Kelly Criterion for Prediction Markets — Optimal Position Sizing for Trading Bots

import httpx

client = httpx.Client(base_url="https://api.rekko.ai/v1", headers={"Authorization": "Bearer YOUR_API_KEY"})
signal = client.post("/signals", params={"wait": "true"}, json={"market": "kalshi/KXFED-26MAR19"}).json()
print(f"Kelly fraction: {signal['size_pct']:.1%} → ${signal['size_pct'] * 10000:.0f} on a $10K bankroll")

What this page covers

The Kelly criterion formula and why it works for prediction markets
Full Kelly, half Kelly, and fractional Kelly
Manual calculation walkthrough
Automated Kelly sizing with the Rekko signals API
Portfolio Kelly with correlation adjustment
Common mistakes and practical considerations

Why position sizing matters

Most prediction market traders focus on finding edge — buying underpriced outcomes. But even with consistent edge, poor position sizing destroys returns. Oversize and a few losses wipe you out. Undersize and you leave money on the table. The Kelly criterion solves this: given your estimated probability and the market price, it calculates the position size that maximizes long-term growth rate.

The Kelly formula

For a binary prediction market with two outcomes (YES/NO):

kelly_fraction = (p * b - q) / b

Where:

p = your estimated probability of YES
q = 1 - p (probability of NO)
b = payout odds = (1 / market_price) - 1

For prediction markets where you buy at price c and receive $1 if correct:

kelly_fraction = (p - c) / (1 - c)    # for buying YES
kelly_fraction = (q - (1-c)) / c       # for buying NO

The result is the fraction of your bankroll to risk on this position.

Example

A market prices YES at 0.60 (60 cents). You estimate the true probability is 0.72.

p = 0.72       # Your estimated probability
c = 0.60       # Market price (cost to buy YES)
edge = p - c   # 0.12

kelly = (p - c) / (1 - c)  # (0.72 - 0.60) / (1 - 0.60) = 0.30

Kelly says risk 30% of bankroll. On a

10,000 bankroll, that is a

3,000 position.

Full Kelly is aggressive

Full Kelly maximizes the long-term growth rate, but it is volatile. A few consecutive losses at full Kelly can draw down your bankroll 50% or more. In practice, most traders use fractional Kelly.

Fractional Kelly

Multiply the full Kelly fraction by a dampening factor:

Strategy	Formula	Aggressiveness
Full Kelly	`kelly`	Maximum growth, maximum drawdown
Half Kelly	`kelly × 0.5`	75% of full Kelly’s growth, much lower drawdown
Quarter Kelly	`kelly × 0.25`	Conservative, suitable for uncertain estimates

Half Kelly is the standard recommendation. You sacrifice ~25% of long-term growth but reduce variance significantly.

full_kelly = (p - c) / (1 - c)
half_kelly = full_kelly * 0.5

# From the example: full Kelly = 30%, half Kelly = 15%
position_size = half_kelly * bankroll  # $1,500 on $10K bankroll

When to use which fraction

Your confidence in the probability estimate	Kelly fraction
High (backtested model, large sample)	0.5 - 0.75
Medium (solid research, some uncertainty)	0.25 - 0.5
Low (rough estimate, limited data)	0.1 - 0.25

Manual calculation in Python

def kelly_size(
    estimated_prob: float,
    market_price: float,
    bankroll: float,
    fraction: float = 0.5,
) -> dict:
    """Calculate Kelly-optimal position size for a prediction market."""
    edge = estimated_prob - market_price
    if edge <= 0:
        return {"recommendation": "NO_TRADE", "edge": edge, "size_usd": 0}

    full_kelly = edge / (1 - market_price)
    adjusted_kelly = full_kelly * fraction
    size_usd = adjusted_kelly * bankroll

    return {
        "recommendation": "BUY_YES",
        "edge": round(edge, 4),
        "full_kelly": round(full_kelly, 4),
        "adjusted_kelly": round(adjusted_kelly, 4),
        "size_usd": round(size_usd, 2),
    }

# Example
result = kelly_size(
    estimated_prob=0.72,
    market_price=0.60,
    bankroll=10_000,
    fraction=0.5,
)
print(result)
# {'recommendation': 'BUY_YES', 'edge': 0.12, 'full_kelly': 0.3,
#  'adjusted_kelly': 0.15, 'size_usd': 1500.0}

# Kelly sizing is a calculation, not an API call.
# Use the Rekko signals API for automated sizing:
curl -X POST "https://api.rekko.ai/v1/signals?wait=true" \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"market": "kalshi/KXFED-26MAR19"}'

function kellySize(estimatedProb, marketPrice, bankroll, fraction = 0.5) {
  const edge = estimatedProb - marketPrice;
  if (edge <= 0) return { recommendation: "NO_TRADE", edge, sizeUsd: 0 };

  const fullKelly = edge / (1 - marketPrice);
  const adjustedKelly = fullKelly * fraction;
  const sizeUsd = adjustedKelly * bankroll;

  return {
    recommendation: "BUY_YES",
    edge: Math.round(edge * 10000) / 10000,
    fullKelly: Math.round(fullKelly * 10000) / 10000,
    adjustedKelly: Math.round(adjustedKelly * 10000) / 10000,
    sizeUsd: Math.round(sizeUsd * 100) / 100,
  };
}

