How Kelly Criterion Affects Trading Allocation Strategy

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Generated Jan 15, 2026 at 12:06 PM
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Market Measures is a weekday research segment that tests trading concepts with real market data. This segment focuses on the Kelly criterion and its importance in position sizing, potentially even more so than strategy. The Kelly criterion helps identify how sizing mistakes can limit growth and how to avoid them using real options examples.
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The Kelly criterion is an interesting mathematical theorem applicable to both poker and options trading. It relates to concepts like expected value and implied value, making its conceptual understanding crucial for traders.
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The Kelly criterion, presented as a growth formula from April 25th, 2025, helps determine the optimal fraction of capital to allocate. Its purpose is to maximize long-term growth while simultaneously reducing the risk of ruin. In essence, Kelly aims to maximize growth and control risk through proper sizing, based on an existing edge, implied value, and expected value.
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The Kelly criterion formula is expressed as F = P - Q / B. In this formula, F represents the optimal capital percentage to allocate, P is the probability of profit, Q is the probability of loss, and B signifies the net odds received per dollar bet. Notably, Q is also equivalent to one minus P.
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Using an iron condor as an example with a $100,000 portfolio, an 85% probability of profit (15% loss probability), and 20% net odds, the Kelly criterion recommends allocating 10% of capital. This allocation is deemed optimal for long-term growth with minimal risk of ruin.
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The risk of ruin is directly tied to bet size; if a bet size is too large, it prevents the trader from absorbing variance. This inability to absorb variance eventually leads to the depletion of capital, even if the strategy is otherwise sound.
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With a 10% capital allocation, the sample portfolio is expected to achieve a 25% final profit after 100 trades, with zero chance of depleting capital. This means a mean final value of $125,000 (a 25% expected gain), despite an average drawdown of 37%.
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The significant average drawdown of 37% indicates that even with expected gains and a zero ruin rate, substantial temporary capital reductions can occur. Higher allocations exacerbate these drawdowns. A Monte Carlo simulation of 100 runs projects a zero ruin rate, though more simulations (e.g., 5,000-10,000) would more accurately account for tail events and expected value.
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A key takeaway is to consider if the perceived results of a trade or adjustment would be positive if run a thousand times; if so, it likely represents a positive expected value situation. The ruin rate is the most critical factor in trading.
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Trading with overly large position sizes or using all buying power on a few trades inevitably leads to ruin because it leaves no room to absorb volatility. Even in years with strong annual returns (20-30%), there are periods of extreme volatility, such as a VIX of 60, which are often forgotten due to short-term memory.
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If the success rate remains 85% but the net odds change, the optimal Kelly allocation will also adjust. Higher odds allow for larger, more aggressive position sizing. For example, odds increasing from 15% to 25% would raise the Kelly allocation from 15% to 25%.
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Lower odds result in negative mean returns, significant average drawdowns, and a substantial ruin rate, even with only a 5% shift in odds. When the probability of profit is lower, it is necessary to reduce position size to mitigate increased risk. Conversely, higher odds justify larger allocations due to a significantly greater proportion of winning trades.
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Transforming losing trades into smaller losses or scratches significantly enhances year-end results. Increasing allocation, such as from 10% to 25% due to higher odds, can effectively double the average drawdown, underscoring that drawdowns remain significant even with optimal allocations.
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Kelly provides a clear mathematical framework for optimal position sizing. Many traders opt for fractional Kelly (e.g., 25-75% of the calculated amount) to reduce overall volatility. Option strategies are particularly well-suited for Kelly analysis because their probabilities and payouts are known before trade entry.
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A critical takeaway for defined risk strategies is matching probabilities; for instance, do not sell an at-the-money spread without collecting 50% of its width. An at-the-money spread has a 50/50 probability, so not collecting proportional premium indicates an unfavorable trade.
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The Kelly criterion helps traders identify when a trade is mathematically in their favor or when they should avoid forcing a trade.
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A study from March 28th, 2025, investigates what to expect after a 10% market decline. The general expectation is that the market will be higher six months after such a decline.
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A 10% drop in the S&P 500 within one month is uncommon, historically taking an average of 25 days for the first 10% correction in any 30-day period. These drops, despite occurring in bull markets, can feel like the world is ending.
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Sizing is crucial because a 10% drop can extend to 15-20%, leading to fear and preventing full commitment. Many traders believe a 10% drop won't happen in their trading year and size up accordingly, but it eventually occurs.
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Accounting for eventual market drops by staying with smaller position sizes creates a significantly different trading experience, especially in the S&P 500. The S&P is predictable in that such drops will happen but have historically recovered over time.
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Analyzing the 30-day window after the initial 10% market drop reveals that the market fell further in 32% of occurrences. Only two instances (11%), both in 2008, saw prices rally back to pre-drop levels. The average return during this 30-day period was less than 1%.
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These findings confirm that the market recovers much more slowly from large drops than it declines, aligning with the "escalator up, elevator down" adage. It is difficult to accurately time the market's descent.
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Market recovery chances improve with extended duration; higher recovery probabilities emerge after two months, though less than half of events see a full recovery after three months. A full recovery from a 10% correction represents a substantial approximately 20% gain from the new, lower price point.
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This year, the market experienced a nearly 20% downside correction and subsequently rallied more than 40-50% higher within a couple of months.
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It typically took less than a month to recover 50% of the original price, which is quicker than generally expected. Only one instance, in 2022, took longer than six months to achieve a 50% recovery.
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The period between 2020 and 2022, especially 2022, was characterized by heightened and extended volatility due to the COVID pandemic. During this time, VXX, UVXY, and VIX were elevated, with implied volatility at 25-30%, and markets reacted wildly to news events like presidential press conferences.
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A full recovery from all losses typically took about three months. While partial recovery is more realistic initially, maintaining some negative delta and selling premium at high implied volatility (IV) can be beneficial before full recovery.
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Given the median three-month full recovery period, it is advisable to lean bullish into market drops, perhaps by acquiring some delta or planning to offset delta to the upside for quick recoveries. A personal strategy involves picking up longer-dated deltas (one to two months out) to account for recovery time and market unpredictability.
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Sizing remains critical because unexpected events can always occur, and forecasts cannot account for every future development.
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