Stats

Premises:1 prior analysis paired price/adjusted opening gaps on factor-change dates through2025;2 numpy seed92104,10000 bootstrap samples each18 XLE or9 EEM events, replacement;3 mean adjusted-minus-price difference. Source https://runway.adityaperswal.workers.dev/data/stock-bars . XLE95% percentile range86.1168–99.2930bp,EEM97.2951–148.7577bp. These are conditional sampling intervals for a mechanically selected basis difference,not next-gap ranges,price paths,win odds or expected PnL. Event independence is an assumption;quarterly regime clustering and small samples limit inference. Reuse one-share risk:10%joint gap on67.37+64.31=13.168USD,1.317775% of999.26;gap-through-stop can exceed nominal4.10risk. No calibrated liveKelly:0closed trades, so bootstrap does not authorize size increase;140cap binding. Established mandate size retained.

Premises:1 training1076 paired opening gaps through2025;2 fixed67.37/64.31 dollar exposures;3 numpy seed92102 draws10000 paths each12 contiguous5session blocks. Source https://runway.adityaperswal.workers.dev/data/stock-bars. Sixty-session opening-gap sum P5 -12.51026,median1.56015,P95 14.03219 USD. Preserves within-block dependence; omits intraday returns, reinvestment, stops, targets, fees and execution. Therefore not cumulative investable PnL, not expected return, not probability of exit. No new repeated barrier forecast on unchanged weekend bars; earlier exit diagnostics remain limited by15min venue cadence. A common10% gap costs13.168 or1.317617% of999.38 equity. Stress can exceed historical support. Do not infer Kelly from these percentiles or resize.

Premises:1 same1075 paired daily gaps through2025 as statistical analysis;2 numpy seed92100 samples paired rows iid10000paths of60sessions;3 scale constant67.37/64.31. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Maximum net joint opening-gap loss along each path P50=3.138277 P90=4.951984 P99=4.970863 dollars. Net allows cross-name gains to offset; different from prior gross-loss diagnostic. This is NOT cumulative PnL or probability of stop/target. No prior exits, price compounding, serial dependence, within-day extremes, dividends, fees or executable15minfills. Historical support bounds sampled extremes; new shocks can exceed them.2026 reserved chronological comparison but previously inspected, not unseen OOS. Not a backtest and not calibrated odds for Kelly. Purpose only attack naive negative-correlation protection at actual holding scale. Keep mandated1share, no resizing from simulation.

Premises:1 paired raw SIP gaps Sep2021–Dec2025 N1076 preserve same-day dependence;2 fixed5-session blocks,10000paths,60sessions,seed200908;3 scale each day to unchanged67.37/64.63 holdings and compare1.89/2.53 risk budgets. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Across paths maximum gross opening-gap loss P50/P90/P99=3.0080/4.96784/4.98122 dollars; maximum sum of individual stop-budget excess=0/1.56542/1.65664.36.48%of paths have any excess. Gross losses clip gains per name; not net portfolio PnL. This assumes continued exposure for60days, ignores prior stop exits, profit ratchet, within-day prices, actual gaps-through fills, slippage and dividends; NOT stop probability or calibrated live loss bound. Training excludes2026 but that year already inspected elsewhere; no claim of unseen test. Maxima are capped by historical support; novel shocks can exceed them. Keep one share; two would exceed140 fund capacity even if some gap tests passed. No sizing from model frequencies or invented halfKelly.

Premises:1 jointly sample EEM/XLE raw split-normalized OHLC/priorclose relatives Sep2021–Dec2025 N1076;2 paired contiguous5day blocks,10000 paths,seed200906,60sessions;3 static starts67.37/64.63,stops65.48/62.10,targets74.59/77.97. Source https://runway.adityaperswal.workers.dev/data/stock-bars. Compare same paths close-only vs daily low/high barriers, stop-first on ambiguous day. Close EEM stop66.89%,target17.57%,neither15.54%; OHLC71.52/17.46/11.02%. XLE close59.86/15.28/24.86%,OHLC67.88/15.12/17.00%. Both-barrier ambiguity0 in sample. Unstopped combined terminal P05/50/95=-17.24573/3.05739/23.70781 dollars. Daily extremes increase modeled stops4.63/8.02pp; they do not prove executable15minute or extended-hour exits. Omitted profit ratchet, actual quotes/spreads, gaps-through stop fills and slippage; model frequencies NOT live odds or backtest profits. Fixed one-share size remains; no Kelly from static barrier frequencies. No retest of accepted momentum edge.

Premises:1 SIP raw/all paired daily bars split-normalized, source https://runway.adityaperswal.workers.dev/data/stock-bars ;2 1255returns endingSep18,paired5session blocks,seed200904,10000paths each,60sessions;3 common sampled blocks start67.37/64.63 and dailyclose barriers65.48/74.59 and62.10/77.97. {"total_proxy":{"n":1255,"exit_frequencies":{"EEM":{"stop_first":0.6264,"target_first":0.2315,"neither":0.1421},"XLE":{"stop_first":0.5419,"target_first":0.178,"neither":0.2801}},"unstopped_terminal_p05_p50_p95":[-13.692639696010037,5.5778139751457445,25.07779318050785]},"price_only":{"n":1255,"exit_frequencies":{"EEM":{"stop_first":0.6462,"target_first":0.2176,"neither":0.1362},"XLE":{"stop_first":0.5616,"target_first":0.1642,"neither":0.2742}},"unstopped_terminal_p05_p50_p95":[-14.488618360514453,4.665241971145377,24.212728061139096]}} Conclusion: total-return proxy target frequencies exceed price-only by1.39pp EEM/1.38pp XLE; neither equals actual execution odds. Price-only excludes dividend cash wealth, total-return proxy reinvests payouts as price and therefore mismatches price barriers. Both omit live gaps/slippage,15min checks,profit ratchets,costs and regime change. Not a strategy backtest or calibrated Kelly input. Keep one share; do not select a favorable convention to justify doubling.

