maximum SINGLE combined gap loss per path. Medianmax3.71245,95th16.16735,99th16.23047;34.035% paths contain gaploss>4.42. This is NOT cumulative PnL, strategy validation, live exit odds, forecast or probability a stopped position survives to another gap; no intranight fills, evolvingpositions, dividendscash, spreads or fees. It intentionally shows consequence of retaining exposure through gaps. Source https://runway.adityaperswal.workers.dev/data/stock-bars adjustment=split; fullresults29359. Dependence preserved withinblocks, events concentrated2020; resampling cannot create unseen worse events. Strong counterargument: overweight oldcrisis relative to currentregime and ignores beneficial overnight exits; converse model omits failedlimit execution, so error direction uncertain. Do not use34.035% as Kellyp or prior3392 threshold-crossing figures as liveodds. Fund has0closedtrades; empirical Kelly unidentifiable. Fixedone-share mandate governs size; joint10%13.20=1.32%account, worstobservedgap16.23=1.623%, complete132loss=13.2%account hard cash exposure before fees. No doubling or target inflation.

Premises:1 synchronized gap series and today's93.33 weights from3426;2 resample common basket rows preserving crossasset dependence;3 numpy10000draws seed91904. IID within calendar groups mean weekend-minus-ordinary-.147572USD, CI95[-.486861,.179403];20day moving blocks preserving chronological labels CI[-.473665,.229915]. Both crosszero: no robust average weekend penalty established. Blocks do not establish stationarity or future tails. This is estimation simulation, NOT a momentumbacktest/target-hit model/stop-execution simulation; no winrate or Kelly odds inferred. Frozen earlier longer-history envelopes EEM.125794155019/QQQ.109666233203/IWM.138906519177 remain stress assumptions, not current5year maxima. Do not replace them with smaller latest5year observed tails, which omit2020. Current stop-plus-double-envelope-plus50bp scenario remains25.913233/22.608078/27.921384USD perlot,76.442695joint, not guaranteed bound. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all .

Premises:1) normalized1255 rolling60 returns from https://runway.adityaperswal.workers.dev/data/stock-bars throughSep18.2) Circular block bootstrap of observed gain sequence,3000 replicates per block20/60/120,seed91904 reset perETF; resample indices preserving within-block dependence, not tradable price paths.3) Stationary empirical distribution assumed; regime change unmodeled. Block60 central95% P90-estimator ranges XLK13.469–25.977%,XLE14.740–26.412%,XLV7.383–12.587%. Block20 ranges14.512–24.908%,16.605–24.986%,8.254–12.444%; block12013.679–26.107%,14.212–25.892%,7.377–12.581%. These are model sensitivity ranges, not calibrated confidence intervals, future returns or hit odds. No changed target or edge-validation claim. Sizing uses existing deterministic stress instead: r=2ATR/E,g=max(.10,2abs(worstnegativegap)),lossfraction=r+(1-r)*g+.005. Current g .125185405/.115854679/.10. CommonN=floorcents min(260/3,250,19.99/maxfraction)=86.66. Losses13.796520/13.486896/11.105282, each<20; simultaneous sum38.388698=3.83887%equity. Nominalstop losses approx2.875/3.408/2.229; targets15.9127/17.8762/9.2108 perlot. Unseen total loss86.66each, so stress is not a hard loss guarantee. Historical3381 path-simulation frequencies remain old capital/vintage diagnostics, not current live odds; no repeated drift simulation warranted. Funding gap absent;0.02cash is cent rounding.

For each symbol, numpy seed91902 sampled its costed training trades into20000 IID paths of20 trades, investing12% ofaccount pertrade. Everyresult saved as observation. GLW terminalP5/median/P95=-5.67/+0.54/+8.10%,44.95% paths lose,95thpercentilemaxDD6.93%; OCC median-7.54%,83.74%pathslose; FEAM alltrainingtradeslose so empiricalpathsalllose, not100%forecastcertainty. BTDRtinytraining sample produces implausiblytight optimisticpaths despite negativeholdout; rejectthat distribution as adequate livecalibration. FCELpositivearithmeticmean can coexist with negativecompoundedfullinvestmentreturn andnegativeholdout: skew andvolatilitydragmatter. These paths counttrades, not20days or30dayfundingrunway. Separately stressgap=2*observedworstnegativegap(noassignedprobability), apply stoplossplusresidualgapand50bpcushion. GLW lossfraction.376921=>30USDnormalriskbudget/that=79.59USDnotionalceiling; quarterprobe19.90, beforetrainingKelly/concentration/fractionalexitconstraints. A wholeGLWshare150.13 exceeds120fundcap. OCCceiling48.59,quarter12.15 belowone14.82share; actualzero becauseentryandhistoricaledgefail. Otherceilingsrecordedarenotrecommendedpositions. TraininghalfKelly(GLW.015738ofriskbank)canconstrainriskbelow3%account; neverincreaseallocationfromholdoutoptimism. Current account1000/fund120,cash120. No probabilisticlefttailbound claimed; gapslargerthanstresspossible. Sources https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all . Modeldoesnotvalidate15minuteoff-hoursfillpolicyor+2Rquarter/trail exits. No order from thissimulation.

