The analysis is based on the following premises: the data is from the SIP all/split OHLC, with a vintage date of September 2021 and completion date of September 2018; the endpoints selected are from September 2018 to 2021 onward, with a pre-window previous close; the factor used is all close/split close; and an event occurs if the absolute daily factor change is greater than 0.001. The data source is https://runway.adityaperswal.workers.dev/data/stock-bars. Through 2025, the XLE18 events had a mean split opening gap of -0.752930%, an adjusted gap of 0.171235%, and a difference of 92.4165 basis points; the ordinary mean difference was 0.08361 basis points. The EEM9 events had a split gap of -1.356927%, an adjusted gap of -0.124978%, and a difference of 123.195 basis points; the ordinary difference was 0.07104 basis points. A chronological check for 2026 showed that the XLE2 events had a difference of 67.5283 basis points, and the EEM1 had a difference of 53.1497 basis points, which is too small for stable inference. All 20 XLE detected dates matched the issuer ex-dates found at https://www.ssga.com/library-content/products/fund-data/etfs/us/spdr-etf-historical-distributions.xlsx. The EEM dates were not independently matched. The conclusion is that dividend adjustment materially changes gap interpretation, but does not stop execution. A counterexample is the ordinary 2026 XLE worst gap of -5.78457%, which remains a genuine price risk beyond the accounting effect. The selection by factor change makes the difference partly mechanical; this is a measurement audit, not a causal return premium or backtest. There is no strategy fit or claim of unseen out-of-sample data.
The automated trading fund manager made some observations about the performance of a hedge. The manager used two main ideas: first, it looked at daily stock prices from a website, and second, it compared the opening price to the previous day's closing price, with a special preparation period. The manager did not fill in any missing prices. From September 20, 2021, to December 2025, the manager found a correlation of 0.354556 between two sets of data, but from 2026 onwards, the correlation was -0.483819. This means that the relationship between the two sets of data changed over time. The manager also found that the difference in performance between two periods was 26.487% versus 11.173%. The manager had previously left out some data, but when it added it back in, it found that the performance difference was small. The manager had already looked at recent data, so it was not a surprise. Because there were no closed trades, the manager could not calculate some important metrics, such as the win rate or average win and loss. The manager noted that a negative correlation does not necessarily mean the hedge is not working. The manager decided to keep the current strategy and not change it, and to maintain a minimum of one share.
The automated trading fund manager analyzed the stock R92100 and found that the correlation between its gap, which is the difference between the opening price and the previous closing price, and another stock changed sign. The analysis used raw split-normalized stock prices from September 2021 to December 2025, which showed a positive correlation of 0.349289, but from 2026, the correlation became negative at -0.483819. The dollar exposures were 67.37 and 64.31. The joint gap percentile was -3.442735 in the training period versus -2.640043 recently, indicating changing dependence between the two stocks. However, the recent sample size is too small to establish a reliable hedge. The analysis excluded dividend mechanical gaps and missing first fetch-day gaps, and no zeros were imputed. There were no closed live trades, so win rate, mean win/loss, session slippage, and Kelly criteria could not be identified. The prior fixed premium was accepted, but this analysis does not refit or retest the mandate. Buying one share of each stock would result in a 10% gap cost of 13.168, which is 1.3168% of equity, but not the maximum possible loss. Buying two shares per slot would exceed 140% of the book value. A common risk-off shock could make both stocks negative, regardless of their average correlation.
A study analyzed daily stock market data from June 2020 to September 18, 2026, using raw SIP daily bars, with a one-time repair of the XLE split on December 5. The data was scaled to compare daily open and prior close gaps. The study found a correlation of +0.43058 before 2026 and -0.48382 in 2026, which does not prevent individual stock losses. The study used a dataset from https://runway.adityaperswal.workers.dev/data/stock-bars. Before 2026, 1404 events exceeded their budgets 8 times, while in 2026, only 2 events exceeded their budgets. The maximum joint gap loss was $6.68195 before 2026 and $3.86693 in 2026. The sum of excess losses beyond individual stop budgets was $2.26195 before 2026 and $1.97693 in 2026. The 99th percentile of excess losses was $0 before 2026 and $1.35215 in 2026. Note that this analysis does not account for actual stop fills, premarket enforcement, or changes in holding price and spread. The study also notes that 2026 is a chronological comparison and not an unseen validation, and March 2020 is absent from the data. Additionally, the study does not retest momentum or calculate Kelly/winrate from this statistic, and the analysis is based on a single share.
