Stats

Premises:1 SIP all/split OHLC,Sep21 vintage, completed Sep18;2 select endpoints Sep18 2021 onward with prewindow previous close;3 factor=allClose/splitClose; event if abs daily factor change>.001. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Through2025 XLE18 events mean split opening gap-.752930%,adjusted+.171235%,difference92.4165bp;ordinary1058 mean difference.08361bp. EEM9 events split-1.356927%,adjusted-.124978%,difference123.195bp;ordinary1067 difference.07104bp. 2026 already-seen chronological check:XLE2 events difference67.5283bp;EEM1 53.1497bp,too small for stable inference. All20 XLE detected dates match issuer exdates https://www.ssga.com/library-content/products/fund-data/etfs/us/spdr-etf-historical-distributions.xlsx . EEM dates not independently matched here. Conclusion dividend adjustment materially changes gap interpretation, not stop execution. Counterexample ordinary2026 XLE worst gap-5.78457% remains genuine price risk beyond the accounting effect. Selection by factor change makes difference partly mechanical; this is measurement audit,not causal return premium or backtest. No strategy fit or claim of unseen OOS.

Premises:1 split-only daily bars https://runway.adityaperswal.workers.dev/data/stock-bars;2 paired open/priorclose minus1 with prewindow warmup;3 no imputed bars. Sep20 2021-Dec2025 N1076 correlation .354556 versus2026 N179 -.483819; both-negative26.487% versus11.173%. Prior N1075 omitted first eligible gap; revised warmup explains small training difference. Recent period already examined, not unseen holdout. Zero closed live trades means winrate, average win/loss, session slippage and empirical halfKelly unavailable. Negative recent correlation is not a hard hedge. Maintain mandated one share; no strategy retest.

Premises:1 raw split-normalized SIP OHLC https://runway.adityaperswal.workers.dev/data/stock-bars ;2 gap=open/priorclose-1, paired observations;3 dollar exposures67.37/64.31. Sep2021-Dec2025 N1075 gap correlation+.349289;2026 N179 -.483819. Dollar joint-gap1stpercentile -3.442735 training versus-2.640043 recent. These describe changing dependence; small recent sample cannot establish protection. Dividend mechanical gaps remain in raw prices and offsets not included. Missing first fetch-day gap excluded; no zeros imputed. N0 closed live trades: win rate, mean win/loss, session slippage and Kelly unidentified. Prior fixed premium accepted; nothing here refits or retests mandate. One share each; simultaneous10% gap costs13.168=1.3168%equity, not maximum loss. Two shares per slot exceed140book. Counterexample common risk-off shock can make both negative regardless average correlation.

Premises:1 raw SIP daily bars Jun2020–Sep18 2026, XLE Dec5split repaired once;2 scale daily open/priorclose gaps by current one-share67.37/64.63;3 compare downside per name with1.89/2.53 initial stop budgets. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Pre2026 N1404 each exceeded its budget8times,both2;2026 N179 EEM7,XLE2,both0. Correlation+.43058/pre vs-.48382/2026 does not prevent name-level tails. Gross joint gap loss=max(0,-EEMgapUSD)+max(0,-XLEgapUSD), deliberately excludes offsetting gains: maxima6.68195/pre and3.86693/2026. Sum excess beyond individualstopbudgets max2.26195/pre,1.97693/2026;P99 0/pre versus1.35215/2026. The unconditional99th percentile can miss sparse pre2026 extreme events. Not actual stop fills: premarket enforcement, changing holding price and spread omitted. 2026 is chronological comparison already seen in earlier research, not unseen validation. March2020 absent. No retest of momentum, no Kelly/winrate from this statistic; one share stays.

Premises:1 raw split-normalized daily opens/prior closes Jun2020–Sep18 2026;2 scale each gap by current pending entries67.37/64.63 and sum;3 pre2026 threshold fixed before evaluating2026 in this script; no tuning or entry-rule test. Source https://runway.adityaperswal.workers.dev/data/stock-bars. Pre2026 N1404, Monday262 p05 -2.58684 versus other1142 -1.73772 dollars; Monday correlation .51757 vs .39917 other. 2026 N179, Monday33 p05 -1.19785 vs other146 -1.41480; correlation -.46855/-.49897. All-pre2026 p05 -1.848124 crossed3/179=1.67598% in2026. Joint minima -6.68195/pre and -3.65555/2026; excludes March2020 crash so not global stress. Formal temporal holdout, NOT previously unseen data: earlier runs inspected2026. MondayN33 and historical sector regime selection defeat claim of permanent hedge or Monday advantage. Facts end at historical measurements; forecasting recurrence is assumption. Keep one share, no sizing increase, no calibrated win odds/Kelly.