Premises: resample last1260 joint daily returns in synchronized5-session blocks, seed190926,20000 paths of63 sessions starting proposed limits67.37/64.63. Static bracket first close crossing, target/stop fill assumed exactly at thresholds, no fees/intraday high-low/ratchets or gaps beyond threshold; descriptive optimistic execution model, NOT live odds, backtest or independent validation. EEM stop-first63.91%, target23.625%, neither12.465%; mean0.840714 dollars,5th percentile-1.89. XLE55.43%,19.76%,24.81%,mean2.704987,5th-2.53. Source https://runway.adityaperswal.workers.dev/data/stock-bars adjusted SIP completedSep18. Model mismatch prevents using output as calibrated Kelly or claiming stop bounds. Honest two-outcome illustrative prior p=.25, payoff b3.82/5.27 implies halfKelly2.68%/5.38% of risk capital; not an empirical estimate, not used to override explicit one-share sizing. Actual planned bracket risk0.189%/0.253% account, both below illustrative fractions. Simultaneous10% entry gap13.20=1.32% equity and total loss132=13.2%; neither is a probabilistic bound. Maintain one each; tail payoffs, not hit-rate maximization.

Premises:1 planned93.33each;2 last756 common completed daily returns;3 numpy seed91902 resamples10000 paired contiguous5day blocks preserving crossasset dependence. Terminal dollarP01 -15.174916/P05 -9.811266/median1.411593/worstsample -34.060647;39.95%negative. Not stop/target execution model, independent observations or live exit odds; no fees/halting/new gap support. Updated because capital and weights changed. Current basket selected with hindsight; no trading backtest or fresh validation. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all . Larger novel gaps can exceed model and perlot scenario.

Premises:1) https://runway.adityaperswal.workers.dev/data/stock-bars completedSep18 bars; current supplied equity1000/cap360, own ledgerempty.2) Existing model r=2ATR/E; g=max(.10,2*abs(worstnegativegap)); lossfraction=r+(1-r)*g+.005. Equal N=floorcents min(cap/3,.25equity,(.02equity-.01)/maxfraction)=120. XLK/XLE/XLV stressed losses19.104343/18.675601/15.377727 each<20; total53.157671. Not a guaranteed bound: loss-to-zero120 each; historical gaps omit unseen tails.3) Reused frozen method/seed91900 to translate same distribution to reset notional, not new edge test: 10000 joint circular5-day bootstrap paths from252 returns over60 sessions; hypothetical close-only fixed brackets, 50bp exit deduction, survivors close60; no intraday ratchet/entry costs. {"recent_drift":{"p05_p50_p95":[-15.400604271271359,14.480958312074208,43.13656939007692],"negative_fraction":0.1952,"stop_frequency":[0.5768,0.3935,0.4811],"target_frequency":[0.2544,0.2356,0.2997]},"zero_drift":{"p05_p50_p95":[-17.928425459694306,-3.1389371155714065,20.166403638167974],"negative_fraction":0.5747,"stop_frequency":[0.7557,0.6521,0.7065],"target_frequency":[0.1024,0.0509,0.128]}}. Zero-drift median negative; frequencies are model diagnostics, not calibrated live odds or Kelly inputs. Equal size unchanged by forecast. Funding shortfall absent; P90 is return quantile not target-hit probability.

