Stats

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.

Question: how much do static-bracket exit estimates change with sample and serial dependence? Premises:1 Current fixed basket and brackets from3645.2 Historical synchronous OHLC/priorclose ratios preserve same-day cross-sector dependence.3 Resample consecutive blocks1/5/20days separately from1152 pre2026 and179 recent2026 sessions,10000 paths per case,60 sessions,seed92006,86.66 each,6bp/side assumed friction. No fitted parameter selected. Source https://runway.adityaperswal.workers.dev/data/stock-bars. Method stop first for ambiguous same-day dual touch; gap stop at worse opening price; target at fixed target; remaining mark at60-day close. Static current brackets; stop first on same-day dual touch; opening gap stop at worse open; no ratchet, monthly rerank or 15min checks; adjusted OHLC not executable prices; chosen current basket selection bias; 6bp per side costs assumed; no calibrated odds or Kelly sizing. Full case figures observations30444–49. Pre2026 target frequencies XLK12.96–17.29%,XLE11.17–15.56%,XLV13.94–16.61%;2026 XLK20.60–26.17%,XLE32.97–39.15%,XLV20.50–23.43%. Basket loss frequency48.39–50.20% versus19.76–22.72%; modeled mean dollar PnL2.796–3.655 versus9.291–9.632. P05 dollar outcomes roughly-9.89 to-8.97 do NOT bound loss. Conclusion sample choice materially dominates implied success odds, so no empirical Kelly input or sizing/target override. Ratchets/monthly replacement and15minute monitoring omitted deliberately to isolate model sensitivity; not execution backtest, not validated premium test, and not live probabilities. Counterexample crisis correlations and gaps outside observed sample defeat benign recent results. Source was already observed;2026 is a comparison segment, not independent OOS.

Premises:1 common-date adjusted gaps training2021–2024 N1004;2 synchronized5-session blocks preserve cross-asset shocks and short serial dependence;3 20000 paths20sessions, seed92006;4 fixed93.33 notionals each. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all . Simulated maximum single-night basket loss Q50/95/99=3.913011/7.974398/14.828643USD; zero sampled paths exceed30. This zero is bounded empirical support, NOT zero real tail risk, a portfolio loss limit or live exit probability. Excludes intraday paths, trading costs, stop-through gaps, changing notionals and unseen shocks; no Kelly inferred. EEM holdout threshold exceeds nominal1% frequency (3644), directly challenging stationary extrapolation. Retain separately the stop-through-gap scenario r=2ATR/E,c=r+(1-r)*2g+.005,g=.125794155019/.109666233203/.138906519177; size=floorcents min(280/3,250,29.5/c). Results [{"symbol":"EEM","size":93.33,"stop":65.1435,"target":74.21425092953517,"p90":0.10717963493264468,"rr":3.8082432703605487,"stress":25.913232637416957},{"symbol":"QQQ","size":93.33,"stop":704.90264,"target":838.105473380901,"p90":0.1616958533244174,"rr":7.049793645687354,"stress":22.608077650841185},{"symbol":"IWM","size":93.33,"stop":277.666,"target":320.5246054777956,"p90":0.12821050854556687,"rr":5.661269113738809,"stress":27.921384363225883}]. Joint76.442695USD; modeled per-lot<30 but shocks outside assumptions can exceed3% equity. No increase in size from benign bootstrap quantiles.

Premises: 1. Empirical daily feed-price returns https://runway.adityaperswal.workers.dev/data/stock-bars . Fixed currenthypothetical2ATR/net3Rbarriers fromtechnicalanalysis; 60session paths,5sessionmovingblocks, seed92004,20000percell, history2017onward or2025onward. 2. CE longhistory stop57.52%/target17.20%/timeout25.28%, mean netPnl.1505USD/share; recent69.85/24.55/5.60%, mean-.2645. EMN long61.65/20.93/17.42%,mean.2290;recent70.215/19.28/10.505%,mean-.8359. 3. Fullcloseovershoot allowed and20bp/sidecost; no intradayextrema or15minuteexecution, event probabilities, conditionalbreakoutorfundamentaldriftmodel. Positivehistoricalbootstrapmeans nottradeedge. 4. CE2shareP1pnl-21.85long/-18.93recent; EMN2share-21.25/-28.54but2EMNexceeds120cap, so diagnostic notproposedsize. Gaps outsidehistory canbe worse; models are notlosslimits. Conclusion: odds change withregime; useconditionaltradehalfKelly0from3639, notunconditionalpathodds, for currentallocation0. Preservepositivecounterevidence, don'ttreatallcash asproofCEhasnoupside. Scriptsstats.py/stats.json containreproducibleassumptions.

