# Comparison of Risk Management and Position Sizing Frameworks

## Introduction to Capital Preservation

In quantitative finance and systematic trading, the generation of alpha through predictive entry signals is fundamentally secondary to the mathematics of survival. Expectancy models dictate that without rigorous position sizing and risk management frameworks, even strategies with positive mathematical expectations are vulnerable to the risk of ruin [cite: 1, 2, 3]. The core dilemma of portfolio management rests in balancing the mathematical optimization of geometric capital growth against the psychological and operational constraints of drawdown tolerance [cite: 4, 5]. 

Trading systems are frequently evaluated by their win rates and profit factors, but realized performance relies heavily on the sizing architecture deployed. As historical market events dictate, poor position sizing can transform a theoretically profitable strategy into an unprofitable one, whereas sophisticated frameworks can substantially enhance risk-adjusted returns [cite: 6]. This analysis examines the three dominant paradigms in risk management and position sizing: the fixed-fractional framework (including the 1-2% rule and the Kelly Criterion), the fixed-ratio framework developed by Ryan Jones, and volatility-scaling methodologies utilizing Average True Range (ATR). By analyzing the mathematical foundations, institutional applications, and structural market vulnerabilities associated with each model, this report provides a comprehensive evaluation of how capital is preserved and scaled across diverse market regimes.

## The Fixed Fractional Framework

The fixed-fractional approach forms the bedrock of modern position sizing. The core principle dictates that a trader risks a consistent percentage of their total account equity on each individual trade [cite: 7, 8]. As account equity grows, the absolute dollar amount risked per trade increases, compounding gains; conversely, as equity contracts during a drawdown, the absolute dollar risk decreases proportionally [cite: 8, 9]. This dynamic creates a geometric growth curve during winning streaks and an automatic capital-preservation mechanism during losing streaks, preventing rapid account depletion.

### The Kelly Criterion and Mathematical Limits

The mathematical extreme of the fixed-fractional framework is the Kelly Criterion. Originally developed by John L. Kelly Jr. in 1956 for information theory and telecommunications, the formula was later adapted for financial markets by Edward Thorp [cite: 8, 10, 11]. The Kelly formula identifies the exact fraction of capital to risk that mathematically maximizes the long-term compound growth rate of a portfolio. The basic formula for discrete outcomes is expressed as:

$$f = \frac{(b+1)p - 1}{b} \quad \text{or} \quad f = p - \frac{q}{b}$$

Where $f$ represents the optimal fraction of capital to risk, $p$ is the historical probability of a winning trade, $q$ is the probability of a losing trade ($1 - p$), and $b$ is the ratio of the average winning trade to the average losing trade [cite: 12, 13]. 

While the Kelly Criterion provides the mathematical maximum for asset growth, it operates under the theoretical assumption of infinite divisibility of capital and absolute certainty in historical probabilities [cite: 3, 14]. In practice, utilizing the "Full Kelly" fraction exposes a portfolio to extreme volatility. Strategies operating at this theoretical limit routinely experience drawdowns exceeding 50%, and in severe scenarios, can approach 99% relative drawdowns during prolonged losing streaks [cite: 4, 15]. Because these fluctuations are psychologically unbearable for discretionary traders and violate the maximum drawdown parameters set by institutional proprietary trading firms, practitioners typically deploy "Fractional Kelly" approaches. Risking half ("Half-Kelly") or a quarter ("Quarter-Kelly") of the calculated optimal fraction captures the majority of the geometric growth benefits while disproportionately reducing portfolio volatility and the risk of catastrophic ruin [cite: 4, 16, 17].

### Optimal f and Terminal Wealth Relative

Expanding on the Kelly Criterion to accommodate the variable trading outcomes inherent in financial markets, Ralph Vince introduced the concept of "Optimal f" in his 1990 publication, *Portfolio Management Formulas* [cite: 13, 18, 19]. Unlike the Kelly model, which assumes uniform win/loss ratios, Optimal f calculates the ideal capital fraction based on a distribution of historical trades. The primary objective is to maximize the Terminal Wealth Relative (TWR), which serves as the ratio of final capital to initial capital [cite: 13, 20, 21]. 

The calculation requires iteratively finding the value of $f$ (a fraction between 0 and 1) that maximizes the geometric mean of Holding Period Returns (HPR) across all historical trades in a given dataset:

$$HPR_i = 1 + \left(f \times \frac{-\text{Return}_i}{\text{Largest Historical Loss}}\right)$$
$$TWR = \prod_{i=1}^{n} HPR_i$$

While Optimal f perfectly optimizes historical capital allocation, its reliance on the exact metric of the "Largest Historical Loss" creates an inherent operational vulnerability [cite: 13, 22]. If a future trade incurs a loss exceeding the magnitude of the largest historical loss used to calculate $f$, the account can face immediate ruin. Furthermore, Optimal f remains highly aggressive, often requiring traders to endure significant drawdowns to achieve the optimized TWR. Consequently, Optimal f is often diluted or combined with "Secure f" methodologies that algebraically constrain the formula based on a trader's maximum acceptable drawdown limit [cite: 11, 13, 22].

### Practical Applications of the Fixed Percentage Rule

To bypass the mathematical complexities and extreme drawdowns associated with Optimal f and Full Kelly, the retail and institutional proprietary trading industries heavily rely on the 1-2% rule. This heuristic dictates that a trader should never risk more than 1% to 2% of total account equity on any single trade setup [cite: 23, 24, 25]. 

The 1-2% rule serves as a structural buffer against the inevitability of losing streaks. At a 1% risk parameter, an account can withstand twenty consecutive losses before experiencing an approximate 18% drawdown [cite: 9, 26].

[image delta #1, 0 bytes]

 This survival capacity creates the longevity necessary to navigate periods where a trading strategy's expectancy temporarily underperforms. The mathematical breathing room afforded by strict percentage limits is essential for strategies with low win rates. For instance, momentum trading champions like Mark Minervini utilize asymmetric expectancy—targeting a 3:1 reward-to-risk ratio. Under this matrix, a strategy only requires a 30% win rate to maintain profitability, provided the downside is strictly capped at 1-2% per execution [cite: 23].

However, the 1-2% rule is not universally optimal across all trading frequencies. For high-frequency or algorithmic day trading systems that execute dozens of trades per session, a 2% risk per trade aggregates to a massive daily exposure, leading to unacceptably high risks of ruin [cite: 24]. For such high-velocity systems, fractional percentages (0.1% to 0.5%) are strictly required to avoid rapid account depletion during adverse market events [cite: 9, 24].



## The Fixed Ratio Framework

While fixed-fractional sizing scales position risk symmetrically based on total account equity, the Fixed-Ratio method, developed by Ryan Jones in his book *The Trading Game*, bases position sizing exclusively on accumulated profits [cite: 8, 27, 28]. This model addresses the perceived inefficiencies in fixed-fractional sizing, particularly for small accounts attempting to build capital without taking on the catastrophic ruin probabilities associated with the Kelly Criterion.

