Stats

A study on HUBB sizing used a Monte Carlo method, which is a way of using random samples to make predictions. The study looked at trade cash returns from May 2026, using data from WCC, HUBB, and SPY stocks. It used 20,000 simulated paths with 20 trades each, replacing 5, 10, and 25 percent of the account exposure at random. The results showed a loss probability of 49.5 percent, a median return of 1.09 to 5.53 percent, and a 95th percentile drawdown of 0.26 to 1.31 percent. Another simulation, called a nested bootstrap, used a different random seed and found a loss probability of 7.58 percent and a 95th percentile drawdown of 0.76 percent. This study also calculated the quarter Kelly, which is a measure of the optimal bet size, and found it to be 0.11, but this was not approved due to other factors. A daily barrier diagnostic, which checks for stop and target prices, found that the target was hit first in 2 cases, the stop was hit first in 1 case, and there was 1 ambiguous case. The study also looked at the maximum favorable excursion, which is the maximum profit that could have been made, and found it to be between 1.5 and 6.7 percent. A news scan found the headline was not available, but the data was from a source at https://runway.adityaperswal.workers.dev/data/stock-bars.

A study on WCC sizing used a Monte Carlo simulation to analyze parameter uncertainty and its effect on loss odds. The simulation was based on observed trade cash returns from 2026, sourced from https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=WCC,HUBB,SPY&timeframe=1Day&feed=sip&adjustment=all. The simulation created 20,000 paths with 20 trades each, using independent and identically distributed replacement at 5%, 10%, and 25% account exposure, with a seed of 2026090906. The results showed loss probability percentages of 32.23%, 32.74%, and 33.23% for 5%, 10%, and 25% exposure, respectively. A nested bootstrap simulation with a seed of 2026090907 was also run, resulting in a loss probability percentage of 39.50% for 10% exposure. The raw quarter Kelly was 0.0321, and the indicative USD was 27.33, but the trade was not approved due to failed confidence interval, training, entry, and venue gates. A daily barrier diagnostic was also run, with results showing that the target was first reached in 4 sessions, and the stop was first reached in 4 sessions. The maximum favorable excursion percentages were also calculated, ranging from 0.60% to 12.98%. No stop or target order was inferred from the average range.

A fund manager analyzed data and came to several conclusions. First, they looked at past results from September 2026, where LIN had a 37.5% win rate, with an average win of 2.67676% and an average loss of 2.69251%, and APD had a 42.857% win rate, with an average win of 2.14510% and an average loss of 2.20104%. Both of these had negative expected outcomes. They also used a computer program to simulate 20,000 trades with 10% account exposure and found that LIN had an 86.365% loss rate and APD had a 69.025% loss rate. The source of this data is https://runway.adityaperswal.workers.dev/data/stock-bars. However, these simulations do not account for certain factors like event clustering and 15-minute exits. The fund's past record only has two winning trades and no losses, which is not enough to estimate replacement probability or slippage. Based on this analysis, the conclusion is to have a zero allocation, not 10%. The fund's risk capacity and position capacity are 8.5099 and 212.7475, respectively, which are maximum limits, not targets.

A study analyzed helium utilization using observations from 17195 to 17220 and 17359. It referenced SEC filings from Aspiotopes. The study used assumed prior probabilities, including a triangular joint utilization rate of 0.25 to 1, with a most likely value of 0.70, and a helium price range of 300 to 900 USD per million cubic feet, with 85% of the price uncontracted and 15% contracted at a lower price of 600. The study also considered liquefied natural gas prices and annual operating costs. Using a computer program with 100,000 random draws, the study calculated potential revenue and operating results. The results showed a wide range of possible revenue and operating results, with only 11.452% of the scenarios resulting in a positive operating result. The study concluded that the frequency of different scenarios cannot be used to predict company profit or stock performance. It also noted that higher utilization rates and lower costs could significantly change the results, but the current model is not reliable for making precise predictions.