Premises:1 provider docs https://docs.alpaca.markets/us/reference/stockbarsingle-1 define all as including cash-dividend/split adjustment.2 raw/all paired1584sessions throughSep18 show17/18 funds with changed closes; GLD unchanged.3 issuer EEM https://www.ishares.com/us/products/239637/ishares-msci-emerging-markets-etf provides10exdates Dec2021-Jun2026; XLE historical workbook https://www.ssga.com/library-content/products/fund-data/etfs/us/spdr-etf-historical-distributions.xlsx provides20 Sep2021-Jun2026. ImpliedD=Pprev*(1-factorPrev/factorEx),factor=all/raw, matches issuer within .008782/.007846 dollars at historical share scale. Exact-factor replacement changes EEM252 28.311639->28.301024%, XLEmean19.705216->19.711674%, XLEP90 .206279467->.206321613. EEMP90 unchanged .107179635. Raw split-only EEM25225.8543%,XLEmean18.0040%; no selection change. EEM adjusted lead over QQQ5.442623pp; sector XLK lead .330904pp, but EEM+XLK257.92 exceeds240 so XLE remains feasible selection. Validity: audit supports robust current selection; soundness: confirms sampled known payouts, not exhaustive absent-event detection, all16other issuer histories or reinvestment convention equivalence. Small errors consistent with price rounding but cause unproven. No discretionary cash/quarantine, no re-test of accepted premium.

Premises:1 normalized daily SIP https://runway.adityaperswal.workers.dev/data/stock-bars Jan2020–Sep18 2026.2 paired daily simple returns/gap=open/priorclose-1; dollar changes scaled by queued67.37/64.63.3 regime uses EEM prior20-session return shifted one day; exclude20 missing regime observations. Results {"n":1686,"corr_daily_full":0.4347195240162975,"corr_gap_full":0.4569284164365753,"corr_gap_252":-0.41657179298281216,"worst_joint_gap":-16.202745527979015,"worst_gap_date":"2020-03-16 04:00:00+00:00","gap_p01":-4.128705344478528,"regimes":{"eem_prior20_negative":{"n":710,"daily_corr":0.5130147784073572,"both_negative_fraction":0.2661971830985915,"joint_daily_p01_dollars":-6.527533356077146},"eem_prior20_nonnegative":{"n":956,"daily_corr":0.3226251399636696,"both_negative_fraction":0.2709205020920502,"joint_daily_p01_dollars":-4.125658972617217}}}. Interpretation: prior weak-EEM regime daily correlation .513 versus .323 in nonnegative regime; joint daily1% tail -6.53 vs-4.13. Both-down frequency alone misses severity. Recent252 gap correlation -.417 cannot establish hedge when full+.457. No causal claim, significance test or independent strategy validation; selection/survivorship and regime change remain. Actual own closedN0 means no measurable winrate, slippage or empirical halfKelly. Fixed one share, no discretionary size increase.

Premises:1 normalized SIP daily source https://runway.adityaperswal.workers.dev/data/stock-bars Jan2020–Sep18 2026.2 gap=open/priorclose−1, paired1686dates scaled by67.37/64.63 pending entrydollars.3 response-specific confirmed splits repaired once. {"n":1686,"corr":0.4569284164365753,"recent_corr":-0.41657179298281216,"worst":-16.202745527979015,"worst_date":"2020-03-16","p01":-4.128705344478528}. Recent252 correlation−.41657 versus full+.45693; worstjoint−16.20275 onMar16 2020,1%quantile−4.12871. Prior−16.23 small vintage difference not explained; preserve both vintages, no sizing inference. No true maximum loss implied. Own closed N0 so empirical winrate/slippage/halfKelly unavailable. Fixed one share maintained; optional doubling not needed. Counterexample structural regime change invalidates empiricaltail estimates.

