Kelly Criterion vs Fixed-Fraction Position Sizing: Navigating Misestimated Edges

The Consequences of Misestimating Your Edge

Suppose a trader estimates a 60% win probability on a particular strategy using the Kelly criterion. They calculate their optimal bet size and aggressively invest based on this estimate. However, the true win probability is only 40%. This misestimation leads to significant losses, as the trader's position sizes are too large, exposing them to extreme volatility. The result could be a substantial drawdown, potentially wiping out a significant portion of their capital. Such scenarios highlight the risks associated with aggressive strategies when edge estimates are inaccurate.

Understanding the Kelly Criterion

The Kelly criterion is a formula designed to determine the optimal fraction of capital to wager in order to maximize the long-term growth of wealth. The formula is expressed as:

\[ f^* = \frac{p}{l} - \frac{q}{g} \]

where:

• \( f^* \) is the fraction of wealth to bet,
• \( p \) is the probability of a win,
• \( q \) is the probability of a loss (where \( q = 1 - p \)),
• \( g \) is the fraction gained on a win, and
• \( l \) is the fraction lost on a loss [2].

For example, if a trader believes there is a 60% chance of winning (p = 0.6) with a 10% gain (g = 0.1) and a 10% loss (l = 0.1), the optimal bet size would be calculated as follows:

\[ f^* = \frac{0.6}{0.1} - \frac{0.4}{0.1} = 6 - 4 = 2 \]

This suggests the trader could leverage their position to 200% of their capital, which could lead to significant returns if their edge is accurate.

Fixed-Fraction Position Sizing Explained

Sizing at a fixed fraction well below Kelly (for example half Kelly) is a more conservative approach, where a trader risks a fixed percentage of their capital on each trade, regardless of their edge estimate. This method is simple and reduces the risk of substantial losses, as the trader does not overexpose themselves based on potentially flawed edge estimates.

For instance, if a trader decides to risk 2% of their capital on each trade, they would consistently apply this fraction regardless of their confidence in the trade's success. This method can be particularly useful in volatile markets or when edge estimates are uncertain, as it mitigates the potential for catastrophic losses.

Mechanics of Position Sizing: A Worked Example

Let's compare the outcomes of both position sizing methods using the same edge estimate. Assume a trader believes they have a 60% chance of winning each trade, with a 10% gain or a 10% loss.

Using the Kelly Criterion:

• Optimal bet size: \( f^* = 2 \) (200% of capital)
• If the trader starts with 10,000 units of capital, they would invest 20,000 units, risking 2,000 units (10% of the position) on a single trade.

Using Fixed-Fraction Position Sizing:

• Fixed fraction: 2% of capital
• Investment per trade: 0.02 × 10,000 = 200 units.

Assuming a win:

• Kelly: 10,000 + (20,000 × 0.1) = 12,000 units.
• Fixed-fraction: 10,000 + (200 × 0.1) = 10,020 units.

Assuming a loss:

• Kelly: 10,000 - (20,000 × 0.1) = 8,000 units.
• Fixed-fraction: 10,000 - (200 × 0.1) = 9,980 units.

At f = 2 the break-even win rate is 55.03%: if the true win rate is 55% instead of 60%, growth is −0.014% per trade, and at 50% it is −2.04% per trade, while a 0.2-fraction position still grows at 55% (+0.18%) and loses only 0.02% per trade at 50%.

Failure Modes of the Kelly Criterion

The Kelly criterion relies heavily on accurate edge estimates, which are often difficult to ascertain in real-world trading. Failure modes include:

• Over-leveraging: As seen in the worked example, if a trader misestimates their edge, they may take on excessive risk, leading to significant drawdowns.
• Extreme Volatility: The criterion can lead to large fluctuations in account balance, which may not be tolerable for many traders, especially those with lower risk tolerance.
• Model Error: The assumption that edge estimates are static can lead to poor decision-making in dynamic market conditions, where probabilities can shift rapidly.

Comparing Trade-offs: Kelly vs. Fixed-Fraction

When comparing the Kelly criterion and fixed-fraction position sizing, several trade-offs become apparent:

• Risk Profile: The Kelly criterion can lead to higher returns but comes with increased risk of ruin due to overexposure. Fixed-fraction sizing is more conservative, leading to steadier growth but potentially lower returns.
• Ease of Use: Fixed-fraction sizing is simpler to implement and requires less continuous assessment of edge estimates, making it more accessible for many traders.
• Performance under Uncertainty: In scenarios where edge estimates are unreliable, fixed-fraction sizing tends to outperform the Kelly criterion, as it avoids the pitfalls of excessive risk.

Proposed Experiment: Testing Edge Variability

To empirically test the impact of varying edge estimates on both position sizing strategies, one could conduct a simulation with the following steps:

1. Define a range of edge estimates: Create a set of scenarios with varying probabilities of success (e.g., 30%, 40%, 50%, 60%, 70%).
2. Simulate trades: For each edge estimate, simulate a series of trades using both the Kelly criterion and fixed-fraction sizing.
3. Analyze outcomes: Measure the final account balances, drawdowns, and volatility for both strategies across all edge estimates.

This experiment would provide insights into how each method performs under different conditions, helping traders make more informed decisions about position sizing.

Questions readers ask

What is the main advantage of the Kelly criterion?

The main advantage of the Kelly criterion is its ability to maximize the long-term growth of wealth by determining the optimal bet size based on the estimated edge.

How does fixed-fraction sizing mitigate risk?

Fixed-fraction sizing mitigates risk by limiting the amount of capital risked on each trade, which helps prevent catastrophic losses, especially when edge estimates are uncertain.

Can the Kelly criterion be used in all trading scenarios?

No, the Kelly criterion is best suited for scenarios where edge estimates are reliable. In volatile or uncertain markets, fixed-fraction sizing may be more appropriate to manage risk effectively.

Sources

1. Kelly criterion - Wikipedia

*Corrected 2026-10-30: The worked example's money figures were wrong: a 20,000 position at 10% risk gains or loses 2,000, so Kelly ends at 12,000 or 8,000 and the 2% position at 10,020 or 9,980. A 60% win probability was called a 60% edge; the edge is 2%.*

*Corrected 2026-10-30: One more place called a 60% win probability a 60% edge; it now says a 60% chance of winning.*