A news scan found the source https://runway.adityaperswal.workers.dev/data/stock-bars. This source used a frozen costed ten-session next-open rule in sessions 1312-1322. The numpy seed was 2026090902. The analysis included 20,000 bootstrap means and 20,000 independently and identically resampled 20-trade paths per symbol at 10% equity exposure, using 2026 completed trade returns. The same random number generator advances were used across names. The results showed that SEI had 6 trades with a 100% loss-path probability, a median account return of -18.6672%, and a 95th percentile drawdown of 23.2374%. LEU had 6 trades with a loss of 91.285%, a median return of -9.4346%, and a 95th percentile drawdown of 21.6087%. HUT had 6 trades with a loss of 18.22%, a median return of 5.2125%, and a 95th percentile drawdown of 7.2227%. OESX had 4 trades with a loss of 99.95%, a median return of -15.8911%, and a 95th percentile drawdown of 22.7591%. These estimates are conditional empirical stress estimates, not stock forecast probabilities or 15-minute stop/target odds. The independently and identically distributed assumption ignores regimes and small sample sizes, which can badly miss tails. The QuarterKelly formula, which is a method to determine the optimal bet size, was used to calculate the allocation for each symbol. The results were: HUT had a point value of 0.04950, ALM had a point value of 0.123063, and CCJ had a point value of 0.09631. However, these symbols do not qualify for allocation because their mean confidence intervals include 0, the samples are small, the universe was selected after current moves, and actual stop execution is untested. The mean confidence intervals for HUT and ALM were -7.22352% to 12.92386% and -7.82064% to 16.67254%, respectively. The premises of this analysis are that the payoff distribution must estimate future setup and exits before sizing, but these samples do not establish either. A counterexample of a genuine new structural event may improve future payoffs, but that would need prospective independent evidence. The actual sizing was enforced at 0, not point Kelly, and the 1% equity risk was 8.5099, with a position cap of 212.7475, which would also bind any future qualified order.

A recorded trade ledger, called 1302 costed 24 trade, was used instead of a bullish stock path. This analysis used a random number generator, called Numpy RNG, with a seed of 2026090900, to make 20,000 mean bootstrap draws. The analysis was done in blocks of 3 consecutive trades, with 7 block starts per path, and each path was trimmed to 20 trades, making a total of 20,000 paths. The initial cash was included in the peak. When the equity exposure was 10% per path, the probability of loss was 88.865%, the median loss was -4.502515%, and the 95th percentile drawdown was 10.590189%. When the equity exposure was 25%, the probability of loss was 89.61%, the median loss was -11.144542%, and the 95th percentile drawdown was 24.447057%. These results are based on repeated independent block starts and an unchanged payoff distribution, and do not forecast the probability of future stock losses. The average win was 16.456597% and the average loss was 7.115503%, which means the strategy is not profitable. The quarter-Kelly support is zero, which means the strategy does not have a good expected return. The data came from https://runway.adityaperswal.workers.dev/data/stock-bars. The analysis notes that small history, unseen fat tails, and price gaps can make outcomes worse. Since the base strategy did not work, no trade stop or target was invented, and no expensive 15-minute optimization was done to try to rescue it. A different, independently tested rule may work, but it would need to be preregistered and tested on new data.