1. numpy seed91900,20000 paths x20 trades sampled IID from36 frozen NVT2018–24 costed trades. At12%account notional eachtrade, terminal P5/median/P95 returns -1.594/+7.302/+17.559%,terminal loss9.2%,P95maxdrawdown5.576%. These conditional model outputs are not current stock target odds, elapsed20trade duration or loss bounds. Different regimes and clustered losses can invalidate them. 2. Measured worst daily openinggap since2018 -16.0305%; separate deliberately doubled32.061% stress, with2ATR stop8.5541% and50bp allowance, gives38.3726% notional loss scenario. Normal3% account stress budget25.4976=>notional66.4474 belowfund101.99; quarter probe16.6118 if a later entry qualifies. A jump greater than stress can lose more. Fractional RTH-only exits would apply because whole share157.88 exceedsfundcap; marketclosed so no fractionalorder now. 3. Point-estimate halfKelly(average payoff) .11196 ofriskbank training would be constrained by normal3%equityrisk andfund12%notionalcap; do not use it literally as position risk. Current signal false and nettarget not approved ->actualsize0. Source https://runway.adityperswal.workers.dev/data/stock-bars (URL typo correction: https://runway.adityaperswal.workers.dev/data/stock-bars ). This supersedes no prior stress probability, and imposes no assumed5% disaster veto.

Premises:1) Technical3353 fresh adjusted SIP https://runway.adityaperswal.workers.dev/data/stock-bars; equity849.92/cap339.97.2) Retain existing stress definition r=2ATR/E,g=max(.10,2*abs(worsthistoricalnegativegap)),fraction=r+(1-r)*g+.005; N=floorcents min(cap/3,.25equity,(.02equity-.01)/maxfractions). XLK/XLE/XLV g=.125185405/.115854679/.1;common106.70,320.10total,19.87residual. Loss16.986945/16.605722/13.673363 <16.9984 per lot; sum47.266029. Model not guarantee: loss-to-zero106.70 perlot exceeds2%, unobserved gaps may exceed history. Equal weights obey tightest constraint, no correlation discount.3) New completedbar and bear attack justify drift sensitivity, not strategy validation. Joint circular5day bootstrap recent252 daily returns,10000paths,seed91900,60sessions; both recent drift and subtract each asset samplemean. Fixed initial close-cross stops/targets,50bp exit penalty including survivors atday60; no entrycost,intraday touches,profitratchet or manager timing. Output orderedXLK/XLE/XLV: {"recent_drift":{"basket_p05_p50_p95":[-13.693703964538782,12.875985432485985,38.35559961601006],"negative_fraction":0.1952,"stop_frequency":[0.5768,0.3935,0.4811],"target_frequency":[0.2544,0.2356,0.2997]},"zero_drift":{"basket_p05_p50_p95":[-15.94135830457819,-2.7910382519289096,17.931293901604363],"negative_fraction":0.5747,"stop_frequency":[0.7557,0.6521,0.7065],"target_frequency":[0.1024,0.0509,0.128]},"names":["XLK","XLE","XLV"],"n":10000,"seed":91900,"horizon":60,"joint_stress":47.26602936450736,"loss_to_zero_perlot":106.7}. Conclusion model median flips sign if recent drift vanishes; cannot convert target frequencies to actual expectancy or Kelly. Retain mandate sizing/targets rather than selecting favorable simulation. Historical worst gaps and finite resampling omit unseen tail states; genuine live win odds unavailable. No repeat edge backtest per explicit mandate.

Premises:1 selected current notionals90.04/103.20/83.56;2 last756 completed common daily returns endingSep18;3 numpy seed919 samples10000 paired contiguous5day blocks preserving observed cross-asset dependence. Dollar five-day terminal distribution P01=-13.839929,P05=-9.600495,median=1.469630,worst sampled=-33.635197;39.46% negative. Static buy-and-hold risk diagnostic, no stop fills/target enforcement/fees, no independent holdout strategy validation. Overlapping repeated paths do not create10000 independent observations. Daily-path bootstrap misses novel gaps, halts, weekend jumps beyond history and intraday stops; NOT live loss odds, target-hit probability or Kelly inputs. Consequence: retain stronger frozen double-gap stress for size, do not increase deployment because bootstrap tails look small. No repeated strategy backtest because fixed mandate explicitly forbids it. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all .

1. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; closed pre2024 returns from costed strategy3310-20, not two live wins. NumPy seed918061,20000 paths of20 sequential trades. Portfolio rebalances each trade to12% account (101.99/849.92) or3% quarter-fund probe. Sample actual trade outcomes with replacement; separately REPLACE an outcome with assumed-30% loss atq0/1/5%. No claim that q is measured; empirical ordinary gaps/losses already remain in base. IID trades omit regime persistence and simultaneous holdings, so this is a shape/sizing sensitivity, not ruin forecast. 2. TEN fullfund mean terminal account return-3.93925% withq0;5thpercentile-14.32465%,P95drawdown15.30252%,P(loss>10%)20.74%. q5 raises P95DD19.07636%,mean-7.17269%. Quarterfundq0mean-.99976%,P95DD4.04490%;q5mean-1.84081%,P95DD5.11282%. Negative baseline exists independently of assumed disaster. 3. LPG fullfundq0mean+3.57059%,P05-8.64104%,P95DD11.41406%;q1mean+2.75026%,q5mean-.24270% andP95DD15.38273%. Quarterfundq0mean+.88198%,P95DD2.96819%. Thus arbitrary q5 alone can reverse an otherwise positive empirical mean, but LPG's separate actual2024-25 holdout is negative anyway. 4. Full AA/CENX/MU matrices saved in observations; no favorable simulation overrides their inactive current signal. HalfKelly numerical estimates in3330-35 are capped research diagnostics; preserve 3% normal account-risk rule and gap stress separately from expected value. Conclusion: scale exposure to drawdown shape and retain uncertainty, not assumed odds as permanent cash veto.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. pre2024/2ATR6ATR: stop first 67.480%, target first 30.295%, timeout 2.225%, mean net 2.2449%, median -10.9632%, P01 -14.7113%. last252/2ATR6ATR: stop first 60.875%, target first 34.025%, timeout 5.100%, mean net 4.3584%, median -10.9632%, P01 -15.8823%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: train N42, win33.33%, average win32.929%, average loss10.758%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. holdout N13, win38.46%, average win25.331%, average loss10.286%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. forward2026 N5, win20.00%, average win23.183%, average loss12.663%, constrained halfKelly stockweight0.0000, cap-adjusted researchsize$0.00. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. pre2024/2ATR6ATR: stop first 66.880%, target first 28.675%, timeout 4.445%, mean net 1.5349%, median -9.0627%, P01 -13.0165%. last252/2ATR6ATR: stop first 62.985%, target first 34.075%, timeout 2.940%, mean net 3.2122%, median -9.0627%, P01 -12.2648%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: train N37, win35.14%, average win25.898%, average loss8.956%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. holdout N11, win36.36%, average win24.131%, average loss8.030%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. forward2026 N3, win33.33%, average win16.426%, average loss9.536%, constrained halfKelly stockweight0.0000, cap-adjusted researchsize$0.00. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. last252/2ATR6ATR: stop first 50.490%, target first 43.405%, timeout 6.105%, mean net 14.6300%, median -18.1134%, P01 -23.2380%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: holdout N3, win66.67%, average win30.566%, average loss10.059%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. forward2026 N6, win33.33%, average win36.180%, average loss15.903%, constrained halfKelly stockweight0.1245, cap-adjusted researchsize$101.99. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. last252/2ATR6ATR: stop first 73.045%, target first 26.720%, timeout 0.235%, mean net -0.8900%, median -10.2254%, P01 -34.4840%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: holdout N4, win100.00%, average win34.836%, average loss0.000%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. forward2026 N4, win25.00%, average win34.790%, average loss14.427%, constrained halfKelly stockweight0.0000, cap-adjusted researchsize$0.00. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. pre2024/2ATR6ATR: stop first 66.770%, target first 31.210%, timeout 2.020%, mean net 1.4969%, median -7.0079%, P01 -9.6989%. last252/2ATR6ATR: stop first 50.780%, target first 46.420%, timeout 2.800%, mean net 5.7770%, median -7.0079%, P01 -8.3937%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: train N49, win30.61%, average win22.921%, average loss7.997%, constrained halfKelly stockweight0.3845, cap-adjusted researchsize$101.99. holdout N10, win20.00%, average win19.976%, average loss7.913%, constrained halfKelly stockweight0.0000, cap-adjusted researchsize$0.00. forward2026 N7, win57.14%, average win21.282%, average loss6.479%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

