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The fund uses a method called binary sizing to decide how much to invest. This method uses real data to estimate the probability of winning, which is 2 out of 4, and the amount won, which is 18.8951 times the amount invested. The fund's target is to make 80% of the possible profit, and it uses a formula called Kelly to determine the investment amount. The full Kelly investment would be 47.354% of the $100 book, and the half Kelly investment would be 23.677%. The fund invests $18, which is 18% of the fund and 1.803% of the $998.40 equity, and this is below the 3% limit. This is a rough estimate and not based on exact probabilities. The fund also looks at how much it could lose or gain each day, and it found that in 3 out of 4 cases, it would stop investing first if it lost 3% or gained 10%. However, the fund does not have complete data on what happens when it stops investing. Since there is no current bid, the fund cannot guarantee that it will stop investing when it loses 50%, and it will consider the premium it pays as the maximum amount it can lose. For example, if the true probability of winning is 1 out of 4, the fund's investment method would still work, but only because the potential profit is very high, and the fund might not be able to capture this profit if it stops investing too early.

A fund manager analyzed the stock MG. The analysis started with the stock price at 20.75 on October 16, with a put option premium of 0.12 plus 0.02 per share for friction, resulting in a total loss of 14 USD. The target price was 1.702273, with a cap of 170.2273. If the stock price reverts to 19.84, the gross payout would be 16 USD. The probability of a break-even event is 87.5% if every other path results in a total loss. To reach a price of 18.2977 or below, the probability of hitting the target must be more than 8.2243% for a positive outcome and 10.7959% to fund 14 USD at an equity value of 999.26. These are required probabilities, not forecasts. The analysis used 100,000 paths per 18 scenarios with a seed of 92104. The results showed a pre-expiry downside probability of 1%, 5%, and 10% at prices 19.84, 18.30, and 17, respectively. The independent stop-survival rates were 1, 0.25, and full survival. The models used were conservative and did not account for realistic fill models. The conclusion was that there is no defensible minimum contract size based on these odds. The old breakout empirical Kelly value of 45.97 USD is no longer calibrated to the current cash-deal regime. This analysis does not veto indefinite simulation, as new deal terms or actual event evidence could change the conclusion. The analysis did not include actual stop or target history, 15-minute option paths, or American exercise modeling. The sources used were https://www.sec.gov/Archives/edgar/data/1436126/000114036126037107/ef20082419_8k.htm and https://runway.adityaperswal.workers.dev/data/option-chain/MG?feed=indicative, as well as a script research/mg_audit.py.

A news scan found the following text: Premises include empirical normalized signed terminal payoffs, which means actual profits or losses, capped target, and deducting a premium of $0.02 per share for friction, or costs. The goal is to optimize the mean log wealth, which is a measure of overall profit, over a range of 0 to 0.99, then half, using $999.38 in equity. On October 20, 2020, at a target of $80, the mean profit was $1.7023, with a mean profit of $14.37 per contract, and a half Kelly, which is a betting strategy, of $45.97 USD. A 25% payoff haircut, which means reducing the profit, resulted in a mean profit of $7.28 per Kelly of $31.98. A 50% haircut resulted in a mean profit of $0.186 per Kelly of $1.30. At a 3x premium target, the mean profit was -$8 per Kelly of $0. A call option, which is a type of financial instrument, with a target of $0.7023 had a Kelly of $14.89, which is below the minimum of $18. A DSXP3.13 with a target of $80 had a mean profit of $5.667 per Kelly of $119.13. A 25% haircut resulted in a mean profit of $0.501 per Kelly of $15.84, and a 50% haircut resulted in a mean profit of -$4.666 per Kelly of $0. A 3x premium target had a mean profit of $2.551 per Kelly of $75.65. This general Kelly strategy includes partial profits, which means profits from some but not all trades. A binary target-or-full-loss diagnostic Kelly of $0 does not supersede this strategy. Path stress uses actual historical 20 daily close paths, with assumptions including a 4% rate and an implied sigma of 17.8845% for MG and 54.4913% for DSX. Bootstrap results, which are a type of simulation, showed a mean profit of $18.15, $16.90, and $15.89 USD for MG, with 5 or 6 stops and 1 or 6 targets. For DSX, the mean profit was -$5.08, -$10.88, and -$11.84, with 7 or 8 stops and 1 or 8 targets. Neither daily close checks nor BSM, which is a type of financial model, captures 15-minute venue execution, American exercise, IV changes, or real bid. Outcomes are unvalidated and not a permanent veto. A terminal sample of all P760, which is a type of financial instrument, was worthless, with a mean profit of -$20. A TRMDP, which is a type of financial model, of 32.5 signed 0 or 11 all worthless despite an absolute P80 pass. The conclusion is that one contract of MG12 or DSX13 is a plausible capped probe only with fresh quotes and honest exit-aware assumptions at an authorized session, not an automatic model trade. The full premium risk is less than or equal to $29.98, with a maximum of 4 and a total of 100. A nominal 50% stop is not loss-bound. Sources include https://runway.adityaperswal.workers.dev/data/stock-bars and option-chain, as well as research/sizing.py/path_model.py. Small N selection and regime break remain binding uncertainty, which means that the results are limited by the small sample size and the potential for changes in the market regime.