A news scan found the headline about MATX conditional bootstrap and quarter-Kelly retain zero sizing. The details are as follows: a computer program used a random number generator, called Numpyseed, set to 2026090808, to analyze 20,000 random samples, called IID bootstrap means, from 13 past trades that were not used in the original analysis, called holdout costed trades. This analysis found that 95% of the time, the average return was between -1.70934% and 1.71237%. The probability of this happening by chance is 0.46153846, the average win was 0.03488118, and the average loss was 0.03056249. A formula called the Kelly criterion, which is used to determine the optimal amount to bet, was also used, but it resulted in a negative value, so it was adjusted to a quarter of the original value, called quarter-Kelly, and set to 0. This means that no trades were made. The analysis also looked at the potential losses, called equity exposure, and found that there was a 55.23% chance of losing 10% of the initial investment, with a median loss of -0.147805%, and a 95% chance of losing 2.392424%. If the investment was increased to 25%, the chance of loss increased to 55.555%, with a median loss of -0.413686%, and a 95% chance of losing 5.919851%. The data used for this analysis came from a website called https://runway.adityaperswal.workers.dev/data/stock-bars, and a fixed entry ledger analysis of 1144 trades was also used. It's worth noting that these results are based on past data and do not predict future probabilities, and that 13 trades were not included in the analysis because they were not relevant. The initial cash investment was included in the peak value, and no trades were made without a verified exit probability, so the capital was set to zero. Additionally, two historical operator wins were not included in the analysis because they did not have a verified average loss.

A computer program called a Monte Carlo simulation, which uses random samples to predict outcomes, was used with a set of rules, or strategy, for the stock CF. The simulation used 20,000 random samples of past returns to estimate the possible range of future returns, which were between -3.05764% and +0.392927%. The simulation also tested the strategy with different sets of trades, and found that the strategy would likely result in a loss, with a 97.495% probability of loss at 10% equity exposure and a 97.615% probability of loss at 25% equity exposure. Another simulation was run with a different set of random samples, which found that the strategy had a positive average return of +0.68369%, but this was due to the overall upward trend of the stock in 2026, and not because of the strategy itself. The simulation also found that the strategy would result in a loss of 22.34% if it were actually used, and that it would not be possible to size the strategy, or determine how much to invest, based on the simulation results. The data used for the simulation came from a website, and the simulation did not take into account certain factors, such as the availability of quotes or the impact of stress on the market. The simulation found that the potential loss of the strategy exceeded the allowed risk budget, even with a stop-loss order in place.

A stress test was run using a method called bootstrap, which is a way to simulate different scenarios, to see how a proposed investment allocation would perform. The test used 20,000 simulated scenarios, each with 20 trades, and assumed a 10% investment in each trade. The results showed a 99.77% chance of loss, with a median return of -2.19837% and a maximum potential loss of 3.20858% in the worst 5% of scenarios. This test is not a prediction of future performance, but rather a way to illustrate potential risks. The test did not take into account potential clusters of bad events, unexpected crashes, or changes in political regimes. As a result, the authorized investment size is 0, meaning no investment is recommended. There are also limits on the amount that can be invested, including a venue limit of 212.7475 per position, 278.67 for the fund, and 8.5099 in terms of nominal risk. A Kelly criterion, which is a way to measure the optimal size of a bet, showed a negative result, which was set to 0. No probability of winning was taken into account.

A test called empirical path stress did not help when validation failed. The test used data from a website and a computer program called numpy with a seed from September 8, 2026. It created 20,000 fake paths with 20 trades in each path, using 10% of the money for each trade, and combining the results. The test found that for the stock ATI, there was a 9.13% chance of loss, the middle return was 2.446817%, and the worst 5% of results had a drop of 1.980979%. For the stock IREN, the results were 99.755% chance of loss, middle return of -6.268158%, and the worst 5% of results had a drop of 9.879742%. This test was just a simulation, not a forecast, and did not look at the chances of hitting a stop or target in 15 minutes. The test had limitations because it only looked at a small sample of data, which might not include all possible crashes or correlated regimes. Even though some of the simulated paths for ATI were positive, they were based on a favorable sample from 2026, despite the stock doing poorly earlier. This did not change the fact that the validation failed. The test did not suggest using 10% of the money for each trade or a positive point Kelly. The actual size of the trade was zero, with a hard position of 212.7475, risk of 8.5099, and a fund ceiling of 278.67, which did not provide an edge.

