Using the Kelly Criterion for Asset Allocation and Money Management

The Kelly Criterion is one of many allocation techniques that can be used to manage money effectively. Investors often hear about the importance of diversifying and how much money they should put into each stock or sector. These are all questions that can be applied to a money management system such as the Kelly Criterion. This system is also called the Kelly strategy, Kelly formula, or Kelly bet.

History of the Kelly Criterion

John Kelly, who worked for AT&T's Bell Laboratory, originally developed the Kelly Criterion to assist AT&T with its long-distance telephone signal noise issues. The method was published as "A New Interpretation of Information Rate" soon after in 1956.

Then the gambling community got wind of it and realized its potential as an optimal betting system in horse racing. It enabled gamblers to maximize the size of their bankroll over the long term. Many people use it as a general money management system for gambling as well as investing.

The Basics of the Kelly Criterion

There are two basic components to the Kelly Criterion. The first is the win probability or the odds that any given trade will return a positive amount. The second is the win/loss ratio. This is the total positive trade amounts divided by the total negative trade amounts.

These two factors are then put into Kelly's equation, which is:

$\begin{aligned} & K\% = W - \frac{\left(1-W\right )}{R}\\ \textbf{where:}\\ &K\% = \text{The Kelly percentage}\\ &W = \text{Winning probability}\\ &R = \text{Win/loss ratio}\\ \end{aligned}$where:​K%=W−R(1−W)​K%=The Kelly percentageW=Winning probabilityR=Win/loss ratio​

The output of the equation or "K%" is the Kelly percentage, which has a variety of real-world applications. Gamblers can use the Kelly criterion to help optimize the size of their bets. Investors can use it to determine how much of their portfolio should be allocated to each investment.

Putting the Kelly Criterion to Use

Investors can put Kelly's system to use by following these simple steps:

1. Access your last 50 to 60 trades. You can do this by simply asking your broker or by checking your recent tax returns if you claimed all your trades. Simply backtest the system and take those results if you're a more advanced trader with a developed trading system. The Kelly Criterion assumes that you trade the same way now as you have in the past.
2. Calculate "W," the winning probability. Divide the number of trades that returned a positive amount by your total number of trades, both positive and negative. This number is better as it gets closer to one but any number above 0.50 is good.
3. Calculate "R," the win/loss ratio. Divide the average gain of the positive trades by the average loss of the negative trades. You should have a number greater than one if your average gains are greater than your average losses. A result of less than one is manageable as long as the number of losing trades remains small.
4. Input these numbers into Kelly's equation.
5. Record the Kelly percentage that the equation returns.

Interpreting the Results

The percentage is a number less than one that the equation produces to represent the size of the positions you should be taking. For example, you should take a 5% position in each of the equities in your portfolio if the Kelly percentage is 0.05. This system essentially lets you know how much you should diversify.

The system does require some common sense, however. One rule to keep in mind regardless of what the Kelly percentage may tell you is to commit no more than 20% to 25% of your capital to one equity. Allocating any more than this carries far more investment risk than most people should be taking.

Is the Kelly Criterion Effective?

This system is based on pure mathematics but some may question if this math, originally developed for telephones, is effective in the stock market or gambling arenas. An equity chart can demonstrate the effectiveness of this system by showing the simulated growth of a given account based on pure mathematics. In other words, the two variables must be entered correctly and it must be assumed that the investor can maintain such performance.

Why Isn't Everyone Making Money?

No money management system is perfect. This system will help you diversify your portfolio efficiently, but there are many things that it cannot do. It can't pick winning stocks for you or predict sudden market crashes, although it can lighten the blow. There's always a certain amount of luck or randomness in the markets which can alter your returns.

The Bottom Line

Money management cannot ensure that you always make spectacular returns, but it can help you limit your losses and maximize your gains through efficient diversification. The Kelly Criterion is one of many models that can be used to help you diversify.