The R92100 HALO put sizing cannot silently assume its stop fills. The premises are based on an October 16 put with an indicative price of 0.18, a target price of 1.93, and an assumed friction of 0.02, which gives a net win of 1.73 per share, with all-in costs of 0.20. A borrow on February 17 was signed with terminal positives as an explicitly optimistic assumed target probability, but it is not observed as the target-before-50% stop probability. The Half Kelly equity allocation is 55.9488 USD with an ideal stop loss of 0.11 all-in, versus 7.8205 USD with a full 0.20 loss. One contract premium is 18, with all-in cost 20 and a cap of 30. Below one-contract allocations cannot be rounded up. The conclusion is that fresh spread/path-aware honest odds are required at authorized entry, with a full premium budget and 50% stop remaining mandatory. Neither scenario establishes trade probability nor permanent cash veto. The source is a data scan from https://runway.adityaperswal.workers.dev/data/stock-bars, with the latest contract metadata OI7 as of September 17, zero indicative bid as of September 18, and 31094 observations, with the current sizing observation.

A test called R92100 event bootstrap and target caps challenge looked at the apparent tail expectancy. The test made the following assumptions: it used 100,000 random outcomes for Nike stock, with a starting price of 35.51, a strike price of 31, and a premium of 0.30, and it assumed a friction of 0.02. The test found that the average net outcome was -2.2825, the median outcome was -32, and 83.315 percent of the outcomes resulted in a loss. However, 16.685 percent of the outcomes had proceeds that were at least three times the premium. This test did not take into account the remaining time value, volatility, path stops, and executable quotes, so the loss frequency and target frequency are not actual probabilities. The test also found that the Nike stock size had no effect on the outcome because the gate failed. The test looked at three frozen events: HALON17, THN4, HALOP95, HALOC130, THP18, and THC27, and found the following target values before deducting the premium and friction: HALOP95 target was 1.93 with a mean of 2.7059, HALOC130 target was 1.83 with a mean of -3.4706, THP18 target was 6.20 with a mean of -25, and THC27 target was 3.58 with a mean of 143.8632. The test concluded that the target-limited strategy was overstated and that the endpoint values did not take into account path stops. As a result, no new calibrated Kelly or trade odds were created, and the existing gross passes were preserved for honest fresh session sizing. The existing 3658 series depletion and full-loss sensitivity remained applicable and were not re-run. A 50 percent stop is required, but a full premium of less than or equal to 30 is a hard risk. The data source is https://runway.adityaperswal.workers.dev/data/stock-bars, with 31092 observations and signed scenarios for this run.

A study was done on the payoff sensitivity of option R92008. It was based on 100,000 resamples of the earnings close reactions of stock WOR, using a fixed stock price of 57.38 dollars, a put option strike price of 55 dollars, and an ask price of 2.14 dollars with 0.02 dollars friction. The results showed a mean contract loss of 156.32 dollars and a median loss of 216 dollars, with 90.716 percent of the contracts resulting in a loss and 63.5 percent having no intrinsic value at the end. This study only looked at the intrinsic value of the option at the end, not the profit and loss or the possibility of filling the option. The size of the option was quantized to zero because the premium of 2.14 dollars was greater than the 30 percent cap, regardless of the model used. The conclusion was that there was no established probability of winning or exiting the trade, and it was advised not to buy the hypothetical cheap fills just because the bootstrap results looked better. New simulations were deemed unnecessary because the prior full premium and shared-loss stress for HALO and TH were retained and did not need to be rerun. The data for this study came from https://runway.adityaperswal.workers.dev/data/stock-bars and /data/option-chain/WOR?feed=indicative.