This analysis is based on three premises: it uses raw split-normalized daily opens and prior closes from June 2020 to September 18, 2026; it scales each gap by current pending entries of 67.37 and 64.63 and sums them; and it uses a pre-2026 threshold that was fixed before evaluating 2026 in this script, with no tuning or entry-rule test. The data comes from https://runway.adityaperswal.workers.dev/data/stock-bars. Before 2026, there were 1404 samples, with 262 Mondays showing a average gap of -2.58684 dollars, compared to -1.73772 dollars for other days, and a Monday correlation of 0.51757 versus 0.39917 for other days. In 2026, there were 179 samples, with 33 Mondays showing an average gap of -1.19785 dollars, compared to -1.41480 dollars for other days, and a correlation of -0.46855 versus -0.49897. The average gap of -1.848124 before 2026 was crossed 1.67598% of the time in 2026. The lowest points were -6.68195 before 2026 and -3.65555 in 2026, excluding the March 2020 crash, which means this is not a global stress test. This analysis used a formal temporal holdout, which means it was not based on previously unseen data, as earlier runs had already inspected 2026. The results show that Monday gaps and historical sector regime selection do not support the claim of a permanent hedge or Monday advantage. The analysis only reports historical measurements and does not forecast future results, which would be an assumption. The strategy is to keep one share, with no increase in sizing, and no calibrated win odds or Kelly criterion.
The R92004 dividend audit was conducted based on certain premises. First, provider documents from Alpaca Markets define 'all' as including cash-dividend and split adjustments. Second, an analysis of 1584 sessions through September 18 showed that 17 out of 18 funds had changed closes, while GLD remained unchanged. Third, the issuer of EEM, iShares, provides 10 ex-dates from December 2021 to June 2026, and the XLE historical workbook from SSGA provides 20 ex-dates from September 2021 to June 2026. The implied dividend was calculated using the formula ImpliedD = Pprev * (1 - factorPrev / factorEx), where factor = all / raw, and this calculation matched the issuer's data within $0.008782 and $0.007846 at the historical share scale. The exact-factor replacement changed the EEM 252-day average from 28.311639% to 28.301024%, the XLE mean from 19.705216% to 19.711674%, and the XLE P90 from 0.206279467 to 0.206321613. The EEM P90 remained unchanged at 0.107179635. The raw split-only EEM 252-day average was 25.8543%, and the XLE mean was 18.0040%, resulting in no selection change. The EEM adjusted lead over QQQ was 5.442623 percentage points, and the sector XLK lead was 0.330904 percentage points, but the EEM + XLK 257.92 exceeded 240, so XLE remains a feasible selection. The audit supports the robust current selection and confirms sampled known payouts, but it does not detect all absent events or verify the equivalence of all 16 other issuer histories or reinvestment conventions. Small errors were consistent with price rounding, but their cause is unproven. There was no discretionary cash or quarantine, and no re-test of the accepted premium was conducted.
A study of the R92002 fund's dependence on prior equity regime used daily stock prices from January 2020 to September 18, 2026. The study paired daily returns with gap openings and prior closes, scaling dollar changes. It used a regime based on the EEM fund's 20-session return, shifted one day, and excluded 20 missing regime observations. The results showed a daily correlation of 0.4347 and a gap correlation of 0.4569. The worst joint gap was -16.20 on March 16, 2020. The study found that in a weak-EEM regime, the daily correlation was 0.513, versus 0.323 in a nonnegative regime. The joint daily 1% tail was -6.53 versus -4.13. The study noted that the frequency of both downs alone misses severity. A news scan found the recent 252-day gap correlation was -0.417, which cannot establish a hedge when the full correlation is 0.457. The study made no causal claim, significance test, or independent strategy validation, and noted selection and survivorship biases, as well as regime change. The actual own closed means no measurable win rate, slippage, or empirical half Kelly. The study used a fixed one share, with no discretionary size increase.
A study used daily stock data from January 2020 to September 18, 2026, to test a trading strategy. The data was normalized and came from a source called SIP. A gap was calculated as the difference between the opening price and the previous closing price minus one. The study looked at 1686 dates and scaled the results by 67.37 and 64.63. The study found that the correlation between two sets of data was 0.45693 over the whole period, but -0.41657 over the last 252 days. The worst loss was -16.20275 on March 16, 2020. The study also found that the 1% quantile was -4.12871. The results suggest that the assumption of a stable hedge is not valid due to a structural regime change. This means that the usual estimates of potential losses are not reliable.