### Mathematical Structure and the Delta Variable

The defining mechanic of the Fixed-Ratio model is the "Delta"—the specified amount of profit per contract required to increase the position size by one additional contract [cite: 16, 27]. The formula for determining the current number of contracts ($N$) allowed is mathematically expressed as:

$$N = 0.5 \times \left[ 1 + \sqrt{1 + 8 \times \frac{\text{Profit}}{\text{Delta}}} \right]$$

To illustrate the mechanics, assume a trader starts with one futures contract and sets a Delta of \$5,000. To increase the position size to two contracts, the trader must accumulate \$5,000 in total profit. However, to increase from two contracts to three contracts, the trader must generate an *additional* \$10,000 in profit (\$5,000 per contract $\times$ 2 contracts). To move from three to four contracts requires a further \$15,000 in accumulated gains [cite: 4, 29]. 

### Asymmetric Scaling Dynamics

This structural requirement creates an asymmetric, geometric scaling path proportional to the square root of profits [cite: 4]. 

For small accounts, Fixed-Ratio sizing is highly aggressive. Because the initial capital base is ignored and only absolute profit matters, the trader increases position sizes rapidly during early winning streaks [cite: 27]. However, as the account grows, the absolute dollar amount of profit required to add subsequent contracts increases exponentially. This acts as a natural "slowing mechanism." While a fixed-fractional model increases contract size linearly as the account grows, the Fixed-Ratio model decelerates the rate of leverage expansion, naturally dampening portfolio volatility and preventing massive drawdowns at higher equity levels [cite: 4, 11, 27].

### Drawbacks and Operational Constraints

Despite its advantages in smoothing the equity curve, the Fixed-Ratio framework contains distinct operational vulnerabilities. First, the model completely ignores the initial account size and risk-of-ruin mechanics if the strategy enters a drawdown immediately upon deployment [cite: 8, 30]. Because the first tier of trading relies on a static contract size (e.g., trading 1 contract until Delta is reached), a string of losses at the onset of trading can deplete the margin of a small account before any profits are accumulated [cite: 30]. 

Second, the determination of the Delta is highly subjective. Jones suggests calculating the Delta based on the maximum expected drawdown of the trading system (e.g., if the expected drawdown is \$10,000, setting the Delta to \$5,000 allows for aggressive scaling, while a higher Delta is more conservative) [cite: 29]. Furthermore, the Fixed-Ratio framework is difficult to implement outside of futures and options markets, as it relies heavily on the granularity of standardized contracts rather than fractional share sizing, making it less practical for standard equity portfolios [cite: 4, 31].

## Volatility Scaling and Average True Range

A critical flaw in both basic fixed-fractional and fixed-ratio methodologies is their general indifference to prevailing market conditions. Risking a static 2% of an account implies taking the exact same position size regardless of whether the market is in a period of historic calm or extreme turbulence. To rectify this, institutional practitioners and sophisticated systematic traders deploy volatility-adjusted position sizing, most commonly utilizing the Average True Range (ATR) [cite: 16, 32, 33].

### Mechanics of Average True Range

Developed by J. Welles Wilder Jr. in 1978, the ATR measures the absolute magnitude of price movements over a specified lookback period (typically 14 days), explicitly accounting for overnight price gaps [cite: 33]. By incorporating ATR into position sizing, traders ensure that their absolute dollar risk remains constant relative to the market's current noise level.

In an ATR-based framework, the distance to the stop-loss is defined as a multiple of the ATR (e.g., a 2x ATR stop). The position size is then calculated by dividing the maximum allowed dollar risk (e.g., 1% of the account) by the absolute dollar distance to the ATR stop [cite: 9, 33]. 

*   During periods of **low volatility** (narrow ATR), the stop-loss is placed closer to the entry price. This tighter stop allows the trader to purchase a larger number of shares or contracts while maintaining the same 1% capital risk.
*   During periods of **high volatility** (wide ATR), the stop-loss is placed further away to avoid being triggered by random market noise. The wider stop mandates a smaller nominal position size to keep the total risk constrained to 1%.

[image delta #2, 0 bytes]





### The Turtle Trader Methodology

This volatility-scaling methodology was famously institutionalized by the Turtle Traders in a 1983 experiment led by commodities traders Richard Dennis and William Eckhardt. They sought to prove that systematic trading success could be taught using rigorous mechanical rules rather than reliance on intuition [cite: 34, 35, 36]. The Turtles calculated market volatility as "N" (their specific term for the 20-day Average True Range). 

The Turtles sized positions in "units," structuring their formula so that a 1N move in any asset—from highly volatile heating oil to slow-moving Eurodollars—equated to exactly 1% of total account equity [cite: 33, 36]. This equalized the risk-adjusted exposure across an entire multi-asset portfolio. Furthermore, the Turtles utilized ATR for pyramiding; they initiated trades on 20-day or 55-day price breakouts and added one additional unit every time the asset moved 0.5N in their favor [cite: 35, 36]. Their initial stop loss was permanently placed at 2N, guaranteeing that no single trade idea, even when fully pyramided, risked more than 2% of the total account baseline [cite: 35, 37]. The rigid adherence to this volatility-scaled risk framework allowed the novice traders to generate an estimated $175 million in profits over five years [cite: 36, 37].

### Institutional Volatility Scaling

In modern institutional finance, volatility scaling extends far beyond basic ATR stops. Quantitative hedge funds and market makers employ volatility scaling at the portfolio level to construct Risk Parity and equal-risk-contribution architectures [cite: 6, 38]. 

Rather than simple moving averages, institutions frequently utilize Exponentially Weighted Moving Average (EWMA) models or GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models to forecast short-term volatility [cite: 6, 38, 39, 40]. Returns are scaled by their recent exponentially weighted volatility, ensuring that an unexpected volatility spike in a specific asset class does not dominate the risk profile of a broader trend-following or multi-strategy portfolio [cite: 6, 38, 41]. This framework allows funds to apply leverage safely to asset classes with historically lower volatility, amplifying convex return profiles without drastically increasing directional beta [cite: 38, 42]. Furthermore, institutions like AQR Capital Management and Two Sigma monetize these dynamics by systematically harvesting the Volatility Risk Premium (VRP), capitalizing on the historical tendency for implied volatility (options pricing) to systematically overprice realized volatility [cite: 10, 41, 43].

### Vulnerabilities in Tail-Risk Events

Despite its robust theoretical foundation, volatility scaling suffers during sudden, aggressive regime shifts, as vividly demonstrated during the March 2020 COVID-19 pandemic crash. The fundamental flaw of ATR and simple EWMA models is that they are mathematically backward-looking indicators. When volatility clusters abruptly—transitioning from historical lows to extreme highs in a matter of days—ATR models fail to widen stops quickly enough to adapt to the new regime. This lag leads to premature stop-outs, whiplash, and cascading losses before the indicator normalizes to the higher volatility environment [cite: 32, 44, 45, 46]. 

Furthermore, traditional GARCH models often link kurtosis directly to variance, causing them to underprice the probability of extreme tail events and conditional skewness in financial returns [cite: 44]. During the COVID-19 shock, correlation breakdowns across asset classes resulted in volatility scaling systems malfunctioning as protective diversification failed [cite: 44, 45].

