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Kelly Criterion Position Sizing Tool
The Kelly Criterion helps identify the optimal fraction of capital to allocate when an edge exists. It balances growth and risk, showing how much of your portfolio should be deployed for long-term growth. Use this tool to test different setups and compare strategies such as Full Kelly, Half Kelly, and Fixed Fraction.
📈 Optimal Capital Fraction
\\( f^* = 0.10 \\) (10% of available funds)
Interpretation: Allocating 10% of your portfolio in this scenario provides the maximum growth rate under the Kelly framework.
⚖️ Position Size Comparison
- Full Kelly: 10% allocation → $1,000
- Half Kelly: 5% allocation → $500
- Fixed Fraction: 2% allocation → $200
Insight: Half Kelly is often favored to balance growth with stability.
🔍 Example Scenarios
Coin Toss Strategy
Setup: 50% win rate, even odds, $1,000 capital.
Result: Kelly suggests no allocation (\\( f^* = 0 \\)).
Strategy: Avoid positions without a clear edge.
Sports Edge
Setup: 60% win rate, 1.5 odds, $5,000 capital.
Result: Full Kelly suggests ~16% allocation.
Strategy: Higher probability + moderate payout → aggressive growth potential.
Stock Trade
Setup: 55% win rate, 1 odds, $20,000 capital.
Result: Full Kelly suggests 10% allocation.
Strategy: Using Half Kelly reduces drawdowns in real trading.
Crypto Volatility
Setup: 52% win rate, 2 odds, $15,000 capital.
Result: Full Kelly suggests 4% allocation.
Strategy: Smaller allocations reduce exposure to volatility.
High Confidence Trade
Setup: 70% win rate, 1.2 odds, $8,000 capital.
Result: Full Kelly suggests 24% allocation.
Strategy: Use Half Kelly for smoother growth path.
Low Edge
Setup: 51% win rate, even odds, $12,000 capital.
Result: Kelly suggests ~2% allocation.
Strategy: Keep position sizes very small in thin-edge scenarios.
About This Tool
Welcome to our Kelly Criterion Calculator, a sophisticated financial tool designed to help traders, investors, and bettors determine the optimal size of a series of bets to maximize the long-term growth rate of capital. The Kelly Criterion is not a crystal ball; it is a strategic framework. Developed by John L. Kelly Jr. at Bell Labs in 1956, this mathematical formula answers one of the most critical questions in risk-taking: "How much should I bet?" By balancing the dual goals of aggressive growth and capital preservation, it provides a disciplined approach to money management that has been used by legendary investors like Warren Buffett and Edward Thorp. This tool automates the complex calculations, allowing you to focus on what matters most—accurately assessing your edge.
FAQs
What is the Kelly Criterion in simple terms?
Imagine you have a repeated opportunity to bet on a coin toss, but this coin is biased and lands on heads 55% of the time. The question is: how much of your money should you bet each time to make the most money over a year without going broke?
The Kelly Criterion is the mathematical answer to that "how much" question. It tells you the optimal bet size that maximizes your long-term growth while minimizing the risk of ruin. In this case, it would calculate a specific percentage of your bankroll to bet on each toss.
Who should use this Kelly Calculator?
This tool is invaluable for anyone who makes repeated, risky decisions with quantifiable outcomes, including:
- Stock & Forex Traders: To determine optimal position sizing based on their perceived edge.
- Sports Bettors: To find the optimal stake for a wager where they believe they have an edge over the bookmaker's odds.
- Portfolio Managers: To allocate capital between various assets or investment strategies.
- Poker Players: To manage their bankroll for individual games or tournaments.
How do I find the "Decimal Odds" (b) for a financial trade?
In investing, "odds" are represented by your risk-reward ratio. You need to estimate two things:
- If you win, what is the net profit? (e.g., a $1,000 profit target)
- If you lose, what is the net loss? (e.g., a $500 stop-loss)
The formula for decimal odds is: b = (Net Profit) / (Net Loss)
Example: If your profit target is $1,000 and your stop-loss is $500, your decimal odds b are 1000 / 500 = 2.0. This means you are getting 2-to-1 odds on your money.
What does a negative Kelly percentage mean?
A negative result is a powerful red flag. It means the expected value of your bet is negative (bp - q < 0). In other words, the probability of winning is too low relative to the odds being offered.
The tool's advice in this scenario is correct: you should not take the bet, as it would, on average, lose you money over time.
The calculator suggests betting a very high percentage. Is this safe?
Not necessarily. A high percentage (e.g., >20%) indicates a very large perceived edge. However, it also signals extreme volatility.
The critical caveat: The Kelly Criterion assumes you know your precise, true probability of winning. In reality, your estimate of p is almost always an educated guess. If you have overestimated your edge by even a small amount, betting the "full Kelly" amount can be very risky.
This is why most serious practitioners use Fractional Kelly (e.g., betting half or a quarter of the suggested amount) to drastically reduce volatility and protect against estimation errors.
What is "Fractional Kelly" and why should I use it?
Fractional Kelly is a conservative adaptation of the strategy where you bet a fraction (e.g., 1/2 or 1/4) of the recommended amount.
Why it's often wiser:
- Reduces Volatility: It smooths out your equity curve, making drawdowns less severe.
- Protects Against Overestimation: It provides a margin of safety if your win probability (
p) is inaccurate. - Almost No Growth Sacrifice: Notably, betting half the Kelly fraction ("Half-Kelly") reduces volatility by about 50% but only reduces the growth rate by about 25%. This is often a fantastic trade-off.
What are the main limitations of the Kelly Criterion?
While powerful, it is not a perfect system. Key limitations include:
- Dependency on Accurate Inputs: "Garbage in, garbage out." The result is only as good as your estimates for
pandb. Overestimation is the single biggest risk. - Volatility: The full Kelly strategy can lead to significant drawdowns, which can be psychologically difficult to handle.
- Simultaneous Bets: The classic formula is designed for sequential bets. Managing multiple, concurrent bets (a portfolio) requires a more complex multivariate Kelly approach.
- Ignores Black Swan Events: It doesn't account for extreme, unforeseen events that fall outside your estimated probabilities.
Is the Kelly Criterion a guarantee of profit?
Absolutely not. The Kelly Criterion is a money management system, not a predictive system.
Its function is to optimally size your bets once you have an edge. If you do not have a positive expected value (+EV) on your bets, the Kelly Criterion will not create one for you. It will only help you lose money at the mathematically optimal rate. Your profit ultimately depends on your ability to consistently find and quantify a genuine edge.
