Stats

A news scan found the text: Python numpy seed 20260908 following backtests, which means a computer program used a specific starting point for random number generation on September 8, 2026, to analyze past trades. The program used 836 daily high, low, open, and close price vectors, or sets of numbers, for the stock EGTX, which were normalized, or adjusted, to the prior day's close price. It then randomly resampled, or reorganized, these sets of numbers into 10 sessions out of 100,000 possible paths, using data from the website https://query1.finance.yahoo.com/v8/finance/chart/EGTX.ST. The simulation started with a stock price of 7.70, stopped trading at 7.34429, and had a target price of 8.23357, with specific rules for when to stop trading or take profits. The simulation included fees of 10 basis points, or 0.1%, and a potential loss of 25 basis points, or 0.25%, per trade. The results showed a mean return of -1.21410%, a win rate of 37.666%, and a 5% loss rate of -5.69831%, with 62.245% of trades stopped and 37.570% reaching the target price. These results are based on historical volatility, or price fluctuations, and do not represent actual probabilities of future events. The simulation also assumed a potential loss of 49.14% for the fund, with a 30% gap of 14.742 and a 50% gap of 24.57, both of which exceeded the risk cap of 8.5099. The full loss bound was 8.5099, and the binding edge failed, so the adopted notional, or potential loss, was 0, regardless of stress capacity, and no estimated regulatory win probability was determined.

The QLV90802 automated trading fund manager used a Monte Carlo simulation and quarter-Kelly method to analyze four swing allocations, but all of them remain at zero. The simulation used 20,000 independent and identically distributed paths, resampling 12 out of 60 historical monthly cohorts, including cash months, for a managed 10-session swing. Each active cohort was allocated 25% of the account equity, starting with $850.99, and costs were included in the backtested returns, but overhead was excluded. The results showed that the SPLV had a 12-month profit and loss range of -16.01794 to 3.58745 USD, with a loss frequency of 84.3%, while the USMV had a range of -15.79918 to 3.46558, with a loss frequency of 84.38%. The EFAV had a range of -13.29565 to 3.25648, with a loss frequency of 83.79%, and the EEMV had a range of -11.40686 to 5.53836, with a loss frequency of 69.21%. These results are based on empirical resampling frequencies, not forecast probabilities or 24-day projections. The holdout period showed that the managed SPLV had a profit of 50%, a win rate of 52.9017%, and a win-to-loss ratio of 1.197975%, while the USMV had a profit of 45.4545%, a win rate of 59.0174%, and a win-to-loss ratio of 1.088297%. The quarter-Kelly method calculated a maximum allocation of 0 for all assets. The EEMV had a positive return of 71.4286% and a win rate of 96.7954%, but the naive fraction was 4.233%, which was not used due to failed training and holdout requirements. The account had a hurdle rate of 41.01223% of $850.99, requiring a uniform daily growth rate of 1.442287% to reach the target. The current capacity of 2 shares of ETFs permits arithmetic calculations, but not allocation. The conclusion is that all actual sizes are zero, and the 12-month simulation should not be scaled into a month-end income pledge.

The manager of an automated trading fund made some notes about how they decide when to exit from option trades. They started with three main points: first, the risk of losing the full premium must be limited to 8.5099; second, the target price for the trade must be reachable; and third, simulated results depend on the assumptions made and are not based on real-world experience. They used a computer program to test 240,000 different paths for option trades, with a hypothetical entry on Tuesday, September 8, based on the spot price from Friday, September 4. They used a formula called Daily GBM to estimate the future price, and they checked the results over the next few business days. They also used a formula called European BS to calculate the exit price, taking into account the quoted volatility, interest rate, and time remaining. The manager noted that the volatility used for entry and exit can be different from the actual physical volatility. They set a stop-loss at half of the ask price, with a minimum of 0.01, and used a diagnostic target to calculate the potential profit or loss. The results showed that the profit or loss for four different trades were -3.3336 USD, -0.0452, +1.3894, and +0.2980. However, if the physical volatility was lower, at 0.8, all of the results would be negative. The manager also noted that the results depend on the daily overshoot, and that capping the profit at the planned target would result in all negative means. They emphasized that this does not mean that the actual orders would be capped, but rather that the expected return should not be based on rare and unmodeled overshoots. The manager also provided some sources for the data used in the analysis, including option chain data for PATH and RIOT, and stock bar data.