## Market Structure and Execution Risks

The theoretical efficacy of any risk-management framework is strictly bound by the microstructure of the market in which it operates. The mechanics of stop-loss execution differ drastically between traditional equities and continuous cryptocurrency markets, fundamentally altering the real-world performance of position sizing models.

### Gap Risk in Traditional Exchange Markets

In traditional equity and commodity markets, trading is constrained by exchange hours. This creates "gap risk"—the probability that an asset's price will move significantly while the exchange is closed due to overnight macroeconomic news, geopolitical events, or earnings reports [cite: 47, 48, 49]. 

For risk management frameworks reliant on hard stop-loss orders (such as ATR-based breakout systems), gap risk is a critical vulnerability. If an equity closes at \$100 and a trader places a hard stop-loss at \$95 based on a 1% risk limit, negative overnight news may cause the stock to open the next morning at \$85. The stop-loss order is executed at the market open, realizing a loss substantially larger than the 1% or 2% mathematically modeled in the trader's position sizing calculation [cite: 47, 49, 50]. This structural reality forces institutional algorithmic traders to reduce overnight exposure, deploy options hedges, and scale positions down ahead of scheduled news events, acknowledging that overnight liquidity gaps bypass continuous hedging and linear modeling assumptions [cite: 47, 48, 51].

### Liquidation Cascades in Continuous Markets

Conversely, cryptocurrency markets operate 24 hours a day, 7 days a week, effectively eliminating traditional overnight gap risk [cite: 52, 53, 54]. In theory, this continuous operation allows stop-loss orders to be executed precisely as modeled at any hour, preserving the mathematical integrity of the 1-2% rule. 

However, continuous trading introduces a different systemic risk: leverage-driven liquidation cascades. Because offshore crypto exchanges and Decentralized Finance (DeFi) protocols allow extreme leverage and utilize cross-collateralization via smart contracts, slight market downturns can trigger automatic, programmatic liquidations [cite: 55]. During weekends or periods of thin liquidity, these algorithmic sell orders overwhelm the order book, driving prices down further and triggering subsequent tiers of liquidations [cite: 51, 55]. In these events, the sheer speed of the crash causes severe slippage. Consequently, an ATR-based stop-loss may execute at a significantly worse price than intended, resulting in the same outsized capital destruction as an equity gap [cite: 55, 56]. 

## Synthesis of Position Sizing Methodologies

To construct a robust portfolio, risk managers must understand the exact tradeoffs of the methodologies employed. No single framework solves the risk puzzle in isolation; institutional survival relies on understanding the distinct advantages and vulnerabilities of each model.

| Risk Management Framework | Core Mechanism | Primary Advantage | Primary Vulnerability | Optimal Application |
| :--- | :--- | :--- | :--- | :--- |
| **Fixed-Fractional (1-2% Rule)** | Risks a static percentage of total account equity per trade [cite: 9, 24]. | Limits catastrophic ruin; provides robust capital preservation during deep drawdowns [cite: 23, 25]. | Ignores market volatility; exhibits inefficient geometric scaling during rapid account growth [cite: 9, 24]. | Retail trading, highly diversified systematic portfolios, foundational baseline risk limits [cite: 25, 57]. |
| **Fixed-Ratio (Ryan Jones)** | Increases position size based exclusively on a fixed dollar profit target (Delta) [cite: 27, 28]. | Asymmetric scaling: highly aggressive for small accounts, dampens leverage as the account grows [cite: 4, 27]. | Vulnerable to early drawdowns before initial profits accrue; difficult to use without standardized contracts [cite: 30, 31]. | Small proprietary trading accounts, futures trading, strategies with high win rates [cite: 8, 28]. |
| **Volatility Scaling (ATR/EWMA)** | Modifies position size and stop-loss distance inversely to recent price volatility [cite: 16, 33, 42]. | Equalizes absolute dollar risk across diverse assets; filters out random market noise dynamically [cite: 16, 33]. | Backward-looking indicator; fails during sudden regime shifts (e.g., COVID-19); vulnerable to gap risk [cite: 32, 44, 46]. | Institutional trend following, multi-asset risk parity, macro-driven algorithmic trading [cite: 5, 6, 38]. |

Professional algorithmic and systematic traders rarely utilize these frameworks in their purest forms. Modern risk architecture favors hybrid models. For example, a robust quantitative system might utilize **Volatility-Adjusted Fixed Fractional sizing**, where a trader limits absolute risk to 1% of equity (Fixed Fractional), but dictates the exact position size based on a 2x ATR stop (Volatility Scaling), while running a "Half-Kelly" calculation in the background to verify that the 1% parameter remains mathematically optimal for the strategy's historical win rate [cite: 4, 12, 16, 17, 57]. 

The architecture of survival in financial markets relies on accepting that predictive models are fallible and market regimes are unstable. While frameworks like the Kelly Criterion provide the mathematical ceiling for compound growth, their inherent volatility makes them operationally dangerous. The 1-2% rule provides a psychological and mathematical safety net but leaves portfolios exposed to shifting market noise. The Fixed-Ratio framework successfully smooths the equity curve for leveraged futures traders but introduces subjective parameter risks. Finally, ATR and EWMA volatility scaling offer the most sophisticated mechanism for risk parity, yet remain blind to sudden gap risks and discontinuous black swan events. Ultimately, sophisticated portfolio management requires the rigorous synthesis of these frameworks—bounding trade size with fixed-fractional limits, adjusting leverage through volatility scaling, and acknowledging the structural realities of the specific market exchange.