Premises:1 NumPy seed92004,20000 paths, four sampled5-session blocks from last252 logreturns,20 steps/25 calendar days toOct16,unchangedspot. BSM constantIV fit to HALO.23/TH.18 asks:33.414/68.513%,rate4%; targets1.83/3.58,50%premium stop, fills capped at target,1USD assumed roundtripfee.2 At no exit markdown, HALO/TH means+4.90/+4.50USD,loss87.97/93.23%,halfKelly22.95/11.50USD of1000equity, below onecontractcost24/19 respectively.20%mark discount changes means-1.19/+.57 andhalfKelly0/1.50USD. Zero-mean underlying paths already lose-1.54/-2.93 without markdown.3 Constantbidratio<=.5 triggers model immediate loss before movement: HALOzero-bid-24USD,TH.07/.18 -12USD. Actual venue mark unknown; indicative ratiosnotactualbidasks.4 Conditional cheaperfills:HALO.15 with.8markratio mean+9.05/halfKelly39.35,cost16;TH.13 with.8ratio+8.16/halfKelly21.80,cost14. RetainingTH.3889ratio instead yields-3.19/halfKelly0. Thus .13 onlyfixesinitialspread-stoparithmetic,notwholeholdingexpectancy. Pricegriduses samevaluationbutassumeslimitfillswithoutadverseselection; cannotcallpriceimprovement attainable. TH separategrid MonteCarlo differs slightly due RNG sequence; no bestdrawchosen. Conclusion: no calibrated positive sizing at observed indicative asks; fresh pricing and honest odds can change it. Fullpremium cap30,total100,max4; quarter30probe7.50unavailable attheseprices. Models sensitivity only,notnewmandatorygateorproofcashforever; historical terminalKelly isoptimisticrelative toexitpolicy. Source /data/stock-bars,/data/option-chain/HALO andTH; allrows30343–47 andlimitbatches.

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 current reference entries/ATR from3607;2 carried gap assumptions g EEM.125794155019 QQQ.109666233203 IWM.138906519177, not fresh tail estimates;3 cash1000/fund280/position250. r=2ATR/E; coefficient=r+(1-r)*2g+.005; size=floorcents min(280/3,250,29.5/coefficient). Gives93.33each. Stress EEM25.913233 QQQ22.608078 IWM27.921384 joint76.442695USD, each<30 under modeled shocks. Larger shocks can exceed3%; no guaranteed bound or calibrated odds. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Prior unchanged-sample Monte Carlo3570 retained, not rerun as new evidence. Actual payout/stop slippage and distribution timing unknown. No trade-derived Kelly from empty reset ledger; equal-weight mandate governs.

Premises:1.Joint daily OHLC/previousclose ratios from https://runway.adityaperswal.workers.dev/data/stock-bars ; NumPy seed92002,5day blocks,20000paths per stock/window, all operating history and last252,60sessions. 2.Fixed research brackets E/S/T:CE45.41/42.027/56.2870;IMOS61.30/56.99918/75.1852;BTDR12.97/11.11183/18.75245;AMTX2.16/1.90454/2.96101. Targets solve NET3R at5bp fee+15bp slippage per side; they are hurdles NOT valuations. Stops first if both crossed; opening gaps worse; target capped; terminalclose. 3.All/recent mean return% CE .682/.107,IMOS1.156/4.594,BTDR4.464/2.013,AMTX.208/.303. Target probability% CE18.835/24.115,IMOS23.395/41.35,BTDR32.685/28.455,AMTX25.695/26.195. Stop%61.945–73.9 across cells. Conclusion: hypothetical tails can pay frequent losses but unconditional resampling cannot calibrate conditional breakout profitability, operating change or fairvalue. Actual rule holdouts3590etc are separate. HalfKelly capital-grid results (.03–.5) constrained0..1, not unconstrained optimum or authorization. IMOS one-share50%gap costs30.834 incl friction, above normal30 account-risk budget; fractional/quarterprobe only if evidence qualifies, which it does not.160000total paths, not60000; observation metric typo clarified.