A test was done on the stock BWEN using a method called resampling, which involves randomly selecting data from a set of past returns. This test used 12 past returns from a source found at https://runway.adityaperswal.workers.dev/data/stock-bars. The test ran 20,000 times, with each run involving 20 trades where 10% of the current portfolio value was invested each time. The results showed that there was a 96.985% chance of losing money, with a median loss of 7.424605%. The test also found that the biggest loss at any point was 14.427294% 95% of the time. This test is not a prediction of what will happen, but rather a way to understand what could happen based on past data. It does not take into account the fact that big changes in the market often happen together, or that unexpected events can occur. The test also does not estimate the chances of actually buying or selling a stock at a certain price, or how quickly trades can be made. The strongest argument against this test is that the stock could become profitable after it is sold, but this test cannot prove that. Because of this, the actual amount of money allowed to be invested in BWEN remains zero. This is because a measure called the quarter Kelly, which helps decide how much to invest, is not positive, and the current signal to invest is false. The fund has 278.67 in cash, and there are limits on how much can be invested, but these do not make a strong case for investing 10% of the portfolio in BWEN.

A fund manager analyzed aluminum trading using computer simulations. The manager used past trade data to predict possible future outcomes. The simulations showed that for the stock AA, the possible returns after 20 trades could be between -2.9641% and +7.6594%. The stock CENX had possible returns between -5.2178% and +7.6125%. The manager also simulated exit strategies, which are rules for when to sell a stock. The simulations used data from 22 to 26 groups of trades that started on the same day. The manager found that for AA, about 49.74% of the time, the stock would be sold because it reached a certain stop price, and for CENX, this happened about 57.03% of the time. The manager also calculated the average return of the stocks, including fees, and found that AA had an average return of -0.0762645% and CENX had an average return of -0.7722893%. Based on these results, the manager decided not to invest in the stocks, keeping the approved capital at $0, despite having $278.67 in cash. The manager used data from a website and analyzed 600 and 601 sets of data, as well as exact exit observations from two other sets of data. The manager did not assign a probability to possible future events that could affect the trade, such as tariffs or wars, and decided to preserve cash.

The automated trading fund manager analyzed antimony scenarios. Here are the results: 1. The manager resampled corrected net-equity returns from 35 stressed historical trades into 10,000 independent and identically distributed paths of 20 trades at a hypothetical 10% capital allocation, using seed 90407. The end-return 5/50/95 percentiles were -7.0841%, +0.1911%, and +8.6712%. The loss frequency was 48.38%, and the 95th-percentile trade-mark drawdown was 8.7577%. These are model-conditioned frequencies, not future win probabilities, and are optimistic due to missing regime shifts, dependency, and between-exit drawdowns. A four-trade block mean interval of [-3.9867, 4.7908]% reinforces uncertainty, according to data from https://runway.adityaperswal.workers.dev/data/stock-bars. 2. A separate economic grid was created with no assigned probabilities. The DLA implied price was 31.7073/lb from accepted 82k/$2.6m, with assumed all-in costs of 13.34, 20, and 28/lb. The accepted 82k yields were 1.50612/0.960/0.304m, while hypothetical yields of 163k and 289k were 2.99387/1.90829/0.60429m and 5.30815/3.38341/1.07141m, respectively. The highest volume includes shipments not yet accepted as of August 11 and some discussed for Q4, so it is not a Q3 forecast. Even the best-illustrated 289k case leaves a deficit of 1.69185m at a fixed existing 7m quarterly operating deficit, although other growth and cost changes could alter this. The cost of 13.34 is a commercial proxy, not a measured military-ingot cost, and the same price is used across cohorts. This information is based on data from https://www.sec.gov/Archives/edgar/data/101538/000110465926094035/uamy-20260630x10q.htm and https://www.sec.gov/Archives/edgar/data/101538/000110465926097708/tm2622899d2_ex99-1.htm. 3. The hard limits are equity 850.99, position 212.7475, fund 278.67, and risk 8.5099. The point quarter Kelly is 0.6842% capital base and 0.2811% stress, assuming a calibrated historical distribution. Lower mean bounds are negative, and train fails and entry false result in approved 0. Two actual operator liquidations have no loss sample, and no Monte Carlo result repairs those gaps. No stop or target order is proposed.

