How Much to Bet on Each Stock?
Most investing education focuses on WHAT to buy. But equally important — and often neglected — is HOW MUCH to buy. Position sizing can be the difference between mediocre returns and exceptional ones.
"Diversification is protection against ignorance. It makes little sense if you know what you are doing."
The Kelly Criterion Explained
The Kelly Criterion, developed by John Kelly at Bell Labs in 1956, gives the mathematically optimal bet size to maximize long-term wealth growth: f* = (bp - q) / b
Where: f* = fraction of capital to allocate, b = odds received (potential gain/loss ratio), p = probability of winning, q = probability of losing (1-p).
| Win Prob | Win/Loss Ratio | Kelly Fraction | Interpretation |
|---|---|---|---|
| 60% | 2:1 | 40% | Strong conviction — large position |
| 55% | 1.5:1 | 18% | Moderate edge — medium position |
| 50% | 2:1 | 25% | Coin flip with good odds — decent position |
| 50% | 1:1 | 0% | No edge — don't bet! |
| 40% | 3:1 | 10% | Low probability but high payoff — small position |
Half-Kelly: The Practical Approach
Full Kelly is mathematically optimal but emotionally brutal — it leads to huge drawdowns. Most professional investors use Half-Kelly (f*/2) or even Quarter-Kelly for smoother returns.
💡 Kelly in Practice
- Full Kelly maximizes growth but creates extreme volatility (50%+ drawdowns)
- Half-Kelly achieves 75% of Kelly's growth with significantly less risk
- Quarter-Kelly sacrifices more growth but is emotionally sustainable
- Never exceed Full Kelly — over-betting guarantees eventual ruin
- Reassess your edge regularly — Kelly fraction changes as conviction changes
Duan Yongping's Concentrated Approach
Duan Yongping famously said: "2-3 stocks is enough." His portfolio has historically been extremely concentrated — sometimes 70%+ in a single position (Apple). This aligns with Kelly theory: when you have high conviction, concentrate.
Position Sizing Rules of Thumb
💡 Practical Sizing Framework
- Core positions (highest conviction): 20-40% each, maximum 3
- Supporting positions (good but less certain): 5-15% each
- Exploration positions (learning/testing): 1-3% each
- Cash reserve: always maintain 10-20% for opportunities
- Never let any single loss exceed 10% of total portfolio value
- Rebalance when a position grows beyond 50% of portfolio
💡 Kelly Criterion — Key Summary
- Kelly Criterion = mathematically optimal position sizing formula
- f* = (bp - q) / b — bet proportional to your edge
- Use Half-Kelly in practice — full Kelly is too volatile for most people
- Concentrated portfolios (2-3 stocks) work when conviction is high
- Never over-bet — exceeding Kelly guarantees eventual ruin
- Position sizing matters as much as stock selection