Premises:1 paired adjusted daily returns from https://runway.adityaperswal.workers.dev/data/stock-bars throughSep18; confirmed split repair.2 numpy seed200902,10000 paths each,60sessions,paired contiguous5day blocks sampled uniformly within fiveyear and recent252 windows.3 begin67.37/64.63; first daily close crossing initial65.48/74.59 and62.10/77.97. Results {"five_year":{"sample":1255,"terminal_unstopped_p05_p50_p95":[-13.916517520707718,5.8303433744541735,25.288007680026965],"EEM":{"stop_first":0.6241,"target_first":0.237,"neither":0.1389},"XLE":{"stop_first":0.5393,"target_first":0.186,"neither":0.2747}},"last252":{"sample":252,"terminal_unstopped_p05_p50_p95":[-3.2249203133477518,11.295509565202536,26.156546836256823],"EEM":{"stop_first":0.5802,"target_first":0.3565,"neither":0.0633},"XLE":{"stop_first":0.3986,"target_first":0.2382,"neither":0.3632}}}. Recent-window terminal5% loss -3.22 vs fiveyear-13.92 exposes sample dependence; endpoint returns are UNSTOPPED dollar changes, not actual strategy PnL. Frequencies omit intraday paths, execution gaps, fees, profit ratchets and changing regimes; not calibrated live probabilities or Kelly inputs. This is risk sensitivity, not revalidation/backtest of the accepted momentum premium. Keep1share per slot; no size changes from favorable recent window.

Premises:1 paired1255dailyreturns in5yearwindow from https://runway.adityaperswal.workers.dev/data/stock-bars.2 numpy seed200900,10000paths,60sessions,5dayblocks sampled uniformly jointly.3 starting67.37/64.63; fixedinitial stop/target, firstclosecrossing; no intraday paths, costs, gaps at stopexecution, or profitratchet. Results {"seed":200900,"paths":10000,"sessions":60,"block":5,"sample":1255,"terminal_dollars_p05_p50_p95":[-13.946045912979042,5.786306726172633,25.56167991248244],"EEM":{"stop_first":0.6359,"target_first":0.224,"neither":0.1401},"XLE":{"stop_first":0.5348,"target_first":0.189,"neither":0.2762}}. Terminal dollarquantiles UNSTOPPED, not strategypnl. Frequencies not calibrated liveodds, cannot supply Kelly. Counterexample nonstationary rate/commodity regime. Record model sensitivity only, no strategy revalidation or resized positions.

Premises:1 source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all paired adjusted close returns last1255observations.2 numpy seed190908,10000paths,60sessions,12 independent uniform5day block starts preserving cross-asset pairing, compound from queued limits.3 fixed horizontal initial brackets; first close crossing recorded, no intraday prices, gaps, costs, ratchets or live execution. Results {"seed":190908,"paths":10000,"days":60,"block":5,"sample":1255,"terminal_p05_dollars":-13.725602935665727,"terminal_median_dollars":6.065331103171697,"terminal_p95_dollars":25.972824647228244,"EEM":{"stop_first":0.6226,"target_first":0.2373,"neither":0.1401},"XLE":{"stop_first":0.5383,"target_first":0.1841,"neither":0.2776}}. Terminal dollar quantiles are UNSTOPPED mark-to-market, not stopped strategyPnL. Counterexample regime shifts or overnight gaps invalidate stationary sampling. Model crossing frequencies are not calibrated live odds; no new sizing/strategy/backtest or Kelly inferred. One share maintained.

Premises:1 source https://runway.adityaperswal.workers.dev/data/stock-bars?timeframe=1Day&feed=sip&adjustment=all&start=2020-09-01&end=2026-09-18T23:59:59Z verifiedsplitrepair29429,1255 rolling60session gains each.2 numpy seed190906;3000replicates for each blocklength20/60/120,uniformvalidblockstarts,concatenateandtrim1255;sample already-computed gains,notpricepaths.3 blockdependence betterpreserved thanIID butstationarity assumed. Percentile2.5–97.5 ranges inpercent: EEM block20[8.4246,14.6764],60[7.7705,15.2419],120[7.2695,14.6641];XLE20[16.7909,24.9857],60[14.2856,26.7455],120[13.1971,27.1555]. MediansrespectivelyEEM10.7581/10.8267/10.6242,XLE20.5145/20.4653/20.5145. These are conditional resampling uncertainty bands for the historical estimator, NOT future-return ranges, stop/target probabilities, or portfolioPnL. No fees/fills modeled because no execution claim. Counterexample structuralbreak defeatsbootstrap; periods demonstrate instability. Conclusion sizing unchanged1each and acceptedqueues preserved; no empiricalKelly inferred. Existing4.42 plannedrisk isnotlossbound. This is distinct from priorgap-path diagnostic, not a repeatedstrategybacktest.

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: 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.