A news scan found a script note that analyzed vessel delays. The script used a hypothetical mixture of 43.6% late arrivals, with a conditional Gamma mean of 6.06 days and different shapes. The results showed that the average vessel delay cannot be used to price storage or a stock trade. For example, the average cost of 40ft storage at 50 USD/day after 14 days ranged from 0.79 to 28.18 USD. Maersk's Option A tariff gives a mechanical 21-day 40ft storage cost of 350 USD and a 30-day cost of 800 USD. A critical assumption is that vessel lateness is not the same as container storage duration. The analysis also found that the mean cannot identify the tail or pricing rent. Maersk's published annual freight sensitivity maps assumed a uniform effect, but this is not forecastable due to seasonal volumes and coverage. An existing stock-path Monte Carlo analysis was rejected due to a 51.51% conditional profit frequency that does not justify sizing. The sources of this information include Sea-Intelligence and Maersk's press room and news articles from August 2026.

A news scan found the text describing a Monte Carlo simulation. The simulation used a Numpy seed of 9060600. It looked at how a joint portfolio of daily returns from six sectors changed over time, using 20,000 possible paths and 20 sessions, with the data split into training and holdout sets. The simulation put fractions of 0, 0.25, 0.5, and 1 of $278.67 into a strategy with equal parts, with the rest, $850.99, kept as cash in the account. The model did not require whole shares, specific trading venues, or fixed weights after considering historical drift. The baseline results showed a profit frequency of 51.51%, a median profit and loss of $0.2704, and a 5th percentile of -$10.5123 and a 95th percentile of $11.8105. There was a 23.875% chance of the account losing more than 1%. The simulation also looked at how sensitive the results were to 10 and 20 session blocks, with profit frequencies of 51.65% and 53.97%, and median profits of $0.2704 and $0.6030. These results are based on resampling frequencies and do not predict future probabilities or monthly funding. The simulation also looked at trend and low volatility scenarios, with profit frequencies of 37.10% and 34.95%, and negative median profits of -$1.4186 and -$0.8456. Another part of the simulation, called exit-odds bootstrap, drew whole entry-week groups 10,000 times, with results of 40.9699% for the target, 53.5117% for the stop, and 5.5184% for the time. The simulation used a quarter Kelly capital formula, which resulted in an allowable size of 0. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and the fund trade source query is query_trades fund=supply IDs 3, 6.

A study examined how changes in helium prices affect distributor profits. It was based on three premises: first, contract shares disclose volume, not realized prices; second, the baseline unit price is 90% contract and 10% spot, with helium revenue at 100 and cost at 65, and all costs are variable; third, certain assumptions about contract repricing, spot price changes, volume retention, and cost inflation were made, but these are not estimates of likelihood. The study used Python to run 192 grid combinations and 100,000 numpy seed draws from September 6, 2026. If contracts and volume remain unchanged, doubling the spot price would result in revenue of 110, and cost inflation of 0, 10, 20, or 40% would result in profits of 45, 38.5, 32, and 19, respectively, compared to a base profit of 35. A 15.3846% unit cost inflation would erase the profit increase. Assuming an 8% helium revenue share for the APD group, this would translate to only a 0.8% group sales uplift before considering costs, mix, and volume. The study found that the 5, 50, and 95 quantiles for profit change are -61.17, -21.31, and +22.20%, respectively. Additionally, 22.199% of draws exceed the base profit, and 6.924% of draws have a profit increase but a margin percentage decrease. These results are based on model geometry and do not represent a 22.199% chance of winning or a forecast. The study notes that fixed costs, working capital, capex, correlations, and repricing clauses could worsen or improve outcomes, and that the Kelly criterion cannot be assigned based on assumed uniform distributions. The valid inference is that the delivered price-cost spread and volume are needed, not just the spot price. The source contract anchor is https://investors.airproducts.com/static-files/1c55c69d-3196-4a46-b646-fd85adeec0f2, and the original model note is 295, observations 5437-5438. The study concludes that no equity-price simulation is justified without an empirical payoff distribution.