## Sources

1. [tlap.io](https://tlap.io/en/forex-risk-management-basics)
2. [aquafutures.io](https://www.aquafutures.io/blogs/futures-trading-risk-management)
3. [pictureperfectportfolios.com](https://pictureperfectportfolios.com/how-to-invest-like-mark-minervini-momentum-trading-champion/)
4. [wizardofvegas.com](https://wizardofvegas.com/forum/gambling/betting-systems/37730-are-betting-systems-equally-useless-when-you-have-an-advantage/)
5. [quora.com](https://www.quora.com/How-do-I-use-the-never-risk-more-than-2-rule-in-Forex-trading)
6. [adaptrade.com](http://www.adaptrade.com/Articles/PositionSizing-Paper.pdf)
7. [tradingblox.com](https://www.tradingblox.com/tbforum/viewtopic.php?t=2651)
8. [leelootrading.com](https://www.leelootrading.com/blog/art-of-position-sizing-in-futures-trading)
9. [quantifiedstrategies.com](https://www.quantifiedstrategies.com/position-sizing-strategies/)
10. [tradingblox.com](https://www.tradingblox.com/tbforum/viewtopic.php?t=722&start=20)
11. [quora.com](https://www.quora.com/What-is-the-best-trading-book-for-beginners)
12. [quora.com](https://www.quora.com/What-are-some-good-books-on-trading-psychology-How-can-it-help-us-become-better-traders-investors)
13. [scribd.com](https://www.scribd.com/document/633648808/25-DAY-TRADING-STRATEGIES-IN-NIFTY-BANK-NIFTY)
14. [ur.z-library.sk](https://ur.z-library.sk/book/Bj4X0qAqj3/profitable-short-term-trading-strategies.html?dsource=recommend)
15. [medium.com](https://medium.com/@navnoorbawa/how-hedge-funds-monetise-options-time-decay-theta-harvesting-the-volatility-risk-premium-insti-f85b987f2a79)
16. [tandfonline.com](https://www.tandfonline.com/doi/full/10.1080/10293523.2025.2553254)
17. [medium.com](https://medium.com/@navnoorbawa/the-black-scholes-formulas-two-hidden-numbers-how-edward-thorp-and-ken-griffin-made-billions-84aa014d02a5)
18. [longboardfunds.com](https://longboardfunds.com/s/Does-Trend-Following-Still-Work-on-Stocks_.pdf)
19. [researchgate.net](https://www.researchgate.net/publication/381803570_Smart_Beta_Investing)
20. [adaptrade.com](http://www.adaptrade.com/Articles/PositionSizing-Paper.pdf)
21. [arxiv.org](https://arxiv.org/pdf/1612.02985)
22. [unknown_url](unknown_url)
23. [pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/PMC8646943/)
24. [pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/PMC9114284/)
25. [finrafoundation.org](https://www.finrafoundation.org/sites/finrafoundation/files/2024-10/market-volatility-general-research-brief-final_0_0.pdf)
26. [a-e-l.scholasticahq.com](https://a-e-l.scholasticahq.com/article/70291-the-dynamic-impact-of-world-pandemic-uncertainty-on-stock-market-crash-risk-an-international-study)
27. [pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/PMC10869766/)
28. [medium.com](https://medium.com/coinmonks/crypto-markets-run-on-inverted-clocks-how-session-patterns-create-alpha-with-256-returns-e76a4c61e79c)
29. [blog.mexc.com](https://blog.mexc.com/news/why-is-crypto-crashing-understanding-the-market-forces-behind-cryptocurrency-declines/)
30. [arxiv.org](https://arxiv.org/html/2510.05711v1)
31. [cryptohopper.com](https://www.cryptohopper.com/blog/crypto-volatility-managing-risk-in-unstable-markets-12772)
32. [ey.com](https://www.ey.com/content/dam/ey-unified-site/ey-com/en-us/industries/financial-services/documents/ey-regulatory-clarity-is-lighting-a-path-for-digital-assets.pdf)
33. [macro-ops.com](https://macro-ops.com/richard-dennis-turtle-trading-strategy-explained/)
34. [turtletrader.com](https://www.turtletrader.com/rules/)
35. [howtotrade.com](https://howtotrade.com/wp-content/uploads/2024/10/The-Turtle-Trading-strategy.pdf)
36. [medium.com](https://medium.com/@trading.dude/discipline-over-prediction-why-the-turtle-trading-rules-still-matter-f0f1d400d58d)
37. [litefinance.org](https://www.litefinance.org/blog/for-beginners/trading-strategies/turtle-trading-strategy/)
38. [scispace.com](https://scispace.com/pdf/the-mathematics-of-money-management-risk-analysis-techniques-114ddzwr7r.pdf)
39. [scribd.com](https://www.scribd.com/document/972712536/Trading-Strategies-Market-Analysis-AsymTrading)
40. [cryptogates.io](https://cryptogates.io/crypto-strategy-engine/)
41. [quora.com](https://www.quora.com/How-much-investment-should-I-put-in-binary-com-when-using-martingale-strategy-using-binary-com-bot-to-take-profit-100-day)
42. [scribd.com](https://www.scribd.com/document/33566667/Mathematics-of-Gambling-4)
43. [quantifiedstrategies.com](https://www.quantifiedstrategies.com/position-sizing-strategies/)
44. [learningcenter.fxstreet.com](https://learningcenter.fxstreet.com/education/learning-center/unit-3/chapter-3/money-management-models/index.html)
45. [quantifiedstrategies.com](https://www.quantifiedstrategies.com/optimal-f-money-management/)
46. [tradingpedia.com](https://www.tradingpedia.com/day-trading-academy/further-talk-on-money-management-money-management-styles/)
47. [researchgate.net](https://www.researchgate.net/publication/315743262_Money_management_methods_in_trading_and_investing)