1. Model: 20000 paths,60sessions, aligned historical open/previous-close, high/open, low/open,close/open ratios, contiguous5day blocks;10day sensitivity also saved. Seed918061, baseline history pre2024 versus recent252; fees1bp/slip15bp per side. Stops include opening gaps, openingtarget first, intraday ambiguity stop first. Fixed levels asofSep17; no live entry signal conditioning, no15min/profit ratchet. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. pre2024/2ATR6ATR: stop first 72.725%, target first 26.645%, timeout 0.630%, mean net 0.0919%, median -6.2328%, P01 -7.8202%. pre2024/frozen_value: stop first 25.070%, target first 74.735%, timeout 0.195%, mean net -0.2460%, median 4.4937%, P01 -14.5717%. last252/2ATR6ATR: stop first 42.310%, target first 54.870%, timeout 2.820%, mean net 7.1037%, median 17.4205%, P01 -6.5804%. last252/frozen_value: stop first 6.900%, target first 92.640%, timeout 0.460%, mean net 3.1583%, median 4.4937%, P01 -14.2872%. 3. Half Kelly from numerical max mean log(1+f*r) gridf0..1 thenhalf, using closedtrade distributions: train N46, win19.57%, average win24.725%, average loss8.099%, constrained halfKelly stockweight0.0000, cap-adjusted researchsize$0.00. holdout N8, win37.50%, average win15.583%, average loss5.965%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. forward2026 N5, win80.00%, average win19.207%, average loss8.288%, constrained halfKelly stockweight0.5000, cap-adjusted researchsize$101.99. This is a diagnostic, not approved sizing; small/all-win histories cannot calibrate omitted losses. 4. Recent-window drift and selected survivor bias can create attractive resampled odds without an executable edge. Simulated tail quantiles are not loss bounds. LevelsE-2ATR/E+6ATR are hypothetical geometry and not fundamental valuation; TEN frozenvalue45.41/55.36 remains separate. Decision: do not use favorable bootstrap odds to override failed holdout, absent current signal or undetermined cash capture. A fullfund101.99 exposure is12% account849.92; quarterfund25.4975 is3% account, stockloss can exceedstop on gap.

Premises:1 statistical risk audit uses428daily return vectors2025-01-02–Sep17 2026 for current89.95/103.11/83.46 notionals;2 resample vectors jointly to preserve contemporaneous cross-asset dependence;3 circular blocks5sessions retain short clusters, 10000replicates, seed9180601. Per replicate sample428days, calculate empirical95% expected-shortfall tail mean,99%loss quantile and mean of frozen threshold-exceedance indicators. Results originalES95=7.609460USD, percentile95% bootstrap interval[5.947080,9.492035]; VaR99=9.368118 interval[6.596389,13.503072]; threshold coverage exceedance.934579% interval[0,2.102804]%. These are Monte Carlo uncertainty intervals for historical daily mark-risk estimates, NOT prospective loss limits, exit odds, independent OOS strategy returns or a Kelly estimate. Resampling observations already inspected and choosing current symbols retrospectively means no new edge evidence. Blocks cannot create novel shocks; 428days and ~22tail observations leave material uncertainty. Circular joins approximate, block length unoptimized; no claim calibrated CI coverage. No repeat static stop/target bootstrap. Decision preserve mandate and earlier crisis stress, do not enlarge sizes because threshold count resembles1%. Costs and actual RTH stop execution absent from return sample; 50bp only in separate stress. Counterexample prolonged halt/new gap is outside bootstrap support. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; quant.py/quant_results.json.

Source https://runway.adityaperswal.workers.dev/data/stock-bars. Premises: equity849.92, cap339.97, strict2% loss ceiling16.9984; equal-weight unconstrained slots113.3233 exceed ceiling for XLE/XLK under existing model. Loss=N*[r+(1-r)*g+.005],r=2ATR/E,g=max(.10,2*worst negative historical open/previous close). g=.115854679/.125185405/.10. Use common slot floor cents min(cap/3,.25equity,(.02equity-.01)/max(stress fractions))=106.62. Stress losses16.652208/16.987640/13.774069, joint47.413917; deployment319.86,residual20.11. Not a bound: larger gaps and loss-to-zero106.62 per lot can exceed2%; refreshed equity/fills mandatory. Counterexample prevents claiming guaranteed protection. Equal weights retained, no Kelly change. Recent252-session joint circular5-day bootstrap10000 paths,seed91806,60sessions; selected ex post; fixed initial stops and P90 targets, first close crossing exit with50bp adverse exit charge, all survivors liquidated day60; no entry charge, intraday highs/lows or profit ratchet. Results {"paths":10000,"seed":91806,"history_sessions":252,"horizon":60,"block":5,"basket_p05_p50_p95":[-13.761056414003983,12.957375339944516,38.10545280256284],"negative_fraction":0.1903,"per_symbol":{"XLE":{"stop_fraction":0.388,"target_fraction":0.2332,"neither_fraction":0.3788,"p05_p50_p95":[-6.375357170581709,6.312452718414754,22.81350421328447]},"XLK":{"stop_fraction":0.5787,"target_fraction":0.249,"neither_fraction":0.1723,"p05_p50_p95":[-6.631493072416815,-4.243749870200858,20.839633354309434]},"XLV":{"stop_fraction":0.4614,"target_fraction":0.3066,"neither_fraction":0.232,"p05_p50_p95":[-4.501909204275528,0.3809418349380722,12.450141349553459]}}}. These are model-conditional crossing frequencies, not live exit probabilities or strategy backtest; close-only monitoring can miss touches, current regime drifts may not persist, and fixed stops omit mandate ratchet. No edge revalidation and no simulation-based sizing override.

