Kelly Criterion for Stock Trading

What is the most important thing to be profitable in trading? Is it the strategy? is it the entry? Or is it the exit? Most times traders are trying to find the best trading strategy which can give them a really good entry with high accuracy and good risk to reward. However, one thing that a lot of traders miss is having great risk management. Position sizing is probably one of the most important criteria to be profitable. It is a difference between having a smooth equity curve and blowing up your account because of too much leverage. That’s where the Kelly Criterion comes in. Kelly Criterion is usually used to find the optimal way of allocating the capital to trade any strategy.

Key Takeaways

1. Kelly Criterion is a formula that tells you how much capital to risk on each trade based on your win rate and risk to reward. 
2. The idea is to size up when the strategy has a good edge and size down when it does not. 
3. Full Kelly gives the best growth but the drawdowns are too big for most traders, so a lot of traders use half or quarter Kelly. 
4. It is important to note that Kelly can fail if your inputs are wrong or if there are black swan events such as gaps and regime changes.

What Is the Kelly Criterion in Stock Trading?

The Kelly Criterion is a position sizing formula that can help a trader to find the most optimal capital to allocate per trade. The Kelly Criterion is essentially dependent on a simple fact. If the strategy has a positive edge then the position sizing should be aggressive so that maximum profit can be made in long term. However, if the position sizing is too aggressive then the volatility and the drawn can lead to risk of ruin. So Kelly criterion is the formula which tries find the mathematical balance between:

• Growth
• Risk of ruin
• Compounding efficiency

Kelly Criterion is extremely popular. It is often used by quant traders and systematic traders. A lot of option traders have also started using this formula and it is also being used by portfolio managers now. It is not a static formula. It keeps on adjusting the position size based on the strategies winrate, the average risk to reward ratio and the edge of the strategy. 

Kelly Formula and the Inputs That Matter

The standard Kelly formula is:

F = bp−q/b

Where:

• f* = optimal fraction of capital to risk
• b = reward-to-risk ratio
• p = probability of winning
• q = probability of losing (1 − p)

Win Probability

Win probability is same as accuracy of the strategy. Strategy is 100 times and the trader is profitable 55 times then the win probability is 55%. 

However it is important to find the wind probability of your strategy before you apply the Kelly  criteria. Some ideas to find the wind probability are

• Backtests
• Forward testing
• Live trading history

Win/Loss Ratio

This is your average reward relative to risk. For example, if on average your winning trade has 2% profit and average losing trade has 1% loss, then the win loss ratio (b) = 2/1 = 2 . The higher your reward-to-risk ratio, the larger Kelly position size becomes.

How to Calculate Kelly Position Size Step by Step

Suppose your trading system has:

• Win rate = 55%
• Average reward-to-risk = 2:1

Now we can use the Kelly formula:

F = (2*.55 – 0.45)/2 = 0.325

This formula is currently suggesting that the trader should trade at a risk of 32.5% of capital. This would obviously sound extremely aggressive in Real world markets. Hence a lot of traders actually do not trade the full Kelly. They can use either of the following:

• Half Kelly
• Quarter Kelly
• Dynamic Kelly caps

Full Kelly vs Fractional Kelly

Full Kelly

Full Kelly means that the trader will take the exact risk as suggested by the formula. It has both pros and cons. Some of the advantages of trading the full Kelly is that mathematically this will maximize the long term capital growth. This is also the most optimble under ideal conditions and efficient for capital compounding. However it can have devastating results as well. It can lead to extremely large volatility and large draw downs and it is sensitive to estimation errors. In real markets, Full Kelly often creates drawdowns that most traders cannot psychologically tolerate.

Fractional Kelly

Fractional Kelly means using only a portion of the calculated Kelly percentage. For example, Half Kelly = 50% of Kelly size and Quarter Kelly = 25% of Kelly size. Most professional traders actually use the fractional Kelly because it can significantly reduce the drawdowns as well as emotional stress. 

Why Pro Traders Use Kelly for Position Sizing

Now why is Kelly criterian so important. Traders like carry because it can help them give statistical age in risk management and long term compounding. Rather than taking arbitrary quantities Kelly forces a traders to think in more mathematical form. Some of the benefits are that it provides capital efficiency. It can give more exposure when the trading edge increases. It also prevents under betting. New traders are hesitant in taking trades due to the risk. But Kelly can give them the optimal quantity that they should be trading as per the strategy matrics. And find it is extremely useful for systematic trading.

Where Kelly Fails in Real Markets

Kelly is powerful mathematically, but markets are not clean probability machines. Kelly does not work always and can fail in case the inputs of the formula are wrong. Even a small changes (50% winrate to 60% winrate) can lead to dangerously large bets. 

Moreover, financial markets has: 

• Black swan events
• Gaps
• Slippage
• Regime changes
• Correlated crashes

One assumption that Kelly has that markets are relatively stable and independent. But this is not the case. A strategy which is looking good in backtest can experience:

• Sudden volatility spikes
• Liquidity collapse
• Massive drawdowns

Kelly vs Fixed-Risk and Volatility-Based Position Sizing

Final Thoughts

The Kelly Criterion is one of the most intellectually powerful concepts in trading risk management. It offers good position sizing based on the strategy win rate and risk to reward. However, Kelly is not magic. Kelly can give wrong results if the metrics of the strategy is overestimated.