48. [tokyotraders.net](https://tokyotraders.net/optimal-f-and-secure-f/)
49. [tlap.io](https://tlap.io/en/optimal-fraction-in-search-of-perfect-mani-management)
50. [thomaspfluegl.com](https://www.thomaspfluegl.com/tips/moneyMan8.htm)
51. [instmath.rwth-aachen.de](http://www.instmath.rwth-aachen.de/~maier/publications/Hermes2016.pdf)
52. [reddit.com](https://www.reddit.com/r/algotrading/comments/j0e1sd/trouble_understanding_optimal_f_example/)
53. [medium.com](https://medium.com/@navnoorbawa/how-hedge-funds-monetise-options-time-decay-theta-harvesting-the-volatility-risk-premium-insti-f85b987f2a79)
54. [quantvps.com](https://www.quantvps.com/blog/automated-futures-trading-strategies)
55. [gov.capital](https://gov.capital/insider-secrets-to-scaling-your-futures-trading-success-comprehensive-analysis-of-pyramiding-position-sizing-and-institutional-growth-architectures/)
56. [scribd.com](https://www.scribd.com/document/317901130/Mechanical-Trading-Systems-Money-Management-pdf)
57. [miniwebtool.com](https://miniwebtool.com/position-size-calculator/)
58. [bitget.com](https://www.bitget.com/ru/academy/12560603877651)
59. [bitget.com](https://www.bitget.com/wiki/are-volatile-stocks-good)
60. [bitget.com](https://www.bitget.com/wiki/do-stocks-change-overnight)
61. [nurp.com](https://nurp.com/algorithmic-trading-blog/top-short-term-investment-options-for-algo-trading-bots/)
62. [jonathankinlay.com](https://jonathankinlay.com/)
63. [medium.com](https://medium.com/@navnoorbawa/da-vinci-trading-volatility-arbitrage-and-crypto-market-making-deconstructed-507755031666)
64. [136.175.10.10](http://136.175.10.10/ebook/pdf/Day_Trading_for_Dummies.pdf)
65. [publikationen.sulb.uni-saarland.de](https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/23447/1/Diss_mkPublication.pdf)
66. [portfolio-tools.s3.eu-west-2.amazonaws.com](https://portfolio-tools.s3.eu-west-2.amazonaws.com/wp-content/uploads/2025/10/17041013/Master-Project-Haijin-Zhu.pdf)
67. [research.ou.nl](https://research.ou.nl/ws/files/43750228/Proceedings_2021.pdf)
68. [higherlogicdownload.s3.amazonaws.com](https://higherlogicdownload.s3.amazonaws.com/TABC/2a6341d8-64a1-4735-9839-09a0094bc417/UploadedImages/ABC_Annual_International_Conference_Proceedings/Proceedings_2021.pdf)
69. [chain.link](https://chain.link/article/tokenized-derivatives-explained)
70. [capital.com](https://capital.com/en-int/learn/glossary/24-hour-trading-definition)
71. [square.htx.com](https://square.htx.com/htx-research-latest-report-on-chain-u-s-equities-from-crypto-perpetuals-to-the-shift-in-pricing-power-2/)
72. [medium.com](https://medium.com/@alymadhavji/the-96b-settlement-tax-wall-street-cannot-ignore-7128fd4f85a4)
73. [arxiv.org](https://arxiv.org/html/2510.05711v1)
74. [icarefinancialsolutions.com](https://icarefinancialsolutions.com/Academy.html)
75. [arabictrader.com](https://www.arabictrader.com/cdn/application/2009/05/28/pdf/v202/07A60519-8570-744D-72D5-2C1D0C69349D.pdf)
76. [thrive.fi](https://thrive.fi/blog/trading/trading-books)
77. [dokumen.pub](https://dokumen.pub/download/trend-following-masters-trading-psychology-conversations-2-0857199994-9780857199997.html)
78. [nexusfi.com](https://nexusfi.com/a/latest/)
79. [researchgate.net](https://www.researchgate.net/publication/303404507_Using_trading_mechanisms_to_investigate_large_futures_data_and_their_implications_to_market_trends)
80. [researchgate.net](https://www.researchgate.net/publication/262002002_Money_management_with_optimal_stopping_of_losses_for_maximizing_the_returns_of_futures_trading)
81. [arxiv.org](https://arxiv.org/pdf/2010.12508)
82. [quantifiedstrategies.com](https://www.quantifiedstrategies.com/position-sizing-strategies/)
83. [learningcenter.fxstreet.com](https://learningcenter.fxstreet.com/education/learning-center/unit-3/chapter-3/money-management-models/index.html)
84. [researchgate.net](https://www.researchgate.net/publication/392759488_Study_of_Pandemic_Investor_Sentiment_and_Stock_Returns_with_Machine_Learning)
85. [stocktitan.net](https://www.stocktitan.net/articles/volatility-clustering-explained)
86. [xtb.com](https://www.xtb.com/en/education/average-true-range-atr-indicator-definition-formula-and-how-to-use-it)
87. [ijfmr.com](https://www.ijfmr.com/papers/2026/3/53679.pdf)
88. [arxiv.org](https://arxiv.org/html/2407.13685v1)
89. [alfatactix.com](https://alfatactix.com/academy/risk-management)
90. [ijhit.info](https://ijhit.info/index.php/ijhit/article/download/82/83/377)
91. [breakingalpha.io](https://breakingalpha.io/insights/position-sizing-algorithmic-trading)
92. [arxiv.org](https://arxiv.org/html/2508.16598v1)
93. [pm-research.com](https://www.pm-research.com/content/iijpormgmt%3A%3A%3A44%3A%3A%3A3%3A%3A%3A25.full.pdf?implicit-login=true&sigma-token=KXuJ336r_VIHN6cuV3b9m7NhyncrdwE6bAASJOB1nZE)
94. [smallake.kr](https://smallake.kr/wp-content/uploads/2023/04/SSRN-id4422374.pdf)
95. [136.175.10.10](http://136.175.10.10/ebook/pdf/Day_Trading_for_Dummies.pdf)
96. [publikationen.sulb.uni-saarland.de](https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/23447/1/Diss_mkPublication.pdf)