A Conditional Monte Carlo simulation, which is a method to estimate the outcome of a process, demonstrated a failure in selected-winner sizing. The simulation used 10,000 independent and identically distributed paths, with 10 trades each, and reinvested 10% of the current capital per trade. It sampled each diagnostic's 3-7 natural returns, but this was not a calendar-time or venue-stop simulation. For example, Maersk terminal returns were 5/50/95 percentiles of -2.259, 2.423, and 7.410 percent, with a loss of 20.38 percent and a drawdown of 95 percent at 3.637 percent. COHU returns were -1.410, 10.877, and 27.477 percent, with a loss of 7.65 percent and a drawdown of 95 percent at 5.466 percent. The AXT selected extreme produced a median return of 11430.9 percent and a 95th percentile return of 1180856.7 percent, which is an implausible investment forecast driven by resampling one huge winner, with no independent tail model. The simulation used plug-in quarter Kelly fractions of 0.475-1.754 across names, but authorized 0 for all, as every mean confidence interval spans zero and the execution model is incomplete. Positions were capped at 212.7475 USD, with a nominal risk of 8.5099 USD, and a fund value of 278.67 USD, but these caps cannot create an edge. Resampled long trend win sizes cannot justify 1-2 ADR swing targets. The results and every measured figure were recorded from May 25 to May 28, and the scripts and trades were archived. The sources of the data are https://runway.adityaperswal.workers.dev/data/stock-bars and https://query1.finance.yahoo.com/v8/finance/chart/.

A trading system using fixed diagnostics and natural payoffs produced 10,000 independent and identically distributed paths, each with 5 trades, reinvesting 10% of changing capital per trade. The results showed terminal percentiles of -2.2383%, 11.7462%, and 28.4979%, a loss frequency of 8.11%, and a 95% trade-step drawdown of 3.1173%. This is an illustration only, without considering calendar holding windows, barrier-touch models, clustered regimes, or unknown tails. A Quarter Kelly plugin estimated a capital fraction of 1.56943, but this is deemed too large and unreliable. As a result, the authorized fraction is 0, due to estimation risk and incomplete exit models. The position cap is $212.7475 and the nominal risk budget is $8.5099, but these do not establish a trading edge. The Generalized Extreme Value (GEV) function, a statistical tool to model extreme events, shows that only 0 whole shares can be traded under the cap, and only fractional exits are allowed during regular sessions. A 10% fund allocation of $27.867 would also require fractional shares. This information comes from a data source at https://runway.adityaperswal.workers.dev/data/stock-bars, with archive numbers 2958-2997, and an audit script called audit.py. No trading order is placed.

A trading fund manager used a computer program to test different trading paths. The program created 10,000 circular paths, each with 19 trades of TSN, PPC, and JBS stocks, and allocated 10% of the changing capital to each trade. The results showed that the TSN stock had a range of -2.530 to 0.220, the PPC stock had a range of -2.709 to 1.100, and the JBS stock had a range of -0.642 to 2.056. The program also calculated the maximum loss, or drawdown, which was 2.627% for TSN, 3.038% for PPC, and 1.144% for JBS. These results are based on historical data and do not predict future events or actual trading outcomes. The initial capital was $278.67, but it was not enough to buy whole shares of TSN or PPC stocks. A test using a quarter of the Kelly capital fraction for TSN and PPC, and 1.665 for JBS, showed that the results were not stable. The JBS stock's mean confidence interval crossed zero, and there was no training data. All authorized trades had a notional value of $0. The program did not account for gaps in the data, 15-minute checks, liquidity, or corporate actions. The data came from https://runway.adityaperswal.workers.dev/data/stock-bars and was tested using the test.py program on dates 1724, 1727, and 1730. Note that the results should not be used to predict political or policy outcomes.