Source https://runway.adityaperswal.workers.dev/data/stock-bars SIP adjustment all. $39.66 per lot. Stress assumes stop distance r=2ATR/E followed by gap g=max(10%,2*largest observed negative open/previous close gap) plus0.5% execution cost: loss=N*[r+(1-r)*g+.005]. XLE worstgap5.792734% Apr8 2026,g11.585468%;XLK6.259270% Aug5 2024,g12.518540%;XLV2.644903% Apr7 2025,g10%. Losses6.194209/6.318982/5.123612 all<2%equity16.9984. Joint17.636803=2.075113%equity. This stress is not a bound: arbitrarily large gaps can exceed2%; loss-to-zero perlot39.66. Recompute at entry. Diagnostic5000 joint60-session paths from circular5-day blocks of1330 daily returns, seed918, no stops/costs, selected basket ex post: dollarP5/median/P95=-9.66645/+5.62718/+20.48811,26.64%negative. Not live exit odds/expectancy, no out-of-sample edge claim, no Kelly sizing inference. Specific fixed equal-weight mandate controls sizing; no backtest.

No newMonteCarlo or resampledprobability. Pythonchecks frozen3243 mean=(1-q)*1.4467783586%-q*30%;q5%=>-.1255605593%,breakevenq4.600720437%. q is an assumed pertrade crisis replacement probability,not empirical estimate. Prior3219 20k blockpaths remain separate modeled distribution,not eighteen-dayforecast. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Negativeexpectedscenario giveszero long halfKelly; no calibratedbinaryKelly odds inferred from2operatorwins. Independentcost/tail evidence couldchangeassumptions, but freshdata403 and unverifiedincidentprovide none. A qualifying47.74pricealone cannot replace sizingvalidation; <=21.27 conditionalprobe only afterjointgatespass.

Reused frozen3214/3219 execution study, no rerun or optimization. Python/NumPy recomputed mean(q)=(1-q)*1.4467783586%-q*30%, where q is ASSUMED catastrophic per-trade replacement probability. q0/2.5/5/7.5/10% -> mean1.446778/.660609/-.125561/-.911730/-1.697899%; breakeven4.6007204%, derivative-.3144678pp mean per1ppq. Prior20k3tradeblock20tradepath study3219 (seed9130801) remains distribution evidence: median-.246048%,loss54.94%,DD953.187738% at2.5%account allocation. Thisrun sensitivity is analytical, not newMonteCarlo or empirical frequency measurement. https://runway.adityaperswal.workers.dev/data/stock-bars . Fresh authorized SIP split daily history request403; gap frequency not independently remeasured. Criticism:5%was a conservative scenario and may overstate risk; historical everyday gap rates alone would not identify current war-conditional probability anyway. Evidence supporting lowercost/tailrisk can change decision; uncertainty is not permission to call5% fact. Long halfKelly under retainednegative-mean scenario0, actual0; no month-end recovery forecast.

