To invest in crypto is to embrace uncertainty. One minute you know where the markets are going, the next you’re clueless. The many factors and quick trend changes make investing feel sometimes like a game of probability.
Or is it?
Imagine you had a 50-50 chance of trading Bitcoin (or your favorite coin) at 50% profits every week. Would you rather play it safe or go all in?
If you “bet” too low, you’re leaving a lot of money on the table. Who knows how long this rally will continue? If you bet too much, a bad streak can leave you broke or chasing losses.
If you bet with the Kelly Criterion, things change.
- 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 better 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 proportion is the proportion to invest from your portfolio to achieve a risk-reward balance.
In short, make the most long-term profits with little to no risk of going broke.
[ f = (bp – q) / b ]
In the Kelly Criterion formula, “f” stands for Kelly fraction, “b” for the expected return of investment (ROI), “p” for winning probability, and “q” for losing probability— all in decimals.
If the f 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 of Bell labs, John Kelly. Interestingly enough, John 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. It’s 100% legal and far from a cheat code, among other reasons because casinos have gone a long way since it came out. Still, many bettors are familiar with it today.
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. It’s common knowledge that “time in the market beats timing the market,” and the Kelly fraction ensures that you’re never forced out of it.
Not losing everything and being able to recover from bad streaks should neither be understated.
This fractional investing approach may remind you of the dollar-cost-averaging (DCA) strategy. Except it’s 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 this coin or other options later.
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 first see what it looks like in theory:
Examples of the Kelly Criterion in Practice
To avoid confusion, note that investors use an alternative expression of the Kelly Criterion:
[ K % = W – (1 – W) / R ]
It’s the same formula as [ f = (bp -q) / b ] with different names. Replace K% with f, W with p, (1-W) with q, and R with b, and you get [ f = p – q/b ]. All three give the same result. For the examples, we’ll use this last one— the shortest.
- 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:
F = 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%. E.g. If you invest $1,300, you have an 80% chance of selling at $1690 every week.
Since cryptocurrencies rarely go to zero, a fraction slightly above 13% can still be secure.
- Example 2
Crypto markets are too volatile, so 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 Tether loses its peg in a year. Let’s say 10%:
F = 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
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 500% ROI:
F = 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 other 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% 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— except for margin trading. So a -0.3 Kelly fraction could 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 long-term
- The Criterion is risk-aggressive because it neither considers reinvesting nor compound losses.
- The strategy doesn’t mention the minimum recommended starting capital. Since you neither know how many attempts you have, a favorable long-term bet can end in a first bad streak.
- It’s uncommon to trade one currency only. Your rate interpretation loses accuracy with every token 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 are more fitting:
- Growth investing is about choosing (typically one big purchase) whatever cryptocurrency has the most price potential long-term. You might buy Bitcoin because of its potential $1M price, Pulsechain token for 100X, or small early projects with innovative tech.
- 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 far-sighted, because they’re not waiting for prices to go parabolic. To profit, they just need prices to return above their “true price” or average— 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/months. Anytime the price is above the average of all past purchases, it’s profitable. You get more opportunity windows without risking buying at the top.
Depending on your frequency and time frame, the probability and reward will change. But if you’re into crypto for the long term, then the Kelly Criterion is definitely worth a try.