A news scan found the following text: Premises for the R92006 finite-fund series are as follows: it uses a NumPy seed of 9200602, 100,000 paths or scenarios, 20 sequential pairs, an initial fund of 100, and no added capital. The premiums are 23 and 18, with target sale proceeds of 183 and 358. There is a 1 USD roundtrip fee for each transaction, and a reserve of 43 before each pair. The probability of loss is assumed to be 5, 10, or 15 percent per leg, with a loss of either 50 or 100 percent. A common uniform mixture of 0, 0.5, and 1 preserves marginals and stresses dependence. If the probability of loss is 10 percent and the loss is half, the mean fund is 413.71, but the median is 32.50, and 57.76 percent of the funds are unable to fund the next pair. If the losses are perfectly shared, the mean is 323.51, the median is 32.50, and 72.883 percent are unable to fund the next pair. If the loss is full, the mean fund is 175.58, the median is 14, and 79.461 percent are unable to fund the next pair, but if the losses are shared, 86.257 percent are unable to fund the next pair. The peak-to-trough drawdowns are 270 and 382.5 USD for half-loss, which may exceed the initial 100 after modeled wins, but not the initial principal risk. The break-even target probability is 7.289 percent for half-loss and 13.115 percent for full-loss. At an assumed probability of 10 percent, the half-Kelly is 26.91 USD for half-loss, but 0 for full-loss. The TH is 2.865 and 5.307. The conclusion is that size cannot ignore full premium loss or minimum contract granularity, and model sensitivity is not prediction, new mandatory veto, or validated trade odds. No portfolio deployment was selected. The full premium hard cap is 30, the total is 100, and the maximum is 4. The source of the stock-derived target levels is https://runway.adityaperswal.workers.dev/data/stock-bars.

The automated trading fund manager made certain assumptions to model option sizing. The premises of the model include using a NumPy seed of 92004, 20,000 paths, and four sampled 5-session blocks from the last 252 log returns. The model also assumes 20 steps or 25 calendar days to October 16, with an unchanged spot price. A Black-Scholes model, or BSM, with constant implied volatility, or IV, was fit to the data for HALO and TH. The model asks for 33.414 and 68.513 percent, with a rate of 4 percent, and targets of 1.83 and 3.58, with a 50 percent premium stop. The model assumes a roundtrip fee of 1 USD. If there is no exit markdown, the means for HALO and TH are 4.90 and 4.50 USD, with losses of 87.97 and 93.23 percent. The half Kelly criterion, a measure of optimal bet size, is 22.95 and 11.50 USD of 1000 equity. A 20 percent mark discount changes the means to -1.19 and 0.57, and the half Kelly criterion to 0 and 1.50 USD. The model also found that constant bid ratio of less than or equal to 0.5 triggers an immediate loss. The actual venue mark is unknown, and the indicative ratios are not actual bid asks. The model also considered conditional cheaper fills, where HALO and TH have means of 9.05 and 8.16, and half Kelly criteria of 39.35 and 21.80, with costs of 16 and 14. The conclusion is that there is no calibrated positive sizing at observed indicative asks, and fresh pricing and honest odds can change it. The model's sensitivity is only considered, not a new mandatory gate or proof of cash forever. The historical terminal Kelly is optimistic relative to the exit policy. The source of the data is from stock bars and option chains for HALO and TH.