**Sources:**
1. [tlap.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEJAbpINIsGtfJTsEeypebs8Qr5_DZT9M6nr44dAzUCV8GUcA4Y1h5MVYMc1VQCtDWJ_abq7iwwRro4KUyNIbKmToyNpEzM4Y2Kr5XTioTE7Yq7jQ8R3LubQ03vCjSPcw_5eATe)
2. [scispace.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEdTjziPJtkqBN2kB_7asIJlQCaPV8ggH50Vi1jiTF703zT4RWV93AgVieO5jqlaOu-PeJSlyQiDOo1BkSv0od4DNUexdpjkXdmP_rUGO8yivMR8Fn6fWzTEJ9A6ywSsoUhC-WELxWMxlPiDMajvauCU2j_17i1Cp9V8buLha2OiMkwsIJYdc9T-gWqzg9DCKEJHV1Y4BeM9s4=)
3. [scribd.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHglEpBacipfQOjIO_cliznIub9IbaY9PV8dw6GlaX-NbhTo128T6Scqq71RXvXcKzw-LbUkk2Zy9LLC7MjQSV-uTzNY7bQxGibuve4tKNUkJ9uj2HmdGNlVke91X-narKSWlGHKuK5ct8u-pMn_JSzXIXdx9inUA==)
4. [gov.capital](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHq0ZEiUVrq0-MyS3fOxHvDgpCIm9RVamiMZHv3Phz1JOAEF-0H2-Z6mkD1gNIY0M_gym-tdqEh4rg4oJ-Idf701WWWs9go0ZtbpdHaefnwmPOf0dW4XxZKBUk5fv-go86GiS1-Lj-v0BDPIU5wjFKXKFL-KHjCRSGmQvKk9yAUrfW0n9vsNjYP1FVfGqcKXbdYhaz-vf1tEGjDXVVEB7EdVHqFCpXUXl2DB5_yP9NHi1RvaIzwmSo5-xLy5w79Ve3bm_RDz7o3as5ph6sVJwsENCwwXsJQ3DHob2df7lM=)
5. [ijhit.info](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHVY2jxi35VcLIVTdELLgkjiRW18OU8Iu8ZgDkw15Hrhfe3INh0MjBZffpQnL_FJJVLXgfP1GpKsOaOErYRshpj3u4KtQwI8AayXxGbadIfQpwQ6uLpNjXsS7f7F5K1bEKwskpyHcbEavoWDTbl3Sa6qUs=)
6. [breakingalpha.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGTGfUixnu8PdNYbOONFRFaCT6zYIh56o2n2k4mBFSGXmFJmIOI4xekaRm6vBxcgfi12XKdgMH9GahYhBV4J-WjIJJipr9PTdgZipviMOTrp9wOe56K1G4Ebq0W3kOgOVSxgKfgfPWudzUNOweSr7GoNf6D3j023rS5NQ==)
7. [leelootrading.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHs2SKg6HVz2s0lJauH40xVWN_Afrx2b89gR_sdpklH16IULsZ9i_BAMoSpmsiaLnyek5XxRepOh5PZbPxRZbHuY9VRc8Irvkr3DL_X_dX4I7NYYNLmjwQP15r6ATrzZYxyF8h1Vh9ogM4pkMG2CHG7WHtEfo16Rgsqn3Ob09SxMsc=)
8. [quantifiedstrategies.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHGtcPnNWksH6Zags5f55VhDifuAqmHOnnuCgzeG2Fz1O7RhF2J2fFYsy6hLyis71c1qBuPf23ji2FK6kCt5W5ShEo3qidimG1vs7Z8i_DcArHfjD5kyjqZeY_1Di9meLMIztyVj8WtkMQua2bk_c9Q7AQAKfk=)
9. [miniwebtool.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGZevrbgMUyZxapcuKmuvO3dAmbiK_RHkWPx6bGFySnQZsGlMOsp8zDo3OUNeqbkFKJMFTE54aA8f_4rf5FWXvAmV-tTvUe5QeG4qYq1RM24PlbYN1y1aT9v8fRYsAaecwWK-8R2lQ=)
10. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFt17su6aKLdFiI3_MlVn_JNhLT2XOEdJtrw4-7hz9X0Lg3sqE8zN1SA5rrvzpM9Qx2KrUvsem609HmDizuQL4fzsLnnTqaWT2Dn9836Dyqa2LL9XHUylxk2G_9Ds71bsxqOJ2MQvQnV5ECtQ2lOF2pAFYLZAH1vGcayqE7DIc5a5Ub7FnCCpGNOkTuRogIZjugMIkqWU08w7ibXbaKxGZ0jQh8nJp_dXNxe1J1xBYRRHCy7HJu30VIy0wYSLvT_g==)
11. [fxstreet.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFSjCUULmONFthKUi6q1etbuy7gqugXzRr9s2R_kwY0zXASHYaNtLzge21aBqsKycyySPv57HyK8-wElHh_y7QHES0qM2C9UJ0ImJGnpNtt-fh1LzjgpfhwHMiJDy7zcQd5pn-arTWw4znyZfArPwQSXZE3IB4dHLeolKQ9pL8YeV7l2PxeO_lROhqmZHHcpDMZUilXoHZtIMBDs1NqkURnaoW7eJ_K)
12. [Link](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHXuoupiucAdt-MRriEg9munl6jeVVTS_QQ0D-4r332aPk65_ucBBdjsH3FyhiK1wbpz6TEco0LKXD7r2hySQqm)
13. [tokyotraders.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFO0pEXMa3mtCA7yxsb0FzlWVE-quiWgOh1o8NQAE5AgONAK4t2SBntGe_osxs6AO2K7-ocZDZRFepDte8nHrN-8rh6jt6VT5A4uBebvR4lD3Ck2ON_r9IMlmuldBIgOBMPZTQDLg==)
14. [researchgate.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHIB_snDbGMabuDimML1udWPGefNqvZjP8Oqrb-Z5VcomZzFh4ZOsDjrwtYuX_1jfN8wzKqyBXrIhc5FYztXQyAsCQnG_wyespo1VO18e3tLrODcrd57LirOHSEaWkIPsEwiSR1zmxFCklWcn6ZJelhRq_MsAVIVsN0gbB4XMZ9UcYfJlDpNUNTryhIAhIDPPyHExvPLJKCxBIfxtdv3gAjUGf9aw81BS_EH69gYy2-K2IMRccnGAwc251FC8s8vsXqGEfs2A9QpT-0KA==)
15. [Link](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEjw32oBQUt3OZNK9H_k_2QKeaw5m0W_CBkS6aQ_nFey-sC6m3Y9odxRVR3UQx80P2rO7JnX6MgswCXd5Lijz_YG9u9QVMCKmA0jNP6_T-JJLbHO_h4)
16. [quantvps.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHr_8rF0F1JRi2EPxlb6rPbvNirOckdSxLwHF66-7BpnohwihcSnOWEIKP4r5dAMntCnoHooIfIsbBv801dP4CG1nnDVN9UvoiHwLP1LvfOfYP8lUAZzQIYdWyJNpUtNQ43RdcpzOvsBBNje2o-LMGPNOOeEipXsQ==)
17. [bitget.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGVkJghYBRMNIhT6516Nx-5v8wWALYza4k-RU-gEj8RIz1BRYMGKWilNGdKnGz2qeoXi1yJDvcCQH8kDlYnCQeYlumTsfyvUNw1COub8NQt-8YWdTmMxu1GP8eT-qLcQ1Kaz_AxpQ==)
18. [reddit.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHqvAp5tbYRAfl0HVG5wywVmYE2Exu9UO5MUJqwjrjwRpaLg100pWZvOTB2dUrXD_F57jhUcSBlz73lPQCZtmU27gaNqdZD9o5Fmy4DfubQeK_p-vbzO3mf8TdyUydKRNXF_eZzW9dNFvDWr9ZHs1-EXAKN22ec8DsxBh0pxtq8mB39rhtWlXKdT3uWPSC10PIOlg==)
19. [nexusfi.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGXZwfaFplfLb00DLFu-JLIcG66BuAgo-4RY6VcEARXuwqbcVXxpCmbmRI9JCj-AVxGbUI010uXLRxd85UdHQ4mAkIoHWZiL1JG8TltiT4wCbdn)
