Kelly Criterion In Crypto: Better Than DCA?

The many factors and quick trend changes involved in investing can sometimes make it feel like a game of chance.

But knowing key strategies and theories can help take some of the guesswork out of buying and trading crypto.

That’s where the Kelly criterion comes into play.
Here’s everything you need to know about this key concept in 2024.

As always, this article does not constitute financial advice.

Quick Takes:

• The Kelly criterion is an alternative, statistical approach to long-term trading and betting. It calculates how much to allocate based on expected returns, win-loss probability, and total capital.
• The Kelly fraction is the optimal investment proportion to maximize returns, where risk is low enough to recover from losses and stay in the game indefinitely.
• The Kelly criterion isn’t always practical for investing because of its fixed assumptions. But it can complement other alternatives like dollar-cost averaging, growth, and value investing.

What Is the Kelly criterion?

The Kelly criterion is a formula that aims to solve the investing risk-reward dilemma. It does this by weighting the chances of winning or losing with the reward size, resulting in the Kelly fraction. This is the amount you could invest from your portfolio to achieve a risk-reward balance.

In theory, it’s a way to find the most long-term profits with the lowest risk of going broke.

[ K% = W - (1 - W) / R ]

In the modified Kelly criterion formula used for investing,  “K%” stands for Kelly fraction, “W” for winning probability, “(1-W)” for losing probability, and “R” stands for the expected return of investment (ROI)—all in decimals.

If the K% fraction equals 0.35, then 35% of your portfolio is the optimal investment. Anything above or below would be risky or inefficient. The fraction ranges from -∞ to 1, where everything under 0 is a bad investment (long-term).

The Origin and History of Kelly Criterion

This simple, game-changing formula was found in the 1950s by an American mathematician and researcher for Bell labs, John Kelly.

Interestingly enough, Kelly himself wasn’t a gambler, even though that’s what this method is best known for. 

But Kelly was into stock trading, and the original purpose was to find the right order size to maximize long-term returns without the risk of running out.

1950s pro gamblers likely used it, although there are no big names that attribute their success to a single betting strategy. 

The most known “testimonials” come from investors like Bill Gross and Paul Samuelson (who later criticized its practical limitations). Even Warren Buffet follows a modified form of the Kelly criterion for money management.

The Benefits of the Kelly Criterion

Different benefits derive from balancing risk-reward with the Kelly criterion. 

Durability alone can make all the difference, especially with the volatile nature of cryptocurrencies. Many people say that “time in the market beats timing the market,” and the Kelly fraction ensures that you’re never forced out of it.

This fractional investing approach may remind you of the dollar-cost-averaging (DCA) strategy. However, this has the potential to be more profitable because there’s no fixed investment size. You could look at market peaks and dips as a lower or higher probability of “winning.”

You also save yourself the opportunity cost of missing better prices on a coin or other options later on.

Kelly Criterion for Crypto Investing

The Kelly criterion can be a great complementary tool for technical analysis, especially during long sideways trends. 

Such scenarios generally offer at least one good exit price, even if you made the wrong call. But long-term investing is where the Kelly criterion truly shines.

The problem is, nothing in crypto is certain. If you bought bitcoin today, how would you know your potential returns in one month? 

Buying higher or lower gives a rough probability expectation, but do you know the exact win-loss rate?

Let’s see what this looks like in theory.

Practical examples of the Kelly Criterion

As a reminder, the version of the Kelly criterion used by investors is:

[ K% = W - (1 - W) / R ]

• Example 1

Let’s say Bitcoin is moving sideways for months and occasionally spikes by 30%. Based on annual data and your research, you believe there's an 80% chance that it spikes over 30% every week. Therefore:

K% = 0.8 - 0.2 / 0.3 = 0.8 - 0.67 = 0.13

(Had it been 70%, it would have been -0.3 instead of 0.13, and a bad decision).

If you invest 13% of your portfolio every week at the same price, chances are you would make back 30%. For instance, if you invest $1,300, you have an 80% chance of selling at $1690 every week.

Since major cryptocurrencies rarely go to zero, a fraction slightly above 13% can still be secure in some cases.

• Example 2

Let’s imagine that, because crypto markets are volatile, you instead want to stake tether for a 10% annual percentage yield (APY). But because it’s fiat-backed and centralized, you believe there’s a chance that it loses its peg in a year. Let’s say 10%:

K%  = 0.90 - 0.1/0.1 = 0.90 - 1 = -0.10

With a negative Kelly fraction, not even staking this stablecoin would be worth the risk. Let’s say another option also offers 10% APY but is safer— only a 5% chance of losing the $1 peg. The Kelly percentage would be 45% (0.45).

• Example 3

Let’s say you decide to raise the stakes with leverage. You're reducing your margin of error and thus increasing the risk of being liquidated. Suppose there’s an 80% losing probability and 20% to get a 500% ROI:

K%  = 0.2 - 0.8/5 = 0.2 - 0.16 = 0.04 (4%)

The Kelly fraction would be negative for any ROI below 400%. 

You can try out your own examples using this calculator.

Given infinite ROI, the maximum fraction will always be the winning chance: 20% in this case, 70% for a 70% success probability, and… that’s where incongruences begin.

Considerations When Using the Kelly criterion

The Kelly criterion is a maximally aggressive formula in that it seeks the highest reward relative to risk. 

It makes sense for an amount you’re comfortable with, but the fraction doesn’t consider your capital amount. 

A 20% Kelly percentage is 20%, regardless of whether you’re betting $100 or your life savings.

So the formula both underestimates risk tolerance and overestimates losses.

The average investor might first be more aggressive and reduce risk tolerance as the portfolio grows. And losing in crypto rarely means going to $0, outside of margin trading. So a -0.3 Kelly fraction could still be sustainably profitable.

Here are other considerations for the Kelly criterion:

• A 10% change in probability can make a positive Kelly fraction negative.
• Crypto markets don’t have fixed conditions for the long term.
• The Kelly criterion is risk-aggressive because it neither considers reinvesting nor compound losses.
• The strategy doesn’t mention the minimum recommended starting capital. Since you don’t know how many attempts you have, a favorable long-term bet can end in a first bad streak.
• It’s uncommon to trade only one asset. Your rate interpretation loses accuracy with every crypto you diversify with.

Kelly Criterion: Far From Infallible

The Kelly criterion relies on fixed parameters that other methods don’t. 

That doesn’t make it a bad strategy, as it can help you contrast with others. It might work for betting and stocks, but when it comes to crypto, other approaches may be more fitting:

• Growth investing is about choosing whatever cryptocurrency has the most price potential long-term, usually in one big purchase. You might buy BTC, PLS, or new projects in anticipation of major growth.
• Value investing involves fundamental analysis to find out the true value of a project and buy when it’s undervalued. Value investors aren’t as farsighted, because they’re not waiting for prices to go parabolic. To profit, they just need prices to return above their “true price” or average, which is somewhat similar to arbitrage trading.
• DCA investing is a periodic buying strategy that disregards market timing, preventing opportunity costs and emotional trading mistakes. Given a token with expected long-term growth, the investor will invest the same dollar amount every few weeks or months. When the price is above the average of all past purchases, it’s profitable. You get more opportunity windows without risking buying at the top.

Despite these drawbacks, the Kelly criterion can still be used as part of an informed and well-rounded strategy for long term investors.

As a result, understanding these types of concepts can give you the competitive edge needed to make better decisions.

To level up your game by learning more key crypto and investment concepts, check out more articles on the Liquid Loans blog.