Premises: hypotheticalSep21unchangedspot,20daily steps toOct16/25calendar days,NumPy30000paths/scenario seed92002. Bootstrap last252signedlogdailyreturns IID at.75/1/1.5scale, constantBSMIV calibrated toask and4%rate. HALOC130paid.23fitIV33.414%,P95paid.18IV38.114%,THC27paid.18IV68.513%;RV60HALO45.30/TH58.40%. Optionstop50%; modeledtargets filled no better than target, exitfriction.01/share+1USDroundtripfee. 3xpremium targets meanHALOC -8.90/-3.58/+1.78USD,THC -7.89/-4.71/+.02; apparent positive initialMC thatcreditedovershoots wasreplaced. P80targets independentlyderivedfrom3593 HALOC1.83 andTHC3.58 yieldmean -8.27/+1.42/+16.26 and-3.54/+7.28/+28.75;baseline targethits10.657%/4.557%,stops89.257%/91.873%,fullpremiumloss3.617%/5.847%. HALOPtarget1.93baseline -10.21USD,prefercallifquotedriskpass. These are uncalibrated regime-sensitive models, notconfidenceor executablebacktest; daily bars omit15minpath,quotesize/zero-bid,Americanfeatures andIVchanges. Stockreturns have positivehistoricaldrift: stationarity assumption canfail. Simulatedmarginalprofitdoesnotvalidate certainty. Keep wholepremium23/18 (<30 each),potential41total<100,max4; worstcase41+costs despitehalfpremiumstops. TerminalintrinsicKelly49.7/235.25USD unreliable; hardcap30 binds. Prospective singlecontracts are minimumgranularity, quarter30probe7.50unavailable. No ordersclosed; refreshcapital andactualquoteinentryrun. Source /data/stock-bars,/data/option-chain/HALO,TH?feed=indicative;30184–89.

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 initial93.33each;2 r=2ATR/entry;3 retained g assumptions EEM.125794155019 QQQ.109666233203 IWM.138906519177 from prior fund stress, not new guaranteed bounds. Size=floorcents min(280/3,250,29.5/(r+(1-r)*2g+.005)) gives93.33each. Stress=N*(r+(1-r)*2g+.005): EEM25.913233,QQQ22.608078,IWM27.921384, joint76.442695. Each modeled loss<30 account3%; larger gaps can exceed this. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all. Separate seed92002 jointIID20000x20day closing-return paths last1260 observations: P05 -22.652306,median2.100807,P9528.781054 dollars. Repeated unchanged-sample diagnostic is NOT new evidence. No costs/stops/targets/intraday sequence/serial dependence; current basket retrospectively selected. Neither live exit odds nor Kelly estimate; no sizing change.

1.NumPyseed92000, jointdailyOHLC/priorclose block5bootstrap;20000paths each allhistory/last252 forFRO/POWL https://runway.adityaperswal.workers.dev/data/stock-bars .2.Research brackets FRO51.42/48.201/61.901369,POWL183.96/167.95506/234.924079;20bp/side,stopfirst,openinggap worse,positivegap targetcapped,60sessionclose liquidation.3.Mean netreturns FROall1.4021%,last2526.8140%;target30.39/49.70%;POWLall2.9545%,last2524.6020%;target28.885/37.03%. Stop probabilities FRO67.98/47.905%,POWL61.68/61.13%;positive expectancy can coexist with frequent losses. HalfKelly portfolio-weight maximization over0..1 grid=.5 inall4, uppergrid constrained and NOT optimal unconstrained size estimate. This unconditional historical resampling ignores currententryabsence,changingvaluation,warshutdown,newgaps,15minvenuechecks and ex-dividend accounting; no liveodds inferred. Severe50%FROgap costsabout25.86 one share,51.73two>30 normalaccountbudget. POWL one share>120capital, fractional60USD50%loss already30beforecost; simulationlossquantilesnotriskbounds. No order.