A news scan found the headline 'PLAY generic four-session bootstrap has negative net mean and cannot calibrate catalyst gaps'. This refers to a problem with a trading model for the stock PLAY. The model used 100,000 paths of 4 daily price vectors from 1004 training days in 2021-24. It got this data from Yahoo. The model kept the price vectors from within each day, but changed the order of the days to avoid patterns. It started with a price of 8.72 and used a stop loss of 8.19 and a target price of 9.51. The model also included fees of 5 basis points and a slip of 10 basis points per trade. The results showed a net mean loss of -0.061527%, with 46.983% of trades winning. The model had a stop loss 29.830% of the time and reached its target 17.638% of the time. It took an average of 52.532% of the time to complete a trade. The model's assumptions were that costs and the path of the stock price matter, and that using a random sample of days does not accurately estimate the payoff. The conclusion was to allocate zero funds to this model and not use the Kelly criterion. The model also found that no single trade lost more than 8.5099 in the sample, but this does not prove that there is no risk of a large loss. If the stock price were to gap down by 30% on 5 shares with a price of 8.72, the loss would be 13.08, and the total notional loss would be 49.14, which is more than the risk. The probability of a gap was not estimated. A strong case could be made for using a different model that takes into account specific events, but the uncertainty of these events and the negative results from the training data already reject this model.

A computer program used a method called NumPy to analyze possible risks in investments. It looked at 20,000 different paths that investments in certain cryptocurrencies, including BTC, ETH, SOL, LTC, LINK, UNI, and XRP, could take from January 2 to September 7, 2026. The program did not use a type of prediction called Gaussian extrapolation and kept the order of events within each block of time. It assumed a fixed position of $212.7475 and did not account for fees or the ability to enter or exit the market during the day. The program found that if the investments lost 1% of their value at the end of the period, the losses would be $25.04 for BTC, $39.35 for ETH, $32.39 for SOL, $25.74 for LTC, $32.66 for LINK, $31.44 for UNI, and $25.41 for XRP. It also found that the expected shortfall, which is a measure of the potential loss, would be $32.01 for BTC and $42.84 for ETH. The program calculated the probability of daily losses exceeding $8.50 and found it to be 15.21% for BTC, 22.73% for ETH, 28.705% for SOL, and 33.725% for UNI. The program also calculated the potential loss at the 99% confidence level, known as the Value at Risk or VaR, which was $72.29 for BTC, $46.01 for ETH, $55.90 for SOL, and $57.58 for UNI. However, these values are only illustrative and not approved for use in actual trades. The program's results are based on three assumptions: that the venue cap is not the same as the risk tolerance, that daily close paths do not capture the full range of possible losses, and that the historical data used is limited. The conclusion is that the actual size of the investment should be zero unless there is a positive independent edge, which requires a quarter Kelly criterion and a planned risk cap with a 15-minute exit latency. One potential counterargument is that using stops could reduce losses, but gaps and latency may defeat this strategy. The program's results are based on data from https://runway.adityaperswal.workers.dev/data/crypto-bars and code from simulate.py and simulation.json. No approval has been given for using the VaR values to size trades.

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.