Automated Kelly sizing with Rekko

The Rekko signals API handles the entire chain: estimate the true probability via deep research, calculate edge against market price, and return a Kelly-derived size_pct:

import httpx

client = httpx.Client(
    base_url="https://api.rekko.ai/v1",
    headers={"Authorization": "Bearer YOUR_API_KEY"},
    timeout=120.0,
)

signal = client.post("/signals", params={"wait": "true"}, json={
    "market": "kalshi/KXFED-26MAR19",
    "risk_limit": "medium",
}).json()

print(f"Recommendation: {signal['recommendation']}")
print(f"Estimated probability: {signal['target_price']:.0%}")
print(f"Market price: implied from edge")
print(f"Edge: {signal['edge']:.1%}")
print(f"Confidence: {signal['confidence']:.0%}")
print(f"Risk rating: {signal['risk_rating']}")
print(f"Kelly fraction: {signal['size_pct']:.1%}")

bankroll = 10_000
position = signal["size_pct"] * bankroll
print(f"Position size: ${position:.0f} on ${bankroll:,} bankroll")

curl -X POST "https://api.rekko.ai/v1/signals?wait=true" \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"market": "kalshi/KXFED-26MAR19", "risk_limit": "medium"}'

const resp = await fetch("https://api.rekko.ai/v1/signals?wait=true", {
  method: "POST",
  headers: {
    Authorization: "Bearer YOUR_API_KEY",
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    market: "kalshi/KXFED-26MAR19",
    risk_limit: "medium",
  }),
});
const signal = await resp.json();
const bankroll = 10000;
console.log(`Position: $${(signal.size_pct * bankroll).toFixed(0)} (${(signal.size_pct * 100).toFixed(1)}%)`);

The risk_limit parameter adjusts the Kelly fraction:

Risk limit	Kelly fraction	Use case
`low`	~Quarter Kelly	Conservative, uncertain estimates
`medium`	~Half Kelly	Standard recommendation
`high`	~Three-quarter Kelly	High confidence, aggressive

Portfolio Kelly

When you hold multiple positions, correlations matter. Two positions on related markets (Fed rate cut + Treasury yields) amplify each other — sizing each independently overstates the safe allocation. The portfolio signal endpoint accounts for this:

signal = client.post("/signals/portfolio", params={"wait": "true"}, json={
    "market": "kalshi/KXBITCOIN-26APR",
    "portfolio": [
        {"market_id": "KXFED-26MAR19", "platform": "kalshi", "side": "yes", "size_usd": 1500},
        {"market_id": "KXINFLATION-26MAY", "platform": "kalshi", "side": "no", "size_usd": 800},
    ],
    "bankroll_usd": 10000,
}).json()

print(f"Recommendation: {signal['recommendation']}")
print(f"Adjusted size: {signal['size_pct']:.1%}")  # Accounts for correlation
if signal.get("concentration_warning"):
    print(f"Warning: {signal['concentration_warning']}")
if signal.get("hedge"):
    print(f"Hedge suggestion: {signal['hedge']}")

curl -X POST "https://api.rekko.ai/v1/signals/portfolio?wait=true" \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "market": "kalshi/KXBITCOIN-26APR",
    "portfolio": [
      {"market_id": "KXFED-26MAR19", "platform": "kalshi", "side": "yes", "size_usd": 1500}
    ],
    "bankroll_usd": 10000
  }'

const resp = await fetch("https://api.rekko.ai/v1/signals/portfolio?wait=true", {
  method: "POST",
  headers: { Authorization: "Bearer YOUR_API_KEY", "Content-Type": "application/json" },
  body: JSON.stringify({
    market: "kalshi/KXBITCOIN-26APR",
    portfolio: [
      { market_id: "KXFED-26MAR19", platform: "kalshi", side: "yes", size_usd: 1500 },
    ],
    bankroll_usd: 10000,
  }),
});
const signal = await resp.json();

The portfolio endpoint provides:

Adjusted Kelly fraction accounting for correlation with existing positions
Concentration warnings when too much capital is in correlated markets
Hedge suggestions to reduce portfolio risk

Common mistakes

Overestimating your edge. If your probability estimate is wrong, Kelly amplifies the error. A 5-point overestimate in edge leads to significant oversizing. Use fractional Kelly to protect against estimation error. Ignoring fees. Kalshi taker fees reduce effective edge. Subtract fees before calculating Kelly. Sizing each position independently. Correlated positions compound risk. Use portfolio-aware sizing. Using full Kelly. Academic Kelly assumes perfect probability estimates. Real estimates have uncertainty. Half Kelly is almost always better in practice. Not accounting for illiquidity. Your position is locked until the market resolves. Size based on capital you can afford to lock up, not your total bankroll.

What’s next

Build a trading bot

Apply Kelly sizing in an automated trading pipeline.

Signals API reference

Full documentation for the signals endpoint.

Portfolio signals

Portfolio-aware sizing with correlation analysis.

Getting Started

Core Concepts

Tutorials

Account

Kelly Criterion Position Sizing

What this page covers

Why position sizing matters

The Kelly formula

Example

Full Kelly is aggressive

Fractional Kelly

When to use which fraction

Manual calculation in Python

Automated Kelly sizing with Rekko

Portfolio Kelly

Common mistakes

What’s next

Build a trading bot

Signals API reference

Portfolio signals

​What this page covers

​Why position sizing matters

​The Kelly formula

​Example

​Full Kelly is aggressive

​Fractional Kelly

​When to use which fraction

​Manual calculation in Python

​Automated Kelly sizing with Rekko

​Portfolio Kelly

​Common mistakes

​What’s next

Build a trading bot

Signals API reference

Portfolio signals

What this page covers

Why position sizing matters

The Kelly formula

Example

Full Kelly is aggressive

Fractional Kelly

When to use which fraction

Manual calculation in Python

Automated Kelly sizing with Rekko

Portfolio Kelly

Common mistakes

What’s next