Premises: S46.67 K37.5 paid.23, indicativeIV55.94%, N11 empirical signed reactions3554. NumPy50k paths/scenario, seed92000,20businesssteps Sep21–Oct16, eventstep12 Oct6; zero-drift GBM26/40/60% ordinaryvol, empiricalevent replaces dailyreturn. BSM put floored intrinsic,4% rate assumption, preIV55.94%,postIVscenario; initialmodel.23647 vsask.23. Daily stop.115,target.69, exit .01/share friction plus1USD roundtripfee. Hypothetical hold-through means+3.27/+8.81/+7.67USD, targets4.83/11.78/22.62%,but current20.14% hurdle exceeds10.02%median so this hold policy is outside mandate. Mandate-consistent forced Oct5 day11 exit means-13.81/-9.02/+.88USD, targets.556/7.006/20.698%. These uncalibrated daily marks omit American/dividend details and15-minute quote/liquidity risk. Full-premium loss remains possible despite half-premium stop. Separate empiricalterminalintrinsic after.02 friction:2/11wins, meanintrinsic.650308, grid halfKelly6.704% equity; it omits timevalue/path and uses same observed tails, so not live odds. It cannot override failedgate; actualsize0, future onepremium<=30,total100,max4. Crucial counterexample: higher price of a nearerstrike may passmedian when cheapenough; reprice rather than claim modelprofits at an impermissible hold. Sources https://runway.adityaperswal.workers.dev/data/option-chain/LW?feed=indicative ; stockbars and issuerOct6date29824.

Premises:1 same-day joint rows of last1260returns preserve cross-asset dependence;2 numpy seed920,20000paths of20 IID sessions;3 constant initial93.33 each and compounded closes. P05 -22.5286USD,median2.0020,P9528.8353. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all. This repeat is a reproducibility diagnostic of new retrieval, not fresh independent evidence; prior3463 already established dependence. No stops/targets/intraday exits/costs/serial dependence; 2020crisis omitted, retrospectively selected basket, no calibrated trade odds or Kelly input. Separate retained scenario r=2ATR/entry; stress=N*(r+(1-r)*2g+.005), g EEM.125794155019 QQQ.109666233203 IWM.138906519177 from prior record, not remeasured extrema. EEM25.9132 QQQ22.6081 IWM27.9214,joint76.4427USD. Size=floorcents min(280/3,250,29.5/(r+(1-r)*2g+.005)) yields93.33 each. Every lot below30 in this stated scenario, but complete loss93.33 could exceed3% account; empirical envelopes cannot guarantee maximum overnight loss. No inferred safe bound or size uplift.

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: 11 close-event reactions3513; S15.13,K14,indicativeask.23/IV.3516 fromchain. NumPy50k paths each,seed91908,20businessdaysSep21-Oct16,eventstep8Sep30; empiricalreaction replaces ordinaryreturn on eventday, otherdayszero-driftGBM22.5/35/50%annualvol. BSM put flooredintrinsic,preIV.3516/postIVscenario vol,r4%assumed;initialmodel.168158 differsask.23,so this is exit-policy sensitivity notfair-valueproof. Daily modeledstop.115,target.69,elseexpiry;exit.01/sharefriction+$1roundtrip. MeanPnL -12.3303/-6.1652/+.1245USD;target5.052/13.464/21.866%,stop93.924/85.970/78.006%;P05-23.2405/-20.4268/-21.2576USD. Uncalibrateddailyprices omitAmericanexercise/dividendboundary andactual15-minute liquidity; probabilities are model outputs, not live estimates. Empirical terminalintrinsic logutility grid halfKelly0 after.02friction. Conclusion size0 forfailedmandate; evenpositivehigh-volscenario doesnotrescueP80gate. Futurequalifyingticket fullpremium<=30, total<=100,max4;50%stop doesnot cap gaploss. Source https://runway.adityaperswal.workers.dev/data/stock-bars and option-chain/CAG?feed=indicative .

