加密貨幣交易中的凱利公式：投注規模背後的數學原理

Ever wondered how pros decide how much to risk on each trade? There’s actually a formula for it—and it’s been kicking around since 1956.

What’s the Kelly Criterion?

Think of it like this: you’ve got a strategy that wins 60% of the time, and when you win, you make 2x your bet. How much should you actually deploy? The Kelly Criterion answers that mathematically.

The formula is deceptively simple: f = (bp - q) / b*

Where:

• f* = the optimal % of your capital to bet
• b = the odds (profit per unit risked)
• p = win probability
• q = loss probability (1 - p)

In the example above: f* = (2 × 0.6 - 0.4) / 2 = 0.4, meaning you’d risk 40% of your bankroll per trade.

It was originally designed to optimize signal-to-noise ratios in long-distance communications, but mathematician Edward Thorp weaponized it for blackjack counting in the 1960s. Then Wall Street caught on in the 1980s.

How to Actually Use It for Crypto

Step 1: Estimate Your Win Rate This is the hard part. You need historical data, backtests, and honest self-assessment of your strategy’s edge. Guessing gets you rekt.

Step 2: Calculate Expected Returns What’s the profit/loss ratio per trade? 1:1? 3:1? This becomes your “b” value.

Step 3: Plug Into the Formula Bet the % it spits out. If it says 40%, that’s your position size—no more, no less.

Step 4: Rebalance as Conditions Change Market conditions shift, your strategy’s edge changes. Keep recalculating and adjusting.

The Catch: Kelly Assumes You’re Not Irrational

Here’s where crypto breaks the model:

Volatility Chaos: Crypto prices can swing 20% in an hour based on a tweet. Your probability estimates? Probably garbage.

Hidden Variables: Regulatory news, macro shifts, exchange hacks—none of these fit neatly into a formula. Kelly doesn’t account for black swans.

Psychological Pressure: When you’re watching 40% of your account evaporate in real-time, most traders panic-sell or FOMO double down. The math assumes you won’t.

Transaction Costs: Slippage, fees, spreads—Kelly ignores these, but they eat into your edge.

Drawdown Risk: Kelly betting can lead to 50%+ portfolio drawdowns. Even if it recovers long-term, most traders can’t psychologically handle it.

Kelly vs. Black-Scholes (Not Really Competitors)

People confuse these sometimes. Black-Scholes prices options based on volatility and time decay. Kelly sizes bets to maximize long-term wealth growth. They’re solving different problems, but can be used together—Black-Scholes for pricing, Kelly for position sizing.

Why Traders Actually Use It

✓ Systematic: Takes emotion out of position sizing ✓ Long-term Optimal: Maximizes compound growth over many trades ✓ Adaptable: Works with any strategy that has an edge ✓ Risk-Aware: Inherently balances growth with survival

Why It Breaks in Practice

✗ Assumes Accurate Probability Estimates: Crypto doesn’t cooperate ✗ Ignores External Shocks: Can’t predict what you can’t model ✗ Too Aggressive for Most: Full Kelly can liquidate accounts during volatility spikes ✗ Mechanical: Doesn’t account for changing market regimes

Real Talk

Most professional traders use fractional Kelly (like 25% or 50% of the formula’s recommendation) to reduce drawdown while keeping the benefits. Pure Kelly is theoretical perfection; practical trading is messier.

Use Kelly as a framework, not gospel. Your actual position size should also factor in portfolio diversification, personal risk tolerance, and current market conditions. The formula is a guide, not a law.