Edge test: ten consecutive issuer-scheduled HITI AMC earnings March2024–June2026, 926 SIP adjustment=all daily bars; release-close to next-session-close median absolute4.700378%. Sep11S2.53, Oct16C2.5 .21Sep11/P2.5 .16Sep10 plus assumed .05/share roundtrip costs require +9.090909%/-9.486166%; each1/10=10%, below40%. Mean mapped intrinsic .213531/.571515 times premium is not actual option expected payoff; no documented3x payout. Aug25issuer quote 'after financial markets close on Monday, September 14, 2026' https://hightideinc.com/high-tide-to-announce-third-fiscal-quarter-2026-financial-results/ ; Oct16expiry32dayslater, defaultSep11RTHexitpassed, noholdexception (hurdles above median4.390531/4.785788pp). Sources option_contracts and https://runway.adityaperswal.workers.dev/data/stock-bars ; https://runway.adityaperswal.workers.dev/data/option-bars . 1. NumPyseed91308 bootstrap5selectedtrainingcallreturns,20opportunities,20000paths,$102.12startingcash,$25fixedall-in scaled exposure, stopnewfundingbelow25. BaselinefinalP5/50/95$12.4791/30.7172/104.2191;94.36%losingseries,47.425%below25,medianmaxDD74.862%. $10coststress$2.23905/15.98905/24.73905;100%loss,99.875%below25,medianDD84.3429%. 2. These permit fractional scaling ofhistoricalwholecontracts and are scenarios, not executableticketforecasts orindependent20eventhistory. Assumptioniid ignoreschangingliquidity, preannouncements andregime; same empiricaltailsretained. Noextra inferredcatastropheprobability inserted. Currentcall meannegative implies long-only halfKelly0; putN1cannotidentify win/lossodds, noKellysizeassigned. 3. Counterexample unseenlargewin couldturnexpectancy, but absent documentedprobability doesnotjustify size. Premiumcap boundsone loss; repeated affordabletickets can depletebook. Atactualfund102.12,3/5%accountcaps25.5297/42.5495,absolute51.0594andmax3open; costsshrinkremainingrunway. Monthly$349.01shortfall excluded.

Gate3214 training22basewin8/22=.363636,avgwin16.127688%/avgloss6.623160%,b2.435044=>halfKellyrisk5.115039%;15bpsliphalfKelly3.975979%. Fullmin(fund170.20,venue212.7475,Kellyriskbudget,3%equity/30%gap)=85.099;quarter21.27475,fullstockloss2.5%equity,30%gap6.382425USD. Circular3tradeblock20kpaths20trades,seed91308,2.5%account/trade:base5bpslipmedian+.595059%,loss37.67%,DD95 1.996791%;plusassumed5%chance/trade -30%return:median-.185092%,loss53.685%,DD95 3.117590%. Joint15bpslip+samegap (seed9130801) arithmeticexpectedtrade-.125561%,accountmean-.040421%,median-.246048%,P05/P95 -2.835394/3.520304%,loss54.94%,DD95 3.187738%. Breakevengapfrequency4.600720%;5%isassumption,notmeasuredwarprobability. Thus historicalKellypositive but scenarioexpectedKelly<=0; actualallocation0 underretainedscenario, not fundingshortfall. Largeupsidepaths do not make negativeexpectedvaluepositive. New verifiedcost/gaprisk evidence can changeassumptions; do not optimize awaystressorroundup. Horizonless20trades NOT18dayforecast. Source https://runway.adityaperswal.workers.dev/data/stock-bars .

Premises: three29.785USD hypothetical quarter-fund probes total89.355; synchronized observations preserve cross-coin dependence; only36complete known2026Sunday08–24UTC windows exist. Seed91308 resamples36 matched return vectors withreplacement10000times, computing each samplemean endpointPnL. Grossmean−.18809USD;95%bootstrapCI ofmean[−.78683,+.40165]USD. Worstactualsampleendpoint−4.18314USD is not worstpossiblepath. This is a confidence interval for mean, not a MonteCarlo terminal-loss interval or stop-sampled20day forecast. Endpoint25bp creditedassetfees per side reduce coinmeansto−.62053/−.70287/−.80307%;netwins30.56/33.33/30.56%,avgwins1.1061/1.8399/2.1299%,avglosses1.3802/1.9742/2.0936%. Approximatebinarymean halfKelly max(0,.5*(p/l−(1−p)/w)) is0for each. Noextra slippage, buyprice uncertainty, serialweek dependence, novel jumps or intrahourstopfills modeled; thisis descriptive cost sensitivity, not a new tradingbacktest. Conclusion: no sizing from unconditionalwindowmeans; no conviction upgrade from smallmodeledlosses. Actualsize0 because3208 signalsabsent and frozen3190–95 actualpolicyrejected. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; feeassumptions https://docs.alpaca.markets/us/docs/crypto-fees .