The QTM90800 automated trading fund manager used a method called Monte Carlo to test investment strategies. This method uses random sampling to predict possible outcomes. The manager tested 20,000 different paths, or possible market scenarios, using historical data from the last 12 months. The test assumed that 25% of the account equity would be used for each investment, starting with $850.99. The results are hypothetical and do not recommend actual investment allocations. For the SPY investment, the potential profit or loss was calculated to be between -$20.89 and $12.05, with a 68.97% chance of loss. For the EEM investment, the potential profit or loss was between -$13.74 and $26.39, with a 30.34% chance of loss. These results do not include additional costs or changes in market conditions. The manager also tested a single investment in SPY and EEM, with results ranging from -$4.19 to $4.74 for SPY and -$4.61 to $5.48 for EEM. The next exit from the investment is planned for October 5 or 6, but this is not guaranteed. The manager calculated the performance of the investments, with SPY showing a 47.46% profit and EEM showing a 59.32% profit. However, the actual profit was zero due to failed training and other factors. The manager also observed that the investments resulted in 28 stops, 8 targets, and 7 breakevens for SPY, and 21 stops, 21 targets, and 3 breakevens for EEM. The data used for these tests came from the website https://runway.adityaperswal.workers.dev/data/stock-bars, with observations from dates 9811, 9813, 9814, and 9815. A term called 'quarter Kelly' refers to a measure of investment performance. 'PDT' refers to a rule about pattern day trading. 'Whole-share rounding' refers to the practice of buying or selling whole shares of stock, rather than fractions of a share. '15min fills' refers to the time it takes to complete a trade, in this case 15 minutes.

A news scan found the headline 'SCHL generic five-session OHLC bootstrap fails after costs'. A test was done using 100,000 paths, each with 5 sessions, and 1004 daily Open, High, Low, Close (OHLC) vectors from 2021 to 2024. The test started with a hypothetical $35.7 and used a stop-loss at $34.77 and a target at $37.09. The daily vectors were resampled to keep the relationships between the Open, High, Low, and Close prices, but this destroyed the patterns over time. The test stopped when both the stop-loss and target were touched, and it accounted for fees of 5 basis points and slippage of 10 basis points on each side. The results showed a net mean loss of -0.151681%, with 47.848% of trades winning, 42.670% stopped, and 34.503% reaching the target, taking 22.827% of the time. The worst 5% of trades lost 3.41830%, and the best 5% gained 3.57985%. This test was done in a generic risk context, not based on earnings forecasts or independent event observations. No trade lost more than 8.5099% in the sample, but this does not prove that there is no risk of bigger losses. If there was a 30% gap, the loss would be 10.71% before costs, but the probability of this happening was not estimated. The test assumed that costs and barriers, as well as rare events, matter. The conclusion was that there is no edge that can be used to allocate funds. The test also found that using a different approach, such as conditioning on specific events, could improve the expected return, but this would need actual, dated, independent data. The test did not use the Kelly criterion, which is a way to size bets, and instead used a size of 0. It also did not add a claim about filling orders in 15 minutes to the daily OHLC model.

A computer program used a method called NumPy to create 10,000 possible scenarios for four assets: BTC, ETH, SOL, and LTC, from September 8 to September 15. The program looked at the daily prices of these assets and simulated buying and selling them based on certain rules. The rules were to start buying when the price closed at a certain level, stop buying when the price went 20% below that level, and aim for a target price 20% above that level. The program also charged a fee of 0.25% and accounted for a 0.10% difference between the expected and actual prices. The results showed that the average profit was 0.8935% for BTC, 2.3668% for ETH, 2.9084% for SOL, and 1.3412% for LTC. However, in 5% of the scenarios, the losses were greater than the expected stop loss. The program also calculated the prices at which to stop buying and aim for the target for each asset: for BTC, the stop price was $76,167.40 and the target price was $84,955.62; for ETH, the stop price was $2,368.03 and the target price was $2,735.32; for SOL, the stop price was $97.0262 and the target price was $117.3761; for LTC, the stop price was $52.3305 and the target price was $60.9550. These prices are not actual orders to buy or sell. The program also calculated the maximum amount of money that could be risked for each asset, but the actual allocation was zero because the program did not find any edge, or advantage, in the market. The data used for this simulation came from the website https://runway.adityaperswal.workers.dev/data/crypto-bars, and the program used a script called stats_daily.py to analyze the data from observations 9492 to 9495. The program assumed a fee of 0.25% for each transaction, which is lower than the actual fee for LTC, which is 1.1145%. The program concluded that the targets of one to two average daily ranges are measured scales, not promised payoffs.