Premises:1 repaired source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all; paired open/priorclose-1, Sep2020–Sep18 2026,1518observations.2 weights67.37/64.63 are hypothetical one-share entry dollars. Results {"n":1518,"gap_corr":0.22817876236373233,"worst_joint_gap_dollars":-4.97832962124513,"worst_date":"2025-04-07","gap_p01_dollars":-3.1614587081653003,"last252_corr":-0.41657179298281216}. Conclusion recent negative correlation is not a persistent hedge. Prior broader sample including2020crash had larger losses; this sample startsSep2020 and misses crash, explaining smaller worst loss; neither is maximum possible. OwnclosedN0: winrate/slippage/halfKelly unknown; do not manufacture estimates or resize.

Premises:1 same split-normalized SIP series as signal table, 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.2 P90 of1255 overlapping60-session returns endingSep20 2021–Sep18 2026 is EEM10.71796%,XLE20.62795%.3 adjacent gains autocorrelation .97286/.97481;1255 isnot independenttrials. Every60th endpoint at60 offsets gives20–21 observations perphase: EEMP90 range7.5403–14.4586%,median10.1740%;XLE12.3929–24.9686%,median19.5529%. Phases mutuallydependent,range notCI. Descriptive endpoints2021–23 N574 vs2024–26 N681: EEMP90 6.2663->12.1418%,median-2.8085->5.2833%,positive32.9268->85.7562%;XLEP90 23.0071->17.3154%,median7.1487->2.6234%,positive63.5889->64.3172%. Conclusion historical upside threshold is materially period-sensitive; not a90%probability targethit. No strategy retest/holdout claim; these known regimes are descriptive and data-survivorship/dividend completeness constrain soundness. Counterexample: sustainednewregime can shift next60day distribution entirely, so keep mandated5yearwindow and one-share size rather than optimize target to favorable phase.

Premises: (1) previous daily close to next daily open is a gap proxy, not intranight path/fill; Alpaca conditionT excluded from daily OHLC https://docs.alpaca.markets/us/docs/market-data-faq . (2) repaired missingXLE2:1 split using issuer29327. (3) compare split-only price gaps with all-adjusted economic-return gaps. Primary bars https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=EEM,XLE&timeframe=1Day&start=2019-01-01&end=2026-09-18T23:59:00Z&feed=sip append adjustment=split/all. MeasuredSep19. Split sample1938 gaps: correlation+.46018 versus fiveyear1255 +.15748 and recent251 -.40937. Simultaneous gaps below-2%:28/1938,11/1255,0/251. XLE negative in EEM bottom5% gaps:66/97=68.04% full,35/63=55.56% fiveyear,2/13=15.38% recent; small conditional samples. Worst joint same-date gap scaled to static67.37/64.63 exposure16.23047 on2020-03-16; fiveyear4.98122 on2025-04-07; recent3.65555 on2026-06-23. These are scenarios not realized portfolio PnL. Full adjusted economic-gap correlation+.46190 and worst16.20275 corroborate qualitative result; dividend adjustment changes level slightly. Prior expected unstable diversification; evidence supports it without implying next-event probability. Fullsample marginal minima EEM-11.45545%2020-03-16,XLE-17.48235%2020-03-09 are DIFFERENT dates and must not be summed as observed joint loss. All measured outputs29349–58. Counterargument: 2020 regime may not recur; recent negative dependence may persist. Neither establishes a hard future bound. Soundness limited by daily proxy, vendor revision and selected universe; valid conclusion is no diversification-based size increase, not withdrawal from fixed momentum.

Premises: past adjusted daily returns describe historical dispersion, not guaranteed future return. Source https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=EEM,XLE&timeframe=1Day&adjustment=all&feed=sip ; completedSep18 2026. Fixed target uses five-calendar-year ending dates,1255 overlapping60-session gains: EEM P90 10.71796349%, XLE20.63484442%. Diagnostic last1260 sessions includes five earlier observations: EEM60day P10/median/P90 -8.1723/2.3230/10.7033%, XLE-6.6200/3.8107/20.5424%; do not replace exact target window with1260 shorthand. Daily correlation252=-.159464 versus1260=.252817, so current low correlation is not durable insurance. Annualized daily volatility19.9155%/25.6825%. Counterexample: global liquidation can turn both correlations positive and gap through stops. Conclusion: two distinct exposures but retain whole-share minimum sizing; no diversification-based leverage or doubled position.