20. [thomaspfluegl.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFvJDp-RWWSlKQbsgl_XTRlHjCtnviqMnYc1h1G6gYuYDcnOl_wAfzNWBoRVU_XgZ0B0iQkuEcp2Wn4xJIBSuzlYj2_a8ZQJ7NmgQRtlOAcj8Wk6LhGV2XsxFmdf8CUZPWOdyuLbQ==)
21. [rwth-aachen.de](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGoVnPJmMcuwR9TD_KD3ofSnxnOzQSmSikG_12qne98_n5ylJXiDGlCmMeisWaorTmI1RDdsjXV0BTaOd2-tfnG2Jpd5b0_nNI7v_nnslXPbkGnM_kJNsAU7L20zRQ2ODmp28iWIqBPqqz4T_RwbG4xYqWz4hPle2ykZA==)
22. [tlap.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEWKu1yjU-o0mFpOUaNjyg8LDusBecKmF9aA8sVwtOYGgPradHJAoXlfq4LzxuI5JK_GaAWcIjaDljG6gEB9HT76b1UqM2vb0tW9_F352O1F4V9NyyH4PMxvJU8qh4WetbNOyusk_zXXJZdzb7lx0nzWxJ_9B0XCf56ucGl0w==)
23. [pictureperfectportfolios.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQH6cHBrKu6Ae4FH4d1ahY4--oI8a9VuZWcMYe7UKoSsM-ocZypWSxBTkjpoAhHI0RVXrt7g_K5Xnf3aaHRPlGJhYToYR2RlkYfXv-GJ1Xb5HzK1RX8q3yq79KyPbsR3WBnSFoaKSujBtWD6uMZ9h60LPfOGgojBAeIsYI0J4cN4f8B0xqEQ6VnMoS3QpFkwVdxwgjd7mxU=)
24. [quora.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHtJOgMKIwbJOj_nBiVVNZdayjoQID9IhGDmzApyg6HKF8OYkzEPaXhueaOA5dqPgeRmAIWGOIOL9QoNTFE_TdxmVUJH9dW6zTnfrkXsFQ9VunTlb3e0bYivmWqHAxkxRzr8I4GZingRQYpBJUWgAUzfgdOiwOOuih94g20F1FMcDm9YocoVdah)
25. [quora.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHNGAme8DL838dvu6v2_IrFRupclHtaLVDSQd8Opu-n7snJJTSi_cofUCcwnNmu8t9bkT-_jKk8er3EdeATXE2HJ2JEhUULO_7FLBj3Wcc_JsSHcaHF8GNtzmgjsD2weUAbgugqr6lB9wAHMVERBp3cqyhDR4ON)
26. [aquafutures.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQG_Qq6QLJTP9FbXuV5Sretzosy8nchV0Bsr-tUbYiVCzlXv0OFdtsXYwLuFANWfBcCeyfE1uQsFpd3rFlgkB90f08tjP_ZvaDU_r4WPDqYKY9vBuwZzf-Ted8VUcdMGgdyjAm2DfwJHCpFQiKRtyValvEniu3s=)
27. [adaptrade.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGDOvOfjESUUE1anAEhjhA7dbOtZ_gfx5I9jcykuRasunYHdKvVrml7uMZ2Q4nbu3t1QK96whps7jwa-u0S5fzYrcddYkSkFOdLG7b-XmHOTRIRRO0rUxzueH1f2i--WPGaAVC--CHyijCw7fXwtfM=)
28. [tradingpedia.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEcxGZtJz_FoZq1UUXiw3vnx267caJFmSDBr56AcImItcigun4XUPVKN089Y1EAQXYk3gKFs_146387zZIEKEjTVugVxdve24tJqGA3MOgFX7ligsS25MGtpvB_6S5er6JB0P7BNwmhwqEnvlpA3iEdBrCc9UUP1iQXDhMMPE9Q_38nIHEKL8HdLRZ8fRcQMrvBFW-tS13LON7KZPB5xK8=)
29. [tradingblox.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFdQP9IZJpkE5SaTj7Dt0IORa6jM0v9cuOwBVaUBQVsVku7UAXFB9QTpNIN8Qo11-u9pKSXEwY6mDuERZE9O4x4UNzJ_eGenHEHzxqR5dkO8altSjpbfYRU78Bhc5BenZfNPSRDOTEpB9BK2aga)
30. [tradingblox.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEtfeHpDVGy8TFE5tGAuSjlvjCIQRI8hZIamGrXh4Ps6OcQAtxjpEJNE_G1pEkpzyKEH0uPAFPjvvbxPE0B38pzhJIPztSm_XIines_kB_nd8KCEFS6c2OHqYjxL2Ag9gtFF2PR5NloyjMwzSEdBj7GS8qQo7Y=)
31. [scribd.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQE6Fscdp49a5-mrE8xwqolW_cVw6Q_rKC4H6obuw6kQtEN-LucAjKrjp-AUIOF7QneAnDg2kjws0eQQutFlZaoB49nhi7oEBEP0TSRQZ2zK4b0XLRTG1eJ30oUpT60zxlIrI9WZ6ymbkjq7GFyZx8XHi2lqBh90DA4xiPSFQRQO3XPVdVW4C4XihGAHYvyK)
32. [stocktitan.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFjRMAIDC1k00J4sJ_M1R_gDFAKvEG5lX8EyAJZ3ahJUu1uwiBtWHDVsQHnD-YWH8RhKWUaxzR0bp_RE060lnQJHlRIQn6bqk6_cL4Dtg1p3ePt6IixSl-HM9kWmRNhPBPXDZOkE9f-ztfM7z-EJ0Ymv2kNA7vBS3E=)
33. [xtb.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGJTuBz_2ODAgTh8Uxfn43PreA_GFbgELfM01Cr4X_1rcRJBkPXO5XT8xMw7u7tr-wAxXF5EO2cJI_qxRzHaT83byiuf-g4JG4MXUDUlIkLWddHpvLI7xd7sHLMXXWccaCpHjnx2SFUFIwRP2Cjdgx7to5OkDmmcxhHuxXKu8pED6m1I8YpLKqRqB4SJSmIRhvJMzFkbGYO3cIioA==)
34. [macro-ops.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFG44ikPvQIczDvPa09uUH9Yhs75l9oHY_BAxBwPo8Sq-ectxTGZoqfa0iYPWjsX3d70y4NJfIvzNA-E4RP9itPKC5KtgRy4yQCgLNgSBgVpdHpGvNyhr25SoFVVMGNrSwHgevAS0jCYGkThDe1_1fHu76TcJn-4D-OXwdz)
35. [turtletrader.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF6yDXMRAW2IXb5DOoM-lkmrF1roRSgAHmxgOQ0q-FOuzRw5Nf6eG7blRYoKeZoV-S7_D1VL6O-Mz0Q54FE1VxfcdcySx_j6YexfoxaoXdKeKwJtcCMMeyy)
36. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHMzgXYhOG9xieuw2EEBTpV3WV8Lp6xKMZXBe2Mmh52qEKCCL7FcEF7xiNvMs5oxHs1mqWNORN6Z0WEtCZXx4Mvtj_JqW1H9rSzAAE9rfEVeIM-VqpUAQUMWtxOX419zWrCg8Rvs-FVY_oxmgM8xT2CFfdKWS4kWO_hv8yDPyldXnjyYtuLpzVkzvpX_J6j2SnZHEwlyxWB6xKo42-vCYQgwDkpWxAPVg==)
37. [howtotrade.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFEOG2g6kzd5IEzoFrKDeliVNubt_kei_r1-b6hHP54-KF1KiOI6r1OeuyiAZeevn6_xkoYr8PGwm38yCz7jTxYcS5SRqbZQTwHvqxIBn7wM0YLk6kb5V0HDVCUMuLZRtxnsuo_HbeflZoIDnAjL_iTc02enjGgVf-_JoSm1V60MxBzoNSC7g==)
38. [tandfonline.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGjJOdExUTFg6sDpBG8F9CSstfPZpgwa7wuAXL6L0y_Y3_EBWzMbc1BOdPBw5mQHQcfovZuVRhPhY8iPnFTdc97m5W6FYMrTvwOirQ6bcw763BtQI5qMP4L_XB-Gp0mNYYMnIgsnMgWVpPL5spLQ6mkovOafiJ82A==)