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's analysis, called QIM90708, used a method called Monte Carlo to test investment sizes and 24-day scenarios with no investment, or zero exposure. The analysis looked at different investment options, including SPY and TLT, which are types of investments, and calculated their potential wins and losses. For SPY, the average win was 0.147373% and the average loss was 0.270744%. For TLT, the average win was 0.126794% and the average loss was 0.194806%. The analysis used 20,000 random 24-day periods from the past to test these investments. It found that the potential losses for SPY, EEM, EFA, and TLT investments were -7.2522%, -5.6375%, -5.6374%, and -4.5511%, respectively. The analysis also found that the frequency of losses was high, at 97.66% to 99.855%. The results showed that there were no gains in the sampled periods. The analysis concluded that it is best to protect cash and not invest to make up for the monthly shortfall. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and the analysis used a seed of 90708 and a statistics program called stats.py.

A five-session simulation of ROIV, using 100,000 paths sampled from 752 daily returns from 2022 to 2024, was conducted with a Numpy seed of 9070800. The mean gross endpoint return was +0.46984%, with a 5th percentile of -12.52714% and a 95th percentile of +14.86795%, and a loss of 49.822%. These results represent generic daily risk, not forecasts of clinical outcomes. The simulation used a descriptive sensitivity analysis with an ATR of 1.1575 and a price of 34.945 to set a stop loss at 3.312% and a target at 4.969%. The simulation also included daily endpoint checks, with a stop loss and target cap, and a fee of 5 basis points and a slip of 10 basis points on each side. The base net mean return was -1.02070%, with a win rate of 45.992%, a stop loss rate of 44.685%, and a target rate of 33.972%, with an average time of 21.343%. The one-share 5th percentile loss was $3.272. The simulation also assumed extra gap probabilities of 1%, 5%, and 10% on the first day, which produced mean returns of -1.29903%, -2.49798%, and -3.96143%, respectively, with one-share loss odds of 9.424%, 4.949%, and 9.894%, respectively. The results showed zero exceedances in the zero added-gap scenario, but this is a finite empirical model result and does not represent zero real tail risk. The overlay probabilities were not estimated, and the IID assumption destroys clustering, while daily checks miss 15-minute and extra-hours paths, and the historical pool already contains news, which may double-count added gaps. The positive unconstrained endpoint mean does not validate a profit-taking strategy. In conclusion, the simulation size was 0, and neither the Monte Carlo simulation of 100,000 nor a generic 3-win holdout supplies independent clinical edge or calibrated Kelly. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and the scripts roiv.py and simulation.py are archived. The model will be frozen prospectively rather than retuning barriers.

A simulation of the QR290706 sizing and exit strategy found weak historical gains that cannot fund the shortfall. The simulation used the SPY stock, which is a type of stock that tracks the S&P 500 index, a measure of the US stock market. The results showed an average win of 1.197682% and an average loss of 0.879921%, which is a type of risk measurement. This implies a raw quarter-Kelly value of 0.605964% of equity, which is a way to measure the performance of an investment, and is approximately $5.16. However, the training Kelly value was 0, which means no allocation was made due to negative cost stress, a type of financial risk. The actual size was 0.2. The simulation ran 2,000 times over 60 months, with a hypothetical 25% account allocation per trade from $850.99. The results showed a terminal profit and loss of $-27.1884, $4.2175, and $35.0681, with 41.515% of the paths resulting in a loss. The 95th percentile monthly realized maximum drawdown, which is a measure of the largest loss, was 4.19024%. Separate 24-calendar-day realized cash flow windows produced a profit and loss of $-3.90996, $0, and $3.31432, with 21.82% of the windows resulting in a loss. The simulation also found 19 targets, 38 stops, and 7 RSI, which is a technical indicator used to measure stock performance, exits. The target frequency was 29.6875%, and the Wilson 95% confidence interval, which is a way to measure the reliability of the results, was [19.9050, 41.7704]. The simulation concluded that cash is the best option, and that no wider targets or risk increase should be made to address shutdown pressure. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and the simulation was run using stats.py and recorded simulation figures.