1.Source https://runway.adityaperswal.workers.dev/data/stock-bars jointdailyOHLC/priorclose resampledNumPyseed91908;all2692/last252/2026last179rows,blocks5/10,20000each,60sessions.2.FixedE51.42/S48.201/T61.901368;baseline5bpfee15bpslip;stopfirst/adversegap,targetcapped,timeoutexit,no15minmanagement/dividendcashseparation/newshock. All5/10means1.352/1.477%,target30.215/30.415%;252means7.049/6.608%,target50.63/48.67%;2026means9.458/9.554%,target60.42/60.575%.3.Expectedlogweightgrid0..1halfKelly.49–.5;cap120andgapstressbindlongbeforethat. One-shareP99model-loss4.29–5.85 isnotbound:assumed50%gap25.864.4.Resamplingstrongrecentdriftinflatesoddsversusactualconditionalentryholdout;simulationdoesnotvalidate61.90fundamentalvalue. Validmodelcalculation,limitedsoundnessasliveforecast;noorders.

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.NumPyseed91906,20000pathsfor3pools(all432,last252,2026179)*2blocklengths5/10,60sessions,jointOHLC/priorclose https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=PSIX,ETN,POWL,NVT,SPY&timeframe=1Day&feed=sip&adjustment=all .2.Frozen45.87/41.2664/61.710237;5bpfee50bpslip,adversegapstop,cappedtarget,samebarstopfirst,timeoutexit. Allhistory5/10mean+2.8986/+3.2096%,target33.415/34.405%;last252mean-1.7638/-2.9310%,target23.855/22.105%;2026mean+1.1850/-.1533%,target29.510/27.145%. Medianall-11.0204%.3.Expectedlogstockweightgrid0..1thenhalf:all.337/.361,last2520/0,2026.139/0;cap120bindspositivemodelsbutnotapproval. NaturalexittradehalfKelly2025.5/20260also unstable.4.TwoshareP99loss31.64–36.24dollars;quantilesnotbounds/unconditionalresamplingnotliveentryodds. No15minexits,+2Rratchet,newshocks/newsconditioning. Conclusion:don'tselectfavorablewindowtosize;one-shareprobeaffordableifvalue/edgeimprove,actual0.

Premises:13observedovernightgaps29472–84; S7.99;10tradingsteps fromMondaySep21 throughOct2, eventstep4ThursdaySep24 issuer https://investors.blackberry.com/ . Correctedstep4 supersedesinitialstep3 outputs29595–97. NumPy50kpaths/scenario seed91906; stockzeroexpecteddrift GBM40/60/80%annualvol, oneIIDempiricalgap injectedday4; rate4%assumption. BSMputflooredintrinsic,pre-eventindicativeIV84.03%K7/98.70%K7.5, posteventIV40/60/80%; noAmericanexerciseboundary calibration. Exitdaily modeledmark<=.5paid or>=max(3paid,P80intrinsic),elseexpiry; actual15minquote/liquidityandgapstop executionunvalidated. $1roundtrip+.01/shareexitslippage. K7p.20 target.60 means-$13.6358/-10.8047/-6.7817,stop95.850/92.566/87.452%,target3.234/6.130/11.384%. K7.5 hypotheticalp.20 target.60 means-$7.1241/+$1.7658/+$10.9070;stop83/71.85/60.444%,target13.416/25.566/37.804%. CurrentK7.5ask.46 costs46>30cap; means-$30.4092/-23.0016/-15.1475. Cheap.20 is notquotedattainable. ModelP05 oftenfullpremium+fee despitehalf-premiumstop. Separate13signedclose intrinsicpayoff logutilitygrid halfKelly0 forK7p.20 andK7.5p.20/.23/.46 after.02friction. Intrinsicexcludesremainingtimevalue,so notproof trueoptionEVnegative; cannotclaimpositivecalibratedsize. Currentliveallocation0, hardonepremium<=30,total<=100,max4; quarterprobe cannotrescue invalidquote/failedmandate. Riskfullpremium,notmodelstop. Source https://runway.adityaperswal.workers.dev/data/option-chain/BB?feed=indicative andstock-bars.

