Kelly Formula Calculator

What is the Kelly Formula?

The Kelly formula is a mathematical and risk management formula developed by John L. Kelly, Jr. in the 1950s. It is used by stock traders, gamblers, and investors to help determine an optimal position size or bet size.

In stock trading, a position size is the percentage of a stock trader's account balance to place on a single trade. By trading with the optimal position size, a trader minimizes risk and maximizes reward potential.

In other words, the Kelly formula helps mitigate the risk-of-ruin (i.e., destroying your trading account) while simultaneously maximizing the growth potential of your account.

How to Calculate the Kelly Formula

The Kelly formula is a mathematical formula defined by this equation:

f = (bp - q) / b

Where:

• f is the optimal percentage of a portfolio to allocate to a trade

• b is the net odds or potential profit of a trade

• p is the estimated probability of winning the trade

• q is the estimated probability of losing the trade

As an example, let b = 2, p = 40%, and q = 60%.

When b equals 2, it means that the trader expects to win twice the amount of profit than the risk or loss amount. So if a trader risks losing $100 dollars, then the profit would be $200, which gives net odds of 2-to-1 where b = 2.

When p equals 40%, or 0.4, a trader estimates a 40% probability of winning a trade. Likewise, when q equals 60%, or 0.6, the estimated probability of losing the trade is 60%.

Therefore:

f = (bp - q) / b
f = (2 x 40% - 60%) / 2
f = (2 x 0.4 - 0.6) / 2
f = (0.8 - 0.6) / 2
f = (0.2) / 2
f = 0.1 or 10%

The above example gives us an optimal position size of 10% per trade, because the net odds are 2-to-1 and the probability of winning and losing the trade is 40% and 60%, respectively. So in practice, if you have a $1,000 trading account, the amount of money to allocate to a single trade would be $100, which is 10% of $1,000.

Use the Kelly Formula with Caution

The Kelly formula should be used with caution because a trader doesn't typically have perfect knowledge of the probabilities of winning and losing. Even if you accurately estimate the probability of winning or losing, those probabilities are not usually constant.

To mitigate the risk of incorrectly estimating the probabilities, traders may use a half-kelly or quarter-kelly to reduce their position sizes even further.

Successful trading requires proper risk management. So it is better to trade with caution and hedge against inaccurate estimations by trading a fraction of the optimal position size that the Kelly formula suggests.