Position Sizing Secrets: Kelly Formula in Prediction Markets

In prediction markets, what's the correct amount to invest?

This question determines the difference between long-term profitable traders and bankrupt traders.

▶Why is Position Sizing So Important?

Scenario: Two traders, same strategy, different position sizing

|--------|------------------|-------------------|---------------|-------------------|

| A | $1,000 | 55% | Fixed 10% | $1,800 |

| B | $1,000 | 55% | Fixed 50% | $0 (Bankrupt) |

Conclusion: Same strategy, different results—position sizing is key.

▶Introduction to Kelly Formula

In 1956, John Kelly at Bell Labs developed a formula for determining optimal bet size.

Standard Kelly Formula

f* = (bp - q) / b

Where:

▪f* = Fraction of bankroll to bet
▪b = Odds (average win / average loss)
▪p = Probability of winning
▪q = Probability of losing (1 - p)

Simplified Kelly Formula

f* = Win Rate - (Loss Rate / Risk-Reward)

▶Practical Calculations

Example 1: High Win Rate Strategy

▪Win rate: 60%
▪Average win: $50
▪Average loss: $40
▪Risk-reward: 1.25

f* = 0.60 - (0.40 / 1.25) = 0.60 - 0.32 = 28%

Recommended position: 28% of account

Example 2: Low Win Rate Strategy

▪Win rate: 40%
▪Average win: $120
▪Average loss: $50
▪Risk-reward: 2.4

f* = 0.40 - (0.60 / 2.4) = 0.40 - 0.25 = 15%

Recommended position: 15% of account

Example 3: Hedging Strategy

▪Win rate: 20%
▪Average win: $400
▪Average loss: $100
▪Risk-reward: 4.0

f* = 0.20 - (0.80 / 4.0) = 0.20 - 0.20 = 0%

Recommended position: This looks like 0%, but can be used as small insurance (1-3%)

▶Half-Kelly Strategy

Kelly's theoretical values are often too aggressive. Most professional traders use half-Kelly or quarter-Kelly.

|----------|----------------|----------------------|--------|

Recommendation: Most traders should use half-Kelly.

▶Special Considerations for Polymarket

→ Consider Settlement Time

Polymarket markets can take days or weeks to settle. While waiting, your capital is locked.

Adjustment: Reduce Kelly by 20-30% for opportunity cost.

→ Consider Liquidity

Some markets have low liquidity. Large orders may not fill at desired prices.

Adjustment: For illiquid markets, reduce Kelly by 50%.

→ Consider Binary Outcomes

Polymarket is usually binary (YES or NO). This simplifies calculation but increases risk.

Adjustment: Ensure your account can withstand worst case.

▶Practical Position Sizing Strategies

Strategy 1: Fixed Percentage (Beginner)

Position = Account × Fixed Percentage (1-5%)

Pros: Simple, limits risk

Cons: Doesn't adjust to edge size

Strategy 2: Edge-Based (Intermediate)

Position = Account × Half-Kelly Value

Pros: Adjusts to strategy edge

Cons: Requires accurate data

Strategy 3: Scaled Entry (Expert)

▪Initial entry: 1-2% of account
▪If price favorable, add 1-2%
▪Maximum total position: 5-10% of account

Pros: Distributed risk, can test market

Cons: Might miss fast opportunities

▶Risk Management Checklist

Before each trade, ask yourself:

▪[ ] If I lose, what % of my account goes?
▪[ ] Will this loss wipe me out?
▪[ ] Can I withstand 10 consecutive losses?
▪[ ] Is this trade's expectancy positive?
▪[ ] Am I following Kelly formula (or half-Kelly)?

▶Case Study: 2024 US Election

Trader A (Over-Aggressive)

▪Account: $5,000
▪Trade: Trump wins @ 60¢
▪Position: 50% ($2,500)
▪Result: Loss

Consequence: Remaining $2,500, need 100% gain to break even

Trader B (Kelly Formula)

▪Account: $5,000
▪Trade: Trump wins @ 60¢
▪Assessed win rate: 55%
▪Risk-reward: 1.5
▪Kelly value: 21.7%
▪Half-Kelly: 10%
▪Position: $500

Result: Lost $500, remaining $4,500, only need 11% gain to break even

Trader C (Scaled Entry)

▪Account: $5,000
▪Trade: Trump wins @ 60¢
▪Initial position: 2% ($100)
▪Price dropped to 55¢: added 2% ($100)
▪Price dropped to 50¢: didn't add (reevaluate)
▪Total position: $200

Result: Lost $200, remaining $4,800

▶Common Mistakes

Mistake 1: Martingale Strategy

> "Double down after losses until you win"

Problem: Exponential growth leads to bankruptcy.

| Trade | Amount | Cumulative Loss |

|-------|--------|-----------------|

| 1 | $100 | $100 |

| 2 | $200 | $300 |

| 3 | $400 | $700 |

| 4 | $800 | $1,500 |

| 5 | $1,600 | $3,100 |

| 6 | $3,200 | $6,300 |

After 6 consecutive losses, you need $6,400 to continue.

Mistake 2: Ignoring Correlation

> "I'm betting on 5 different markets, diversified risk"

Problem: If all 5 markets are affected by the same event (e.g., election), your actual risk is concentrated.

Mistake 3: Overtrading

> "My win rate is 60%, so I should trade frequently"

Problem: High frequency means high transaction costs and more mistakes.

▶Recommended Tools

PolyBaymax Position Calculator

Inputs:

▪Account balance
▪Assessed win rate
▪Average win and loss
▪Risk tolerance

Outputs:

▪Kelly value
▪Half-Kelly recommendation
▪Quarter-Kelly recommendation
▪Maximum loss amount

Want more professional tools?

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