A news scan found the headline about a GIS four-session Monte Carlo simulation. The simulation used 100,000 four-session paths from 857 valid training daily returns from 2020 to 2023, excluding zero or missing adjacent prints. The latest Average True Range, a measure of price volatility, and price defined daily endpoint stops at -3.0163% and a target at +4.5245%. The simulation checked the stop and target first, stopped at the breached endpoint or target capped, or else used the fourth endpoint. A cost factor of 0.999 * 0.9995 / (1.001 * 1.0005) was applied. The base mean return was -0.225076%, with a win rate of 47.193% and a target first rate of 4.568%. The stop first rate was 11.943% and the average time was 83.489%. On a fund notional mean of -$0.11060, the 5th percentile was -$2.05044. An independent assumed 20% negative gap at the first endpoint with a 1/5/10% window hazard resulted in mean returns of -0.416103%, -1.219721%, and -2.190210%. The probability of a loss greater than $8.5099 was 9.801% at full fund. A 0/25/50/100% fund sizing grid was recorded from 8524 to 8527, with 0% size resulting in no dollar loss. The simulation did not forecast dated events, as the pool contains all training days and historical news. A calendar holdout with a probability of 0.6, average win of 0.02035497, and average loss of 0.02779982 resulted in a quarter binary Kelly notion of 0.482913. The risk-unit formula was 0.0134249, which is a different unit and not a notional fraction. The understressed costs notional quarter Kelly was -0.856486, which was clipped to 0. No Kelly estimate was adopted due to the confidence interval crossing 0 and cost stress being negative. The actual size was 0. The source of the data is https://runway.adityaperswal.workers.dev/data/stock-bars, and the code is research/analyze.py, with observations from 8521 to 8527.

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.

A news scan found the headline 'Trade-bootstrap uncertainty does not rescue failed selected rules'. The text that follows is a direct translation of the original notes. Premises were made based on raw selected holdout trades from February 7, 2013, and hourly data from November 23, 2019, to November 9, 2021, with 109.2 independent and identically distributed, or IID, trades. A trade bootstrap, which is a method of estimating the variability of a statistic, was run 10,000 times with a seed of 90607. The results showed that the mean trade confidence interval, or CI, was between -6.616 and -2.326 percent for daily Bitcoin, or BTC, trades, between -5.083 and 6.768 percent for daily Ethereum, or ETH, trades, and between -5.466 and 5.021 percent for daily Solana, or SOL, trades. For hourly trades, the mean trade CI was between -0.848 and -0.376 percent for BTC, between -1.100 and -0.041 percent for ETH, and between -1.112 and 0.257 percent for SOL. A hypothetical 25 percent equity fraction over a resampled trade count yielded a loss probability of 60.36 percent for daily trades and 98.36 percent for hourly trades. These probabilities are based on observed trades and take into account missed serial regimes, model selection, and disputed execution opens. The daily BTC bootstrap narrow interval does not imply high confidence across the population. The conclusion is that the measured selected quarter Kelly, which is a measure of the fraction of the bankroll to bet, is 0, and there is no evidence for fund allocation. The strongest counterargument is that rare large winning trends could dominate, but small samples cannot estimate their frequency, and the hourly cost drain persists. Sensitivity daily positives similarly are not independent validation. All quantiles and probabilities were recorded as observations. The source of this information is https://runway.adityaperswal.workers.dev/data/crypto-bars.

