Guide to Kelly Criterion for Money and Asset Management

 

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. It’s named after John L. Kelly Links to an external site., who developed it in 1956 and is designed to maximize the logarithm of wealth over time.

 

The formula has expanded beyond the betting world because it uses universal principles that can be applied to investing, asset management, and many other areas.

 

In this article, I take a closer look at how the Kelly Criterion works, its pros and cons, the different variations of it, and where/when it might be applicable.

 

How Does the Kelly Criterion Work?

Simply put, the Kelly Criterion is designed to determine the size of investments of any kind based on factors like expected results, probability of success, and your overall capital.

 

The goal is to manage the risk-reward ratio optimally, so you extract the most value of your investment at reasonable risk levels and allow your capital (or bankroll). That’s the simple definition, but let’s look at the math next.

 

The basic Kelly Criterion formula is expressed as

 

In this equation:

 

• K is the fraction of the bankroll to risk
• b is the odds received on the bet (or the potential return of the investment)
• p is the probability of winning
• q is the probability of losing, which is 1-p

 

Theoretically, the resulting K tells you what fraction of your bankroll to bet to maximize its growth over time.

The formula was designed for betting, but you can easily adjust it to work for other investment, as long as you can calculate reasonable estimates for all of the variables included.

 

That last part is critical and leads us to the best and worst of using the Kelly Criterion as a money or asset management tool.

Kelly Criterion Pros and Cons

Like all investing and betting strategies and formulas, the Kelly Criterion is not perfect. There’s no such thing as a foolproof strategy, and if there was, the people who came up with it wouldn’t be likely to share it.

 

You can expect to make profitable investments by simply applying the formula, that’s not the point. It’s designed to maximize your returns if you make profitable investments, so that’s critical. The Kelly Criterion is simply a tool.

 

With this said, let’s look at the pros and cons of the Kelly Criterion.

 

Advantages of the Kelly Criterion

There are multiple reasons to pick the Kelly Criterion for money and assets management, such as the following:

 

• Optimal Growth - The Kelly Criterion maximizes the expected logarithm of your bankroll over time. Of course, the world ‘optimal’ is subjective, but there are tweaks that can be made to fit your definition of it.
• Risk Management - It calculates the optimal investment size, reducing the risk of over or under-investing. The former can lead to significant losses, while the latter can lead to missed opportunities.
• Robustness - The Kelly criterion is used by a wide range of people in different disciplines. Investors, traders, and gamblers all use it. It can be used in any area where odds and probabilities can be calculated accurately.
• Flexible - As we’ll cover in the ‘variations’ section below, the Kelly Criterion can be adapted to a wide range of preferences, such as risk tolerance, desired results, and asset classes.
• Long-Term Focused - The Kelly Criterion optimizes for long-term growth rather than short-term gains. Unlike strategies such as the Martingale, which involve doubling down on losing bets and taking on increasing risk for short-term gains, this one is less risky and focuses on long-term results.

 

Disadvantages of the Kelly Criterion

Naturally, the Kelly Criterion is not perfect and comes with certain downsides that must be considered.

 

• Estimation Errors - The Kelly Criterion depends on you being able to make accurate calculations regarding probabilities and odds. Errors at this stage lead to poor-sized investments and less-than-optimal results.
• Complexity - The real world is never as simple as a formula. For example, in investing, unexpected geopolitical events, market panics, and other factors can occur. It’s almost impossible to account for these. Fees and taxes also need to be factored in, and these vary from region to region.
• Psychological Elements - Sticking to the Kelly Criterion requires a high level of self-discipline and emotional control. Experienced investors, traders, and gamblers know this is easier said than done.

 

The good news is that you can offset some of the formula’s cons by adjusting it for your needs. The next section can help with that.

 

Variations of the Kelly Criterion

The Kelly Criterion can be tweaked, altered, and changed to suit the goals of the investor, trader, or gambler. The following are some common variations.

