Position Sizing using the Kelly Criterion. (2024)

The Kelly criterion is a mathematical formula used by traders to determine the optimal position size for a trade. It was developed by John L. Kelly Jr., a researcher at Bell Labs, in the 1950s. The criterion takes into account the probability of winning a trade, the size of the potential payoff, and the trader’s edge. It can help traders maximize their expected long-term growth rate and manage their risk effectively.

The first benefit of using the Kelly criterion is that it helps traders manage their risk effectively. The formula takes into account the trader’s edge and the probability of winning a trade. If a trader has a higher probability of winning a trade, they can allocate more capital to that trade. Conversely, if the probability of winning is lower, the trader should allocate less capital to that trade. This approach ensures that the trader does not risk too much capital on any single trade, reducing the risk of a catastrophic loss.

The second benefit of using the Kelly criterion is that it helps traders maximize their expected long-term growth rate. By allocating capital to trades that have a higher probability of success, traders can generate higher returns over the long term. The formula also takes into account the size of the potential payoff, which means that the trader can allocate more capital to trades with a higher risk-reward ratio.

To use the Kelly criterion, a trader needs to follow several steps. First, the trader needs to determine their edge in the market. The edge is the advantage that the trader has over the market, which could be based on technical analysis, fundamental analysis, or a combination of both. The edge can be expressed as a percentage, which represents the trader’s expected return on each trade.

Once the trader has determined their edge, they need to calculate the probability of winning a trade. This probability can be based on historical data, technical analysis, or fundamental analysis. The probability can be expressed as a percentage, which represents the likelihood of the trade being successful.

Next, the trader needs to calculate the risk-reward ratio for the trade. The risk-reward ratio is the potential payoff of the trade divided by the amount of capital at risk. This ratio helps the trader determine if the potential payoff is worth the risk.

Finally, the trader can use the Kelly criterion formula to determine the optimal position size for the trade. The formula is:

f = (bp — q) / b

where f is the fraction of the account to allocate to the trade, b is the payout ratio, p is the probability of winning the trade, and q is the probability of losing the trade.

The resulting value represents the fraction of the trader’s account that should be allocated to the trade. If the value is greater than 1, the trader should reduce their position size to avoid taking on too much risk. If the value is negative, the trader should not take the trade.

Let’s assume that you have determined that your edge in the EUR/USD market is 2%, meaning you expect to earn a 2% return on each trade you make. You have also analyzed the market and determined that there is a 60% probability that your trade will be successful, and a 40% probability that it will be unsuccessful. Finally, you have determined that the potential reward for the trade is 3 times the risk.

To calculate the optimal position size using the Kelly criterion, you would use the formula:

f = (bp — q) / b

where:

• f is the fraction of your account to allocate to the trade
• b is the payout ratio (in this case, 3:1)
• p is the probability of winning the trade (60%, or 0.6)
• q is the probability of losing the trade (40%, or 0.4)

Plugging in the values, we get:

f = ((3 * 0.6) — 0.4) / 3 f = 0.2 or 20%

This means that you should allocate 20% of your account to this trade. For example, if you have a trading account with $10,000, you should allocate $2,000 to this EUR/USD trade.

It’s important to note that the Kelly criterion is just a guide and should be used in conjunction with other risk management tools. It’s also important to consider factors such as market volatility, trading costs, and the potential impact of the trade on your overall portfolio. By using the Kelly criterion as part of a comprehensive trading plan, you can improve your chances of long-term success in the forex market.