A trading fund manager used 2160 consecutive hourly log returns from June 9, 2006, to September 7, 2005, UTC, to test a strategy. The test used 10000 paths with a 72-hour seed of 90608.2. The strategy would exit at the first hourly endpoint if it was less than or equal to -1 ADR or greater than or equal to 1.5 ADR, otherwise it would exit after 72 hours. ADR, or average daily range, is a measure of how much a price moves in a day. The ADR for BTC was 3.1492%, for ETH it was 3.8647%, and for SOL it was 5.8714%. The corresponding targets were 4.7239%, 5.7970%, and 8.8071%. The test assumed a baseline fee of 25 basis points, which is a unit of measurement for interest rates and fees, and a 5 basis point lip, which is a small additional fee, on each side. The test preserved the drift, which is the change in price over time, and simulated a mean return of +0.529%, +0.4605%, and +0.8165%. The test was not conditioned on any signal or event. Removing the sample hourly log drift of 1.0681, 1.8273, and 2.0757 basis points and doubling the cost resulted in a mean return of -1.1927%, -1.1830%, and -1.1521%. The test also calculated the target, stop, and neither, which are levels at which the strategy would exit, and found that 57.54%, 52.38%, and 73.08% of the time, the strategy would not reach the target or stop. The simulated 1% tail returns, which are the returns at the extreme ends of the distribution, were -6.7882%, -7.9545%, and -8.9069%, implying a hypothetical notional, which is the total value of the trade, of 125.36, 106.98, and 95.54 to put 8.5099 USD at that quantile, which is a measure of the distribution of returns. However, this is not the actual approved size. The nominal stop sizing, which is the size of the trade at the stop level, was 212.75, 190.61, and 131.50, and had a 9.84%, 21.44%, and 11.63% simulated chance of loss greater than 1% equity under the baseline hourly overshoot. The conclusion is that the sizing is 0 because the strategy holdouts fail, and the quantiles are conditional scenarios, not hard limits. A counterexample is that true positive drift may persist, but it cannot be inferred from selecting the recent 90 days. The data used for this test came from https://runway.adityaperswal.workers.dev/data/crypto-bars and https://docs.alpaca.markets/us/docs/crypto-fees.

A news scan found the text describing an analysis of forecast uncertainty. The analysis is based on 50,000 dependent bootstrap paths. The goal is to quantify forecast uncertainty, but option sizing remains at zero. The analysis uses a Monte Carlo resampling method, which is a way of simulating different scenarios to understand uncertainty, and not a risk-neutral method or an option exit simulation. The method uses a circular block bootstrap resampling technique, which is a way of re-sampling data, with 83 non-overlapping session holdout windows across 7 ETFs. Each path computes the mean loss difference, the ratio of realized variance to predicted variance, and the equal asset mean. The results show a pooled difference of -0.0272720856, with a 95% interval of [-0.084595064, 0.028682371]. The analysis also shows that the variance ratio for GLD is [1.432672, 2.802439] and for IBIT is [0.471998, 0.800341], indicating that model error overwhelms simulation noise. The quarter Kelly formula, which is a method for determining the optimal bet size, is max(0, 0.25 * (p - (1-p) / (W/L))), but it cannot be computed because there are no empirical option outcomes. The analysis does not claim any option return, drawdown, win rate, or exit odds. The data comes from venue-adjusted stock bars and was saved successfully after splitting oversized journal batches.