A trading fund manager used a computer program to test different trading strategies. The program, which used a mathematical technique called NumPy to generate 10,000 possible paths, or scenarios, with a seed value of 905, found that a circular strategy with 3-trade blocks, using 10% of changing equity per trade, resulted in different outcomes for each symbol. The natural exit count, or the number of times a trade was stopped, was 40, 39, 29, 38, 34, and 32 for each symbol. The program also modeled costs and found that the compounded results were: PSIX with 29 trades had a terminal value with a 5th percentile of +2.827%, a median of +11.277%, and a 95th percentile of +20.801%, with a loss frequency of 1.21% and a 95th percentile trade-step drawdown of 3.869%; POWL with 34 trades had a range of -2.060% to +7.829%, with a loss of 18.22%; AXTI with 40 trades had a range of -8.948% to +9.197%, with a loss of 52.57%; AEHR with 39 trades had a loss of 53.15%; and ETN with 32 trades had a loss of 93.78%. These results are based on empirical resampling frequencies, which means they are based on actual data, and do not take into account the probability of future trades or the dependence between different assets. The Quarter-Kelly capital plugin, a mathematical formula used to calculate optimal bet size, resulted in values of 181.55% for PSIX, 101.28% for POWL, 45.53% for VSH, and negative values for AXTI, AEHR, and ETN. However, the plugin's results are unstable and can produce absurd values. The trading strategy is also limited by a 25% cap on venue, but the eligibility criteria bind first, meaning that there are no positive signals, and PSIX has no training data. The actual risk is 0, and the reference ADR, or average daily range, is used to calculate the nominal notional risk ceilings, which are 73.45 for AXTI, 79.83 for AEHR, 212.77 for PSIX, 198.19 for VSH, 212.77 for POWL, and 212.77 for ETN. The start cash is 278.67, and the goal is to achieve repeatable net returns with an independent implementable edge. The data source is https://runway.adityaperswal.workers.dev/data/stock-bars, which provides exact statistics for all six archive stocks. A monthly shortfall of 348.92 does not alter the model.

A Numpy simulation was used to test trading strategies. The simulation used real data from 36 out of 37 tests, with 10,000 different paths, each with 3 trades, and a seed of 501. It marked each outcome and added or subtracted 10% of the changing equity per trade. The simulation did not use fictional Gaussian drift. The results for FRO showed a terminal return of -2.729% at the 5th percentile, 2.062% at the median, and 7.332% at the 95th percentile, with 24.17% of trades losing money, and a 95th percentile trade-step drawdown of 4.478%. For STNG, the results were -2.168%, 1.400%, and 5.000%, with 25.74% of trades losing money, and a 95th percentile trade-step drawdown of 3.592%. This simulation is hypothetical and does not forecast actual results, as it does not take into account downtime, intratrade paths, new gaps, and regime changes. A binary mean-payoff quarter-Kelly capital heuristic was used, which gave 81.88% for FRO and 66.75% for STNG. However, neither of these results justifies investing capital, especially since the venue cap is 25%. The lower confidence mean is negative, so the authorized size is 0. Even with a hypothetical 10% account allocation of $85.108, the median compounded gains are too small and uncertain to justify trying to make up a monthly shortfall of $348.92. The premises of the simulation are that the sampled history is the best available diagnostic, the sampled mean uncertainty spans 0, and the model lacks implementation fidelity. The conclusion is that there is no valid proposal under the required robust edge, but this does not prove that losses are inevitable. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and this is a research simulation, not an actual executed portfolio.