A news scan found the following text: Premises for this analysis are based on a hypothetical scenario where the spot price on September 21 remains unchanged, with 20 daily steps to October 16, which is 25 calendar days, and 30,000 paths per scenario with a seed of 92002. The analysis uses a method called Bootstrap to estimate daily returns, which are scaled at 0.75, 1, and 1.5, and a constant volatility, known as BSMIV, calibrated to the ask price and a 4% interest rate. The results show that for certain stocks, including HALO and THC, the paid premiums and implied volatility percentages are as follows: HALO C130 paid 0.23 with a fit IV of 33.414%, HALO P95 paid 0.18 with a fit IV of 38.114%, and THC 27 paid 0.18 with a fit IV of 68.513%. The analysis also shows that the RV60 for HALO is 45.30 and for THC is 58.40%. The options stop at 50% and the modeled targets are filled no better than the target, with an exit friction of 0.01 per share plus a 1 USD roundtrip fee. The mean premium targets for HALO and THC are -8.90, -3.58, and 1.78 USD, and -7.89, -4.71, and 0.02, respectively. The P80 targets, which are independently derived, show mean values of -8.27, 1.42, and 16.26 for HALO, and -3.54, 7.28, and 28.75 for THC. The baseline target hits are 10.657% and 4.557%, and the stops are 89.257% and 91.873%. The analysis concludes that the whole premium should be kept at 23 or 18, which is less than 30 each, with a potential total of 41, which is less than 100, and a maximum of 4. The worst-case scenario is 41 plus costs, despite half premium stops. The terminal intrinsic Kelly is 49.7 and 235.25 USD, which is unreliable, and a hard cap of 30 binds. The prospective single contracts are minimum granularity, with a quarter of 30 and a probe of 7.50, which is unavailable. No orders were closed, and the capital and actual quote should be refreshed in the entry run. The source of the data is /data/stock-bars and /data/option-chain/HALO and THC, with a feed of indicative, from 30184 to 89.

A simulation of the R92000 exit policy was conducted. The premises of the simulation were as follows: the stock price was $46.67, the option price was $37.5, and the paid premium was $0.23, with an indicative implied volatility of 55.94%. The simulation used 50,000 paths per scenario, with a seed of 92000, and 20 business steps from September 21 to October 16, with an event step on October 6. A zero-drift Geometric Brownian Motion, or a random process used to model stock prices, with ordinary volatility of 26%, 40%, and 60% was used. The Black-Scholes Model, a mathematical model used to estimate the value of a call option or a put option, was used to calculate the put option price, with a floor of the intrinsic value, or the difference between the stock price and the strike price, and a 4% interest rate assumption. The initial model price was $23.647, versus an ask price of $0.23. The daily stop loss was $0.115, the target was $0.69, and the exit price was $0.01 per share, with a friction of $1 USD and a roundtrip fee. The hypothetical hold-through means were $3.27, $8.81, and $7.67 USD, with targets of 4.83%, 11.78%, and 22.62%, but the current hurdle of 20.14% exceeded the median of 10.02%, so this hold policy is outside the mandate. A mandate-consistent forced exit on October 5, day 11, resulted in means of -$13.81, -$9.02, and $0.88 USD, with targets of 0.556%, 7.006%, and 20.698%. These uncalibrated daily marks omit American and dividend details, and 15-minute quote and liquidity risk. A full-premium loss remains possible despite a half-premium stop. A separate empirical terminal intrinsic, or the value of the option at expiration, after a friction of $0.02, resulted in 2 wins out of 11, with a mean intrinsic value of $0.650308, and a grid half Kelly, a betting strategy, of 6.704% equity. However, this cannot override a failed gate, and actual size is 0, with a future one premium of less than or equal to 30, and a total of 100, with a maximum of 4. A crucial counterexample is that a higher price of a nearer strike may pass the median when cheap enough, so it is better to reprice rather than claim model profits at an impermissible hold. The sources of the data are https://runway.adityaperswal.workers.dev/data/option-chain/LW?feed=indicative, stock bars, and issuer October 6 date 29824.

A news scan found the following text: Premises are based on 11 close-event reactions and a stock price of $15.13, with a strike price of $14 and an indicative ask of $0.23. The model uses 50,000 paths, a seed of 91908, and 20 business days from September 21 to October 16, with an event step on September 30. The model uses a geometric Brownian motion with 22.5, 35, and 50 percent annual volatility. A Black-Scholes model put is used with a floored intrinsic value, pre and post IV scenario volatility, and an assumed risk-free rate of 4 percent. The initial model value is $0.168158, which differs from the ask price of $0.23. The model has a daily stop loss of $0.115, a target of $0.69, and an expiry date, with an exit price of $0.01 per share plus a $1 round trip friction. The mean profit and loss is -$12.3303, -$6.1652, and +$0.1245 USD, with a target percentage of 5.052, 13.464, and 21.866 percent, and a stop percentage of 93.924, 85.970, and 78.006 percent. The fifth percentile is -$23.2405, -$20.4268, and -$21.2576 USD. The model does not account for American exercise, dividend boundary, and actual 15-minute liquidity. The conclusion is to size zero for a failed mandate, even in a high-volatility scenario. The source is https://runway.adityaperswal.workers.dev/data/stock-bars and option-chain/CAG?feed=indicative.