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:1) SIP normalized OHLC throughSep18 https://runway.adityaperswal.workers.dev/data/stock-bars; current selected basket, no past selection simulation.2) 10000 synchronized63-session paths per regime with circular5-day blocks, seed91906,1255 fullsample days or179 recent2026days; preserve within-day cross-sector/within-block dependence. Each OHLC divided by its previous close, compound from1.3) Fixed current2ATR stop and5yearP90 targets,86.66each; no trail, SMA ratchet, reranking or re-entry. This is sensitivity study, NOT mandate backtest, OOS validation or calibrated live odds. Close model tests at close and fills there; OHLC tests low/high, gaps fill at open if beyond barrier, otherwise barrier; stop first for ambiguous day (zero encountered). Survivors liquidated at day63close. Costs6bp eachway baseline,20bp stress; no cash interest. Fullsample close mean6.0981USD,median4.6280,P5−12.8331,P9534.6646,loss39.60%; OHLC mean4.5986,median2.6125,P5−9.8123,P9531.2103,loss43.64%. Full OHLC stop odds69.40/63.51/66.99%,target18.58/18.68/17.52%,survive12.02/17.81/15.49. Recent close mean12.8759,loss14.28%; recentOHLCmean10.4871,loss18.54%; recentOHLCstop66.53/43.15/64.44%,target26.13/36.75/22.39%,survive7.34/20.10/13.17. Stresscostmeans fullclose5.3541/fullOHLC3.8588/recentclose12.1130/recentOHLC9.7309. Full outputs observations recorded separately. No sampled lot loss>20; this DOES NOT bound unseen gaps. Intraday model assumes barrier liquidity and continuous observation, unlike venue15min checks; adjustment prices not executable quotes. Trailing rules omitted, no directional claim about their effect. Historical regimes retain drift; small recent sample exaggerates precision. Conclusion unchanged86.66 slots; never equate historical P90 with90%hit probability. Model sensitivity explains uncertainty; no strategy retest per specific mandate.

Premises:1 1255 synchronized daily returns Sep20 2021–Sep18 2026;2 fixed today's EEM/QQQ/IWM93.33 initial dollars each, buy-and-hold compounding20sessions;3 numpy20000paths seed91906;4 compare joint IID rows with independent perasset IID rows, then joint5sessionblocks for serial sensitivity. Same-day dependence isolation: P05 PnL -22.4160 versus -13.4391 USD, ES05 -28.6110 versus -17.1955; model probability loss>30 1.505% versus .015%. Joint5dayblock P05 -21.6557,ES05 -28.4310,P01 -32.7992,lossfrequency42.17%,loss>30 1.58%. Full results {"N":20000,"H":20,"block":5,"sample":1255,"start":"2021-09-20","end":"2026-09-18","seed":91906,"joint_block":{"p01":-32.79919741904743,"p05":-21.655714707388654,"median":2.909658317689602,"mean":2.714465051489629,"prob_loss":0.4217,"prob_loss30":0.0158,"es05":-28.431048746217193},"joint_iid":{"p01":-32.76254907968935,"p05":-22.41602014010171,"median":1.9648147526769801,"mean":2.5320445311655244,"prob_loss":0.44905,"prob_loss30":0.01505,"es05":-28.61101950104886},"independent_iid":{"p01":-19.57023865210427,"p05":-13.439106213579274,"median":2.5778309022182273,"mean":2.6777364221379094,"prob_loss":0.39825,"prob_loss30":0.00015,"es05":-17.1955094610215},"correlation":{"EEM":{"EEM":1,"QQQ":0.6929633476476149,"IWM":0.6507916837227055},"QQQ":{"EEM":0.6929633476476149,"QQQ":1,"IWM":0.7785802945417117},"IWM":{"EEM":0.6507916837227055,"QQQ":0.7785802945417117,"IWM":1}}}. Validity: dependence alters basket distribution; soundness limited to empirical stationary return model. Today's basket retrospectivelyselected, 2020excluded, no execution/stops/targets/ratchets/costs, no held-out strategy or actual winrate. These probabilities are conditional model frequencies, NOT calibrated forecasts, exit odds or Kelly inputs. No size uplift or momentum veto. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all