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 numerical pricing cross-check was done to see if it would recover cash-dividend European parity. This means checking if the numbers make sense when looking at the price of a stock with dividends. The check used 500,000 paths, which are like different possible outcomes, and independent standard normal draws, which are like random numbers, before and after an event. The numbers used were: stock price $46.15, interest rate 0.04, volatility 0.4081799262, time to expiration 14/365, and dividend $2.61. The pre-event stock price was calculated using the formula Spre = Sexp((r-0.5sig²)td + sig sqrt(td)Z1), where sig is volatility and Z1 is a random number. The post-event stock price was the maximum of the pre-event stock price minus the dividend, or 0. The final stock price was calculated using another formula. The payoffs were discounted, which means they were adjusted for the time value of money, and the maximum of the final stock price minus the strike price, or 0, was taken. The results showed that the European call option price was $0.603604336 and the put option price was $2.992489208. The difference between the call and put option prices was -2.388884872, which is close to the analytical value of -2.385554805. This means that the dividend mechanism is working correctly. The American call option price was $1.565900, which includes the privilege of early exercise, and does not need to match the European option price. The put option prices for different strike prices were also calculated. The risk-neutral in-the-money frequencies, which are like the probabilities of the option being in the money, were calculated, but these are not the same as the actual win rates. The model used is a Gaussian model, which assumes that the stock prices follow a normal distribution, and does not take into account things like geopolitical jumps, stochastic volatility, and spread changes. The conclusion is that the arithmetic and model cross-check support the dividend mechanism, but the simulation cannot establish a profitable strategy. No exit odds or actual option backtest were claimed. The sources used were frozen on September 4 and include stock bars from https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=FRO&timeframe=1Day&feed=iex&adjustment=all, issuer D from https://ml-eu.globenewswire.com/Resource/Download/59431810-8e9c-4a39-b3d0-cc2dd63da402, and scripts research_fro/mc.py and verify.py.

A simulation was run to test the effectiveness of a trading strategy. The strategy's past trades had a win rate of 37.9310%, an average win of 2.59139%, and an average loss of 1.60982%. The simulation used 20,000 blocks of six months over 68 months, with no trading in inactive months. It assumed a 25% deployment of equity, starting with $850.99. The results showed a range of possible outcomes, with the median outcome being a loss of $2.61184 and the 95th percentile outcome being a gain of $42.27635. The simulation also found that 54.29% of the paths ended below the starting point, and the maximum drawdown was 5.52915%. A drawdown of more than 1% occurred in 99.48% of the paths. The simulation excluded certain factors, such as overhead costs and cash distributions. The results are based on historical data and should not be considered as forecasts. The strongest counterexample to the strategy's effectiveness is that some paths did show a profit, but this is not enough to create a reliable expected payoff. The simulation was sourced from https://runway.adityaperswal.workers.dev/data/stock-bars and used observations 7818/7821 and stats.py.

A trading fund manager uses a computer program called Premise1, which uses Python and numpy with a seed of 260907, to analyze data from August 1 to September 6 at 13UTC. The program looks at the returns of three cryptocurrencies, BTC, ETH, and SOL, and calculates their average daily range, or the difference between the highest and lowest prices, which is 3.1492% for BTC, 3.8647% for ETH, and 5.8714% for SOL. The program also calculates a target price, which is 1.5 times the average daily range, or 4.7239% for BTC, 5.7970% for ETH, and 8.8071% for SOL. The program uses a method called bootstrap, which is a way to illustrate risk, to test the model. The model makes assumptions about how the prices will move, including a stop-loss order, which is an order to sell a security when it falls to a certain price, and a target price, which is the price at which the program will sell the security. The program also looks at the drift, or the average movement, of the prices, which is +0.5469% for BTC, +0.7386% for ETH, and +1.3458% for SOL. The program subtracts the sample mean, which is the average of the movements, from the drift to get a net movement of -0.6384% for BTC, -0.6627% for ETH, and -0.6992% for SOL. The program also calculates the probability of the prices moving outside of a certain range, which is 8.3% for BTC, 21.49% for ETH, and 20.81% for SOL. The model is not certain and does not provide a hard risk bound, and the bootstrap method understates the risk of large price jumps and ignores changes in liquidity. The conclusion is that the model's optimism comes from recent price movements, not from any inherent value, and that no simulation probability is used for allocation. The strongest counterargument is that the recent uptrend may continue, but this requires independent signal conditioning, which is not present. The data used for the model comes from https://runway.adityaperswal.workers.dev/data/crypto-bars, https://runway.adityaperswal.workers.dev/data/crypto-snapshots, and https://docs.alpaca.markets/us/docs/crypto-fees.

