Kelly Criterion — Optimal Position Sizing

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What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula for optimal position sizing — determining what percentage of your capital to allocate to each trade to maximize long-term growth while minimizing the risk of ruin. In the DCMM framework, Kelly Criterion is applied to each setup using the statistically-derived P_win and R/R Ratio parameters, transforming probability analysis into actionable position sizes.

The Formula

Kelly % = P_win - (1 - P_win) / (TP_year / SLm)

Or in the more general form:

Kelly % = (b × p - q) / b

Where:

  • p = P_win (probability of success, e.g., 0.60 for 60%)
  • q = 1 – P_win (probability of failure, e.g., 0.40)
  • b = TP_year / SLm (the reward-to-risk ratio — how much you win relative to what you lose)

Kelly Criterion Example from DCMM Data

Using a real example from the DCMM Deep dashboard:

LYB (LyondellBasell) with DD=5:

  • P_win = 50% (0.50)
  • TP_year/SLm = 0.57 (R/R Ratio)
  • Kelly % = 0.50 – (0.50 / 0.57) = 0.50 – 0.877 = negative

A negative Kelly percentage means the expected value is negative — this setup does not meet the Kelly minimum criteria. The R/R ratio is too low to justify the 50% win rate.

PPG Industries with DD=4:

  • P_win = 77.8% (0.778)
  • TP_year/SLm = 0.65 (R/R Ratio)
  • Kelly % = 0.778 – (0.222 / 0.65) = 0.778 – 0.342 = 43.7%

A Kelly of 43.7% means mathematically, you could allocate up to 43.7% of capital to this trade. In practice, traders use “Half Kelly” (21.85%) or “Quarter Kelly” (11%) to reduce variance while maintaining positive expected growth.

Why Kelly Criterion is Critical for Position Sizing

Most traders either:

  • Under-size: Miss out on optimal returns by allocating too little to high-quality setups
  • Over-size: Take excessive risk on marginal setups, leading to capital destruction

The Kelly Criterion provides a mathematically optimal answer to the position sizing question, ensuring that capital is allocated proportionally to the statistical quality of each setup.

Practical Kelly Application in DCMM

The DCMM system provides all the inputs needed for Kelly Criterion calculation in every report:

  1. P_win from the TP_year P_win column (Historical Twins win rate)
  2. R/R Ratio from the R/R year column (TP_year / SLm)

Recommended Kelly fractions for different risk profiles:

  • Full Kelly: Maximum mathematical growth, high variance. For professionals only.
  • Half Kelly: 50% of calculated Kelly %. Significantly reduced variance, ~75% of optimal growth rate. Recommended for most traders.
  • Quarter Kelly: 25% of Kelly %. Conservative, low variance. Good starting point for new users.
  • Fixed 1–2% risk: Traditional risk management approach. Use when Kelly percentage calculation shows very high allocations (>30% Kelly).

Diversification and Kelly

When trading multiple DCMM setups simultaneously (e.g., 3–5 stocks from the daily watchlist), the individual Kelly percentages should be scaled down to account for correlation risk. As a rule of thumb, divide the individual Kelly by the square root of the number of concurrent positions:

Adjusted Kelly = Individual Kelly / √(number of positions)

Kelly Criterion and Market Regime

DCMM recommends adjusting Kelly fractions based on the overall market regime (displayed as NORMAL, CAUTION, or RISK-OFF in the report header):

  • NORMAL: Use calculated Half Kelly or Quarter Kelly
  • CAUTION: Reduce to Quarter Kelly or fixed 1% risk
  • RISK-OFF: Minimize or avoid new positions; use fixed minimal risk only

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