 

• The Partial Kelly - Once you've calculated the optimal-sized investment, you only risk a fraction of this. This is a more conservative version of the original Kelly Criterion. For example, if the calculation suggests you should risk 20% of your capital, go for 10% instead.
• Multi-Asset Kelly - Some portfolios contain multiple assets, e.g., stocks, bonds, and commodities. The Multi-Asset Kelly seeks to find the optimal balance between them with the same goal of maximizing total wealth long-term. The math here can get quite complex, but it can be done.
• Bayesian Kelly - This version incorporates Bayesian Links to an external site. inference into the equation. The Bayesian approach can provide a more refined estimation when probabilities and expected returns are uncertain. Where there are unknown parameters, use prior results and update them as new data comes in.
• Risk-Averse Kelly - The original Kelly assumed your goal is to maximize the logarithm of wealth over time. That’s not necessarily everyone’s goal, though. This version suits people who are more conservative in their risk-reward Links to an external site. As with the Partial Kelly, this version involves making smaller investments than the original formula suggests. It’s up to you as an individual to decide what is required.

Overall, Kelly’s reasonable fundamentals and flexibility are why the formula is applicable in so many areas.

 

Where is Kelly Criterion Money Management Applicable?

As stated earlier, the Kelly can be applied across a wide range of disciplines that involve investment, bankroll management, and risk-return evaluation.

 

• Trading - These days, you can trade all sorts of assets online. Forex, stocks, bonds, digital currencies Links to an external site. like Bitcoin, and even futures contracts for commodities like oil can all be bought and sold with a few clicks. The Kelly can help you decide how much to risk on each trade.
• Investment - Investing differs from trading in that it tends to be longer-term and thesis-driven. The Kelly Criterion is designed specifically to optimize long-term wealth, so it’s ideal for those with a higher time preference. Investors often fit this category.
• Sports Betting - Some would argue sports betting Links to an external site. is down to pure chance, but pros like Billy Walters would disagree, and his results suggest he might be right. The Kelly can be applied to sports betting and all sorts of gambling in which the odds and probabilities can be properly calculated.
• Real Estate - While it can be applied to real estate, it’s a little more complex. This asset class has added complexities such as liquidity, high transaction costs, maintenance expenses, etc. It can be done, but there’s a lot more to think about and consider.

 

How to Apply the Kelly Criterion Step-by-Step

Now that you understand all there is to know about the Kelly Criterion, let's wrap up by having a look at how to apply it step by step.

 

• First, calculate the probability of the outcome you are investing in and the odds you are receiving.
• Next, use these estimates to find your Kelly Criterion fraction using the formula outlined above.
• After that, calculate your investment size by multiplying the fraction by your capital to find out how much you should risk.
• Think about any real-world constraints such as slippage, fees, etc. Make sure to factor those in.
• Make your investment. Whether you’re betting on sports or buying a stock, use what you’ve calculated to place your wager.
• Rebalance often. Things change, and in the modern world, they do so rapidly. Make sure you recalculate and adjust your investment sizes accordingly.

 

Conclusion: Is the Kelly Criterion Worth It?

 

There’s no one-size-fits all strategy when it comes to investing, trading, or gambling. The Kelly Criterion will work best for a specific type of personality: someone focused on using math and calculation to maximize long-term wealth or minimize losses.

 

The criterion has several good sides: the ability to make decisions rooted in actual calculation rather than gut feeling or randomness, and flexibility/adaptability. It also has several limitations and is not ideal for markets such as real estate where there’s much more complexity.

 

Ultimately, the Kelly Criterion should be part of a larger toolset investors, traders, and gamblers can use to help with decision-making. It should not be seen as a solve-all, and like all strategies, it has its strengths and weaknesses.

 

If are disciplined enough to follow what the formula suggests and savvy enough to calculate the variables properly, the Kelly Criterion is an excellent tool for money management.