A news scan found the headline about FDA approval of a new prostate cancer imaging agent called Gozellixr. The analysis of TLX is based on 100,000 three-session paths from 2026 daily returns with a 30 basis point round-trip deduction. The descriptive base mean return is 0.739776%, with a win rate of 53.158% and a 5th percentile return of -8.82099%. This is not an approval probability or a validated trading rule. An assumed 20% adverse terminal gap is added independently with 0%, 5%, 10%, and 20% window hazard, resulting in mean returns of 0.73978%, -0.28589%, -1.265995%, and -3.273818%, respectively. The loss over 8.5099 on a 49.14 notional is 0.086%, 3.58%, 7.014%, and 13.746%, respectively. The assumed hazards are not estimated, and the compounding choice is illustrative. The breakeven hazard is approximately 3.7%, which shows fragility and not an actual risk estimate. A daily endpoint barrier proxy is set at a 6.43156% target and a -9.62343% stop, with the target being reached first 20.93% of the time and the stop being reached first 4.049% of the time, and neither being reached 75.021% of the time. This analysis cannot capture intraday orders, gaps, 15-minute venue execution, or bid-ask spreads. The historical pool already includes news, and added gap stress may double-count some hazard. No path quantity creates independent observations. The required edge is unknown, and the quarter Kelly note is not estimable for this event, with a size of 0. The record sources 7723 observations and the FDA early decision is a counterexample, as seen in the news release from Telix Pharma.

A news scan found the headline about Chewy terminal tail scenarios also having zero Kelly, and base-hit exits failing before path testing. Premises for this include: 1. Model probabilities are conditional, not empirical option win rates, meaning they are based on specific conditions, not actual win rates. 2. The intended exit must have a positive realistic payoff before path simulation can justify it. 3. Full premium remains at risk, meaning the entire amount paid for the option is at risk of being lost. The registered 52 step 15 minute exit-path study was cut at its feasibility gate, not run, because range-based targets were less than or equal to entry asks in indicators analysis. Do not replace it with an expiry hold strategy. A separate terminal diagnostic was run with NumPy seed 2026090608, N 100000, 9 sessions, T = 9/252, S 23.67. The formula used was ST = S exp(-0.5 sigma² T + sigma sqrt T Z + J_i - log mean exp J), where J draws uniformly from 16 training earnings log gaps, and common random numbers were used for comparisons. The baseline event sigma was 46.9262%, which is adverse, with 0.5J, 0.8 sigma, diffusion J0, and vol 42.5200%. The payoff was calculated as 100 max(ST-K,0) for calls or 100 max(K-ST,0) for puts, less 100 ask and fixed assumed round trip $0.20/$1.30. This calculation ignores discount/cash interest in physical P&L, American exercise, exercise closing execution, tax, rare unseen jumps, and event dependence, and is not an execution backtest. Calls were made at K 37.5 ask 0.05 and puts at K 17.5 ask 0.06. The results showed that the event $0.20 scenario call mean was -$5.189230, with a win rate of 0.011% (11/100000), average win $92.707951, average loss $5.20, full premium loss 99.989%, and MCSE $0.004165. The put mean was -$5.870908, with a win rate of 0.552%, average win $53.102472, average loss $6.198248, full premium loss 99.39%, and MCSE $0.017642. Raising fees to 1.30 shifts means to -$1.10. Adverse means were -$5.20/-$6.198126 at $0.20, and diffusion was -$5.20/-$6.197772. All 12 scenarios recorded showed no positive results. The qKelly formula, which calculates the optimal fraction of a portfolio to invest, was max(0, [p-(1-p)/(W/L)]/4) = 0 throughout. Zero observed wins in some MC samples is not true zero tail probability, as model uncertainty dominates MCSE. The risks were $5/0.06*100 plus cost fit 8.5099, but negative expectancy and unvalidated quotes mean zero allocation. Actual option history sample was 0, and own trade history was 0. The source of this data is https://runway.adityaperswal.workers.dev/data/option-chain/CHWY?feed=indicative, and adjusted stock bars, with 18 individual issuer date URLs recorded.

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.