A study of stock market gaps used data from a repaired source, which is a website that provides stock market information. The data covered the period from September 2020 to September 18, 2026, and included 1518 observations. The study used hypothetical one-share entry dollars with weights of 67.37 and 64.63. The results showed a correlation of 0.22817876236373233 between gaps, with the worst joint gap loss being $-4.97832962124513 on April 7, 2025. The study also found that the recent negative correlation is not a reliable way to reduce risk. A previous study that included the 2020 market crash had larger losses, but this study started in September 2020 and did not include the crash, which is why the worst loss was smaller. The study did not provide information on win rate, slippage, or half Kelly, and it was recommended not to make estimates or resize the data.
The analysis is based on two premises. First, it uses the same split-normalized SIP series as the signal table, which can be found at https://runway.adityaperswal.workers.dev/data/stock-bars?timeframe=1Day&feed=sip&adjustment=all&start=2020-09-01&end=2026-09-18T23:59:59Z. Second, the 90th percentile of 1255 overlapping 60-session returns from September 20, 2021, to September 18, 2026, is 10.71796% for EEM and 20.62795% for XLE. The autocorrelation of adjacent gains is 0.97286 and 0.97481, which means the 1255 observations are not independent trials. When looking at every 60th endpoint, there are 20-21 observations per phase. The range of the 90th percentile for EEM is 7.5403-14.4586% with a median of 10.1740%, and for XLE it is 12.3929-24.9686% with a median of 19.5529%. The phases are mutually dependent and the range is not a confidence interval. From 2021 to 2023, there were 574 observations, and from 2024 to 2026, there were 681 observations. For EEM, the 90th percentile increased from 6.2663% to 12.1418%, the median increased from -2.8085% to 5.2833%, and the percentage of positive observations increased from 32.9268% to 85.7562%. For XLE, the 90th percentile decreased from 23.0071% to 17.3154%, the median decreased from 7.1487% to 2.6234%, and the percentage of positive observations increased from 63.5889% to 64.3172%. The conclusion is that the historical upside threshold is sensitive to the time period and is not a 90% probability target. There is no claim that the strategy was retested or held out, and the known regimes are descriptive. The data is constrained by survivorship and dividend completeness. A counterexample is that a sustained new regime can shift the next 60-day distribution entirely, so it is recommended to keep a mandated 5-year window and a one-share size rather than optimizing the target to a favorable phase.
The overnight diversification strategy, known as a way to reduce risk by spreading investments, failed a test of stability over a long period of time. This test was based on three main ideas: first, the difference between the previous day's close and the next day's open is used as a proxy for overnight price changes, not the actual path of prices during the night; second, some missing data for the XLE stock was fixed using information from the issuer; and third, the test compared price gaps due to stock splits with overall economic return gaps. The test used daily stock price data from January 1, 2019, to September 18, 2026, for the EEM and XLE stocks. The results showed a correlation of 0.46018 between the two stocks' price gaps over the entire period, but this correlation was much lower over the most recent period, at -0.40937. There were 28 instances of simultaneous gaps below -2% out of 1938 total gaps. In the 97 instances where EEM had one of its worst 5% gaps, XLE was also negative 68.04% of the time. The worst joint gap was on March 16, 2020, with a scaled exposure of 16.23047. These results support the idea that diversification between these two stocks may not be stable, but they do not predict what will happen in the future. The test has limitations due to the use of daily proxies and potential vendor revisions, but the conclusion is that there should not be an increase in investment size based on diversification, and it does not recommend withdrawing from the current investment strategy.
The past daily returns of EEM and XLE, adjusted for certain factors, show how their prices have spread out in the past, but this does not guarantee their future performance. According to data from https://runway.adityaperswal.workers.dev, which covers the period up to September 18, 2026, the returns of EEM and XLE have been analyzed. The analysis uses a fixed target based on five-calendar-year ending dates and 1255 overlapping 60-session gains, finding that the 90th percentile return for EEM is 10.71796349% and for XLE is 20.63484442%. Looking at the last 1260 sessions, which include five earlier observations, the 10th percentile, median, and 90th percentile returns for EEM are -8.1723%, 2.3230%, and 10.7033%, respectively, and for XLE are -6.6200%, 3.8107%, and 20.5424%, respectively. The daily correlation between EEM and XLE over 252 days is -0.159464, but over 1260 days it is 0.252817, indicating that the current low correlation may not be a reliable form of insurance against losses. The annualized daily volatility for EEM and XLE is 19.9155% and 25.6825%, respectively. However, in the event of a global liquidation, both correlations could turn positive and prices could gap through stop-loss levels. Therefore, the conclusion is to retain two distinct exposures to EEM and XLE, with a whole-share minimum sizing, and not to use diversification-based leverage or double the position.