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. The method was published as "A New Interpretation of Information Rate" soon after in 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 Kelly Criterion strategy is said to be popular among big investors, including Berkshire Hathaway's Warren Buffet and Charlie Munger, along with legendary bond trader Bill Gross.

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. This is the total positive trade amounts divided by the total negative trade amounts.

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

The percentage is a number less than one that the equation produces to represent the size of the positions you should be taking. This system essentially lets you know how much you should diversify. The system does require some common sense, however.

Allocating any more than this carries far more investment risk than most people should be taking. 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.

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. FINRA puts it this way: "Don't put all your eggs in one basket. One might remain steady as another loses value.

Diversifying protects you against losses across the board. Scholars have indicated that the Kelly Criterion can be risky in the short term because it can indicate initial investments and wagers that are significantly large.

The formula doesn't change if you apply it to a wager rather than an investment. You're just introducing different but similar factors. The Kelly percentage will tell you how much you should gamble after calculating the probability that you'll win, how much of the bet you'll win, and the probability that you'll lose.

You can also take the easy way out and just purchase an app. 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. Princeton University. CFI Education. University of California, Berkeley.

You may accept or manage your choices by clicking below, including your right to object where legitimate interest is used, or at any time in the privacy policy page.

These choices will be signaled to our partners and will not affect browsing data. Accept All Reject All Show Purposes. Table of Contents Expand. Table of Contents. History of the Kelly Criterion. The Basics of the Kelly Criterion. Putting the Kelly Criterion to Use. My last post was about some common mistakes when betting or gambling, even with a basic understanding of probability.

This post is going to talk about the other side: optimal betting strategies using some very interesting results from some very famous mathematicians in the 50s and 60s. I'll spend a bit of time introducing some new concepts at least to me , setting up the problem and digging into some of the math.

We'll be looking at it from the lens of our simplest probability problem: the coin flip. A note: I will not be covering the part that shows you how to make a fortune -- that's an exercise best left to the reader.

There is an incredibly fascinating history surrounding the mathematics of gambling and optimal betting strategies. The optimal betting strategy, more commonly known as the Kelly Criterion , was developed in the 50s by J. Kelly , a scientist working at Bell Labs on data compression schemes at the time.

In , he made an ingenious connection between his colleague's Shannon work on information theory, gambling, and a television game show publishing his new findings in a paper titled A New Interpretation of Information Rate whose original title was Information Theory and Gambling.

The paper remained unnoticed until the s when an MIT student named Ed Thorp told Shannon about his card-counting scheme to beat blackjack. Kelly's paper was referred to him, and Thorp started using it to amass a small fortune using Kelly's optimal betting strategy along with his card-counting system.

Thorp and his colleagues later went on to use the Kelly Criterion in other varied gambling applications such as horse racing, sports betting, and even the stock market. Thorp's hedge fund outperformed many of his peers and it was this success that made Wall Street take notice of the Kelly Criterion.

There is a great book called Fortune's Formula 1 that details the stories and adventures surrounding these brilliant minds. In probability theory, there are two terms that distinguish very similar conditions: "sure" and "almost sure".

If an event is sure , then it always happens. That is, it is not possible for any other outcome to occur. If an event is almost sure then it occurs with probability 1. That is, theoretically there might be an outcome not belonging to this event that can occur, but the probability is so small that it's smaller than any fixed positive probability, and therefore must be 0.

This is kind of abstract, so let's take a look at an example from Wikipedia. Imagine we have a unit square where we're randomly throwing point-sized darts that will land inside the square with a uniform distribution. For the entire square light blue , it's easy to see that it makes up the entire sample space, so we would say that the dart will surely land within the unit square because there is no other possible outcome.

Further, the probability of landing in any given region is the ratio of its area to the ratio of the total unit square, simplifying to just the area of a given region. For example, taking the top left corner dark blue , which is 0. Now here's the interesting part, notice that there is a small red dot in the upper left corner.

Imagine this is just a single point at the upper left corner on this unit square. What is the probability that the dart lands on the red dot? So we could say that the dart almost surely does not land on the red dot. The same argument can be made for every point in the square. For these situations, it's not sure that we won't hit that specific point but it's almost sure.

A subtle difference but quite important one. Imagine playing a game with an infinite wealthy opponent who will always take an even bet made on repeated independent tosses of a biased coin. Question: How much should we bet each time? This can be made a bit more concrete by putting some numbers to it.

Let's formalize the problem using some mathematics. Then for the n 'th toss, we have:. Let's take a look at that:. It doesn't take a mathematician to know that is not a good strategy. If we're betting our entire bankroll, then we only need one loss to lose all our money. So we can see that this aggressive strategy is almost surely 5 going to result in ruin.

Another strategy might be to try and minimize ruin. You can probably already intuit that this strategy involves making the minimum bet.

From Equation 2, this is not desirable because it will also minimize our expected return. This suggests that we want a strategy that is in between the minimum bet and betting everything duh! The result is the Kelly Criterion.