39. [researchgate.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQH39hR6opzTsvgKtY7TzwX5BGiv1pogHH4fCWIpo-GPGbEzt4ZKpwYUYQZ_neC92xyCRtzFbpEJ8mVYvrrh793v9uQdUyOTsBrogdikjZkS-CPcLqyTuAf7XKDiceZx5hpxu4KnckxNqnqdpgEWd2rkvp48YpF-g8OFJAPDUbnKmQQbkjxyX_6UsjnSJo0LtqH-PPNZGlNZlBaoL6NNRnb9C3QClE16rvW46MmMc2yY_cO4xRk=)
40. [ijfmr.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFi49VaRhv9wlbHWgD3DWqgURVy1TLjiZM1Ch-UyKWbbtGPeKOJnLMfa1qXo24FdbrSBqJir2aEl39o_H4iIGa8vJYmHbDpz2r34eVwvT8iScoKfiQzpohxFB3ypsS2sR8bgw==)
41. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHdCaxe8EUjG0zJIte0JGK4sP8ZQzWyKv3ZyFN3hWlp_zVZD4wgzzAuVIW7t6vPbCFwDbUY6tulmTk6FzR3dUDJ0AR4lOC2jAM1ZNWx8FYxtRVEjAbcIA9jJgd6OzzGUJ3wPR-Jptovwg0kD0sTSbGfC2qMaVR9v-JS4f9BmLPyYwa5mXcmrk-QC07p4Zj_pip69HBuZTqTXbWfJdIhjjT_4S6ZQAZ4qv6gZzIzRZjy77nTfmgCQOPGi2c4YUOsUKYo)
42. [longboardfunds.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFgyQgvTXwuC25Iz3g1tiuCspQteoROD_B95W3VUB0jlVAe4JTDuwZS0kLFb888mgVnGXNyKnYW9QxvgiSparb8FRPcGOYf-aPJw35h_-b_iSE3oGY6rtYXhYj7YX5cZLryG47JRH2o8SgQZZrFzRR9RXf_5iHmOOc0cjx_-sSAwQ==)
43. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHVi6k9hB8yHBQw4uUl_dLIeKkR8IOBpt0OnpDh1v1ZaUa5qCXfzBhzaEZggKzbZyUPmdU7v3_aNYyNnld_EajbJu9i7AaoJYztgUJbGAdlNfwKXqH_S_kOoMW__JVSF8MngEtDguf-wfyUDHkuqeDF9_Tz_tJoi6IPNb4Qsx9-K3DEKNuTT2_8nIDgo-UE7_iI1wEGxqlUB3fbtldknybA8tXUcMFY0qkTpsxjFUQ=)
44. [nih.gov](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFoo8EnRsAwNlzrj7BS__1giLD4qxn5aK7eN0IY5g1uvu0cEppc5ieQ7Ocnm87zPFuXDDPaRxDezhOJCrrJRdwcH7BS79OlbYYG-ieisjBUIysnCiLYp4iQieBlSDiErSXSlKsT4pM=)
45. [nih.gov](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGcOvM-ksX7VBbH37QpKjvSzEd2K2MZ68k_5sNrYTzxettdPl3zYNWdnDgUA0vymI5vdwGZpWBMi1HjzHPMeJ1gCguNTvsRAC_MJLRE-rSY9QIVUciPKPYBZRM3X95sTRrIoMpQyyc=)
46. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFptd5yUpQvQ4bcJ8a3gcxlq3PJII9YN8mFZeeZyKoIEZ_q3fLFeI1lLtZoj-ZtL3mqxmUMFTWY358Ynd5r6kYfUKTTbe3lPZgG0iG033oPSc1bpiEJasHt)
47. [bitget.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEX3mYgNsW97FWtRJSZEpQqn6SYzQz1AJKNXfsNR7KJ-9JsBisnMPZPBxuClCLQEPmxRqpRtrbeuvmoh_1FyX8evpv4P8_KLHNCahPS9ImJsYyHcJ1d9lryDyrg4G0zwl76WBsXMpjplq9Dpg==)
48. [nurp.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHYsJJNm1f8pJGrwLi3jft1-qeXMrboGv6gGGQ2VR61sRYWfqExCOXq237K4qjoBUl1swZpvKGY9UDh3WDHz6wxYt-GqCRjEdD8HR83SEc3SK3-mXFCyiCkFn1UiqNrCztuwOjpAejnqjwV1ZLL_7n4dy8HcOU8zpCYkA2Duj1a9-LPtX3u9qtEKUEFdVJr1fMa97HG3Xuv)
49. [htx.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF9R6bd_SpEmC2PZrHorSYLro97IBNDBuQ8mktEVihw6Cj4NrqI0-kQ_aAeNMQILa9xeIhRy8DRFEXJsM_7cg1WysHYjQo72tHPeu61jUSLhx81YsgrD95WCGrPJH8RlS7Cubd3VFPt0gzvj3MUNh84-in-GOpqULuF2ZWdyMJ9VfFTCU0k2hWWz_zZZBLo587kwyv-k3zI5iACKmo43hBbTCRAC2IFHfMUSjUQ593NjyFr4K0=)
50. [bitget.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEEpHEqi-c6p6BtXMdxGveTFw7GeqdXUN3mOIpL0XWjIMjeamAuvmVViXshd82gKY2ll--hCzeOpaycsL47kYeiGULhN3dCXW2Xz-HHNID6LtyZLwueRPDRmjVC5_6O1iaqXIdyr9tAjDo=)
51. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFn3m_vLGYTBioeR0--pYiLKAjnHWSKF-sJCKOEicfeLjS1uEPb6NuVjQqG_xca3v1YyZJy4RNBZJk0diN-qd5xPez3Hb_SYvH-OJIbjaNXHaJlUQycGtog)
52. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQG8gBW4plH8q5uXq2z6Pi_UxTxsDCgB77lU8T2g7IMUeUC_JI4zrzVhz5jxu4UygH5YjDACT_R1nVJp9y45eakm92lmwqORIyMP-MULrzIFdi2kMqh58TMY5q4_AfyjOrpdwqY1rsoktcH2Vfcv2KefbjakNcfqbhgNPMMCH-RrwpkJ78vOk2tBDT_Px8phBVI7tCLfygORfxAydd6VRNthsctq9vuEr_xSFc42_zNWd9g4Kx2r9YTu)
53. [chain.link](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGoCfWS73jGtvgRXea-xUwDVPphsFmLul2oGAtDTtYcbtaDO1T13_At7eWEGlNf6X-gZwfxy8vA3f6xRx7S9FCJSOHWGfCTAm04AmLTbXhm4pwQ0AXiheTJeJS0P3JEznbzxueZbWKnwBskN9kTPxc=)
54. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGegK9QyJ3dDV0MmwW7Asu57mBm3nIBhUk-iIq9druhwLLGZ5JYtbUH8DlVtzQhhdpauWB3SCyGcw1WVMT_yJFdBiClmX2JEXlr2pXBuRIXB49uzW0BPl93TOGDAXBal5KocPx5M-2PPsLJFiVEpofP0zlsMEzuuGnWht_ZYYW1axysBLT2DwE2mdCTTm9-tUN5rw==)
55. [mexc.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGc19uung6JNyIlE9vNUkqh1t8tdmvJMPwZBYVwggBmhWEk9adN4NeEHJnkLAetDFZcsWXhvyd2p_eYUMKe52DdOGxBTvmJwOvXoUw8XayVqfAWF_Vj1sdhMeQngIeFuVPaG0nULfw7cvspIi9KKCSgQDhrIP33XgfjPmPS2vFnEKhGCo0zrwjdLNApMfBHV1CFVBXSzvKb50CK6XCuf-l7XZGlUU7N)
56. [ey.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGG1tueNeTdJaB2arXdc9knpttgKhfWf4CNOcxtfVVt2KzaquRksRuITDo0kbAam9PiipVj3-F2dxqZkhSI84f6KaMgzB7UTtrzVumQV5uzkw3PhOmhRoq25eHe2tYH8inRVUVlJdUKSgCTCjUDbTjzOCDbbe4_FmT0Xnrdlia4mGyfTF-56fU46MSpPHQRgvIN2VCYKqNlBlKqii6DN30IpIVSeJj3-iVyoxTO_aDWnge_YRaPZZ-xIUnt5ZsSiYoLJRHPx-hFnPvnFCeiF0sppJc1KxDzjFbY)
57. [alfatactix.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF4cFlOJ02JEmF0Ls8l3Pt92qfe0xGTf0akvrhBZHGOpMmT-slhoY4Qg42cY3m6o2Yj9koxacmsFVEKpv_W9LS1OUr3TETbIm4FFZG-3HHSNfts4dMfF_JlLxrGqCQWyN4xhUI=)