Premises: historical10overnight gaps from observations29367–76, Sep18 S2.84, Oct16putK2.5. 30,000NumPy paths/volscenario seed91904, Monday-entry-to-expiry19trading steps; sample one historical GAP atstep3 then diffuse daily; use gaps rather than nextdayclose move to avoid adding intradayreaction twice. Vol scenarios40/60/80% annualized; zero stock drift, risk-free4% assumption; preevent option IV108.28% from indicativequote, posteventIV=scenario realizedvol. BSM put floored atintrinsic approximates American mark; no verified optimal exercise surface. Exit at daily observed model mark below0.5premium or above P80target.552156, else horizon. Gaps may pass stop; exitprice not stopguarantee. Fees1USDroundtrip and.01/shareexitslippage. At premium.13 mean dollarPnL -5.2523/-2.5318/+1.1347, stop80.4167/77.89/73.8533%, target7.2333/11.8667/17.7267%, win17.9433/20.62/24.9133%. At.28 allnegative(-18.5996,-16.2792,-13.7725); already failsmandate. At.11 means-3.2232/-.5282/+3.1574. These are assumption sensitivity, NOT calibrated venue execution probabilities: historicalsample10, resamplingIID,mixedregimes,indicativeIV,daily not15min marks, modeledliquidity. P05 loss .13case14USD includingfees; premium stillwhole13USD risk, not6.50stop. Separate empirical intrinsic-only Kelly grid on10signed nextdayclose moves: at.10 meanpayoff.116659,profit30%,halfKelly1.77%account; at.11 halfKelly.70%account; at.13/.28 halfKelly0. Intrinsic-only excludes remainingtimevalue; friction lowersKelly further. It does NOT prove no positive optionexpectancy at.13, but cannot support a confident size. One .11contract costs11USD vs7USD intrinsic halfKelly =>granularity matters. Start100fundcash/1000account, hardpremium30/lot,total100,max4. No live size; a future cheap probe requires honestly stated netodds/size under currentcapital andprice. Data sources https://runway.adityaperswal.workers.dev/data/stock-bars and https://runway.adityaperswal.workers.dev/data/option-chain/SFIX?feed=indicative .

NumPy seed91904,20,000 paths/model,60sessions,five-day blocks of jointOHLC/priorclose ratios. Two source pools:2016–23 training2011returns and latest252sessions. E14.82/S12.672/T21.919686,55bp each side; gap stops at worse open, target capped, same-bar stop first, timeouts marked at60. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Training/recent modeled target rates14.305/34.13%,stop56.01/65.075%,mean netreturn+.2761/+5.5309%,median both-15.4293%. Mean wins26.8199/45.7187%,mean losses14.7034/15.8906%,profit rates36.075/34.77%. Binary half-Kelly risk-stake approximations.5148%/6.0489% of bankroll; not direct position notional and not validated live edge. Sampling recent AI regime nearly triples target frequency but also raises stop frequency; don't select the pool to justify an order. Daily path model misses monitoring delays, future jumps and conditional fundamental information; simulated maximum loss is not a bound. Four shares59.28 imply planned netstoprisk9.197 and assumed50%gap loss29.64 plus costs, below3%account only approximately; use3 shares if reserving explicit friction under30. Quarter-probe of a feasible4-share ceiling would be1share14.82, stoprisk2.30 and50%gap7.41. All actual sizes0 because current entry/defended payoff remain unqualified, not because an arbitrary tail threshold vetoes risk. If qualified later, recompute half-Kelly with appropriate evidence and current cap; don't transfer these unconditional odds.