A simulation was run to analyze a Thursday gap in stock prices. The simulation used 13 observed overnight gaps from August 29 to September 4, with a stock price of $7.99. The simulation took into account 10 trading steps from Monday, September 21, to October 2, and an event on Thursday, September 24, related to the company BlackBerry, which can be found at https://investors.blackberry.com/. The simulation used a corrected step 4, which replaced the initial step 3 outputs of 29595-97. The simulation used 50,000 paths and a scenario seed of 91906, with a stock price that had no expected drift, and an annual volatility of 40%, 60%, and 80%. A gap was injected on day 4, with an interest rate assumption of 4%. The simulation used a put option model with a floored intrinsic value, and pre-event and post-event volatility assumptions. The simulation did not use American exercise boundary calibration. The exit strategy was to model the daily mark, which was less than or equal to 0.5 paid or greater than or equal to the maximum of 3 paid and the 80th percentile of the intrinsic value. The actual execution used a 15-minute quote and liquidity, and a gap stop, but this was not validated. The simulation assumed a roundtrip cost of $1 and an exit slippage of $0.01 per share. The target price for the K7 put option was $0.20, with a target of $0.60, and the means were -$13.6358, -$10.8047, and -$6.7817. The stop percentages were 95.850%, 92.566%, and 87.452%, and the target percentages were 3.234%, 6.130%, and 11.384%. For the K7.5 put option, the hypothetical target price was $0.20, with a target of $0.60, and the means were -$7.1241, $1.7658, and $10.9070. The stop percentages were 83%, 71.85%, and 60.444%, and the target percentages were 13.416%, 25.566%, and 37.804%. The current ask price for the K7.5 option is $0.46, which costs more than the $0.30 cap. The means were -$30.4092, -$23.0016, and -$15.1475. The $0.20 price is not quoted and is not attainable. The model often shows a full premium plus fee, despite a half-premium stop. A separate analysis used a signed close intrinsic payoff log utility grid, with a half Kelly criterion of 0, for the K7 put option with a price of $0.20, and the K7.5 put option with prices of $0.20, $0.23, and $0.46, after a friction of $0.02. The intrinsic value excludes the remaining time value, so it is not proof of a true option expected value being negative. The current live allocation is 0, with a hard one premium less than or equal to $30, and a total less than or equal to $100, with a maximum of 4. A quarter probe cannot rescue an invalid quote or a failed mandate. The risk is the full premium, not the model stop. The data source is https://runway.adityaperswal.workers.dev/data/option-chain/BB?feed=indicative and stock bars.

A news scan found the headline 'R91904 SFIX gap-bootstrap option paths: cheap limit odds remain regime-sensitive'. This refers to a type of financial analysis. The analysis is based on certain premises, including historical overnight gaps from observations 29367 to 76, and a specific stock price on September 18 and a put option price on October 16. The analysis uses 30,000 paths, or possible scenarios, and a volatility scenario seed of 91904. It also assumes a risk-free interest rate of 4 percent and zero stock drift, meaning the stock's price does not change over time. The analysis uses a type of option pricing model called BSM, which stands for Black-Scholes-Merton, a mathematical model used to estimate the value of a stock option. The model approximates the value of an American option, which can be exercised at any time, and uses a type of statistical analysis called NumPy. The results show that at a premium of 0.13, the mean dollar profit and loss is -5.2523, -2.5318, and 1.1347, and the stop percentage is 80.4167, 77.89, and 73.8533 percent. The analysis also shows that at a premium of 0.28, all results are negative, and at a premium of 0.11, the mean results are -3.2232, -0.5282, and 3.1574. The analysis includes fees of 1 USD round trip and 0.01 USD per share exit slippage, which refers to the difference between the expected price of a stock and the actual price. The data sources for the analysis are https://runway.adityaperswal.workers.dev/data/stock-bars and https://runway.adityaperswal.workers.dev/data/option-chain/SFIX?feed=indicative.