凱利公式計算器

分類： Uncategorized
- August 31, 2026
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Optimize your position sizes based on the Kelly Criterion formula to maximize long-term growth while managing risk

Trading Parameters

%
Your historical winning percentage
:1
Average win amount / Average loss amount
$
0.5
Lower values are more conservative (Half-Kelly = 0.5)

Kelly Criterion Results

Optimal Kelly Percentage
13.8%
of your account per trade
0% Conservative Aggressive 100%
建議倉位大小
$690.00
Based on 0.5 Kelly (Half-Kelly)
Full Kelly Position Size
$1,380.00
Maximum theoretical optimal size
Expected Growth Rate
2.37%
Per trade at recommended size
Probability of Ruin
< 0.1%
Chance of losing all capital
Max Drawdown (95% CI)
12.5%
Expected worst-case scenario
Risk-Adjusted Return
1.85
Higher is better (> 1 is good)

Growth Simulation by Kelly Fraction

Kelly Size by Win Rate/Win-Loss Ratio

Kelly Fraction Comparison

Kelly Fraction 倉位大小 增長率 Max Drawdown 風險水平

About the Kelly Criterion

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets or trades to maximize long-term growth. It was developed by John L. Kelly Jr. while working at Bell Labs in 1956 and has since been adopted by traders and investors to optimize position sizing.

The Kelly Formula

Kelly % = W - [(1 - W) / R]
W = Win probability (decimal)
R = Win/loss ratio (average win ÷ average loss)
Kelly % = Percentage of capital to risk on each trade

Benefits of Kelly Criterion

  • Mathematically optimal for maximizing long-term growth
  • Dynamically adjusts position size based on edge
  • Prevents over-betting which can lead to ruin
  • Provides a systematic approach to position sizing

Limitations to Consider

  • Assumes win rate and win/loss ratio are known accurately
  • Can suggest aggressive position sizes (hence the half-Kelly recommendation)
  • Doesn't account for psychological factors in trading
  • May not be suitable for all market conditions

Best Practices for Using Kelly Criterion

  1. Use a Fractional Kelly Approach: Most professional traders use 1/4 to 1/2 of the full Kelly percentage to reduce volatility while maintaining most of the growth benefits.
  2. Base Win Rate on Historical Data: Use your actual trading history rather than theoretical projections to determine your true win rate.
  3. Recalculate Regularly: Market conditions change, and so should your position sizing. Update your Kelly calculations as your trading performance evolves.
  4. Consider Correlation: If trading multiple positions simultaneously, account for correlation between trades to avoid overexposure to similar risks.
  5. Set Maximum Position Limits: Regardless of Kelly's recommendation, consider setting absolute limits on position sizes as an additional safeguard.

本工具計算什麼

在已知優勢下，能令長期資本增長最大化的下注比例。

公式
f* =（bp − q）÷ b，其中 b 為賠率、p 為勝率、q = 1 − p
計算示例
勝率 55%、賠率一賠一，則 f* =（1 × 0.55 − 0.45）÷ 1 = 0.10，即動用一成資金。
何時使用
在已量度優勢的前提下，計算倉位規模的理論上限。
常見錯誤
實務上全額凱利過於進取，且假設勝率估算完全準確。多數使用者只採用四分之一或一半。