Kelly Criterion

The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your capital to bet or invest on each trade or bet to maximise the long-term growth of wealth. It tells you exactly how much to risk given your win rate and the ratio of average wins to average losses.

What Is the Kelly Criterion?

The Kelly Criterion was developed by John L. Kelly Jr. in 1956 at Bell Labs. It is used in gambling, investing, and trading to determine the optimal bet size.

**Formula:**
Kelly % = W – [(1 – W) / R]

Where:
– W = win rate (probability of winning)
– R = win/loss ratio (average win / average loss)

**Example:**
Win rate (W) = 50%
Average win = Rs 3,000
Average loss = Rs 2,000
R = 3,000 / 2,000 = 1.5

Kelly % = 0.50 – [(1 – 0.50) / 1.5] = 0.50 – 0.333 = 0.167 = 16.7%

This means betting 16.7% of your capital on each trade maximises long-term growth.

Why the Kelly Criterion Matters

Betting too little results in slower capital growth. Betting too much (overbetting) leads to greater risk of ruin and lower long-term growth due to the asymmetric effect of losses.

The Kelly formula balances these two risks to find the mathematically optimal bet size.

Half-Kelly: The Practical Version

Full Kelly can result in very large drawdowns because real-world win rates and risk-reward ratios are not perfectly consistent. Most professional investors and traders use Half-Kelly (bet half the Kelly fraction) to reduce volatility while still compounding at a good rate.

Half Kelly % = Kelly % / 2 = 8.35% in the example above.

Limitations of Kelly Criterion

– Requires accurate estimates of win rate and win/loss ratio, which are hard to determine in advance
– Assumes the same edge is available on every bet/trade (unrealistic in markets)
– Can still result in large drawdowns with full Kelly
– Works over very long periods; short-term results can be very volatile

Practical Example

Rohit has backtested his swing trading strategy and found a 55% win rate with an average win of Rs 2,400 and average loss of Rs 1,500. R = 2,400/1,500 = 1.6. Kelly % = 0.55 – (0.45/1.6) = 0.55 – 0.28 = 0.27 = 27%. He uses Half Kelly of 13.5%, risking Rs 1.35 lakh of his Rs 10 lakh account on each swing trade. This is a well-informed, mathematically derived position sizing decision.

Key Takeaways

– The Kelly Criterion calculates the optimal fraction of capital to invest to maximise long-term wealth
– Formula: Kelly % = W – [(1-W) / R], where W is win rate and R is win/loss ratio
– Most practitioners use Half-Kelly to reduce variance while still growing capital efficiently
– Requires accurate estimates of win rate and win/loss ratio from historical performance
– Overbetting (ignoring Kelly) leads to higher ruin risk; underbetting slows down compounding