The Kelly criterion is a famous mathematical formula that attempts to maximize your long-term capital growth.
In this post, I’ll apply it to a EURUSD breakout strategy and explain some of its potential shortcomings when applied to forex trading.
Traders often search for better position sizing methods to amplify their strategy’s edge.
The Kelly criterion is one option that often pops up in forex forums.
Since it is particularly popular in the gambling world, it naturally attracts much skepticism from traders.
Is it really that bad? Let’s find out!
What’s the Kelly Criterion?
The Kelly criterion is used to determine the optimal bet size that will maximize your strategy’s long-term returns.
To apply it, you need to know your strategy’s win rate and expected returns.
Here’s how it’s calculated for gambling:
Let’s start by determining the value of b.
For example, if your strategy contains a $10 stop loss and a $10 profit target, b will be 1.
If you raise your profit target to $20, without moving your stop loss, b will be 2.
For a strategy with an equal stop loss and profit target (1-to-1 odds in gambling), and a 60% win rate, the Kelly criterion produces an optimal bet size of 20% of your account.
If your strategy’s expectancy (average trade) is zero, the Kelly criterion wisely gives you a bet size of zero.
You can use this Kelly calculator to speed up the process.
Applying the Kelly Criterion to Forex
To evaluate the usefulness of the Kelly criterion, I’ll apply it to a 15-minute EURUSD strategy.
This strategy uses the CCI indicator to detect breakouts, and has a 150-pip stop loss and profit target.
Here’s an example of the strategy in action:
When trading a fixed 0.1 lots throughout the backtest, the strategy yields a pleasant equity curve from 2003 to 2021.
Now let’s apply the Kelly criterion.
With a win rate of 57%, the Kelly criterion tells me I should risk 14% of my account per trade.
Backtest Results
Returns are spectacular! After 587 trades, my account grew from $5000 to $210 000, a 4100% return.
Returns are only part of the equation though.
Unfortunately, with an 8-trade losing streak, the strategy had a whopping 71% maximum drawdown.
With such a drawdown, you’ll need 250% returns just to break even. This is the price to pay if you’re after massive returns.
Traders often overestimate the amount of drawdown they can tolerate in real-time.
Backtests offer the benefit of hindsight; in reality you’ll have to trade through the drawdowns without knowing whether your account will recover.
I’ll need to lower the strategy’s drawdown by risking a smaller fraction of capital per trade. Let’s run the numbers.
Tailoring Fixed Fractional Position Sizing
I varied the fraction of account risked from 1-8%, as shown:
If I were to trade this strategy in isolation, I wouldn’t risk more than 4% per trade, which produces a 27% maximum drawdown.
At this risk level, the strategy still achieved a 9% annual return over 18 years. Nothing like the Kelly returns, but at least I won’t lose sleep at night.
If you’re hungry for better performance, a prudent option will be to trade a portfolio of uncorrelated strategies. Returns are additive, but drawdowns are not, thus giving you better risk-adjusted performance.
Why the Kelly Criterion Isn’t Recommended for Forex Trading
There are two reasons why I believe the Kelly criterion is better suited to the realm of gambling.
1. Does Not Consider Risk
From the example above, you can see the Kelly betting fraction tends to produce huge drawdowns.
This is because its sole purpose is to maximize your long-term returns, without taking drawdown into consideration.
Drawdowns above 50% would be unbearable for the majority of traders.
Even if you’re emotionally detached from drawdowns, be wary that a backtest only represents a single historical run for the strategy. If I were to take the strategy above and trade it for the next 18 years, the equity curve would look different.
For the backtest above, I got lucky because the strategy performed fairly consistently over time. If my losing streak had been longer than 8 trades, the 14% bet size could have resulted in a margin call.
You can simulate alternative backtest runs by randomizing your trade sequence. StrategyQuant’s Monte Carlo simulator can help with this.
2. Only Applies to Binomial Outputs
The Kelly criterion has the following requirements:
- Every trade either results in a win or a loss
- Your win and loss amounts are fixed
For the EURUSD strategy above, each trade would result in either a 150-pip gain or loss.
If you use a fixed stop loss and profit target for your strategy, this won’t be a problem.
But if your trade management includes trailing stops, time stops, or indicator-based exits, you won’t know your win/loss amount in advance.
For example, if you’re a long-term trend follower who lets your profits run, your winning trades could be anywhere from 1 to 1000 pips.
Consider the trade distribution below, taken from a trend following strategy.
The Kelly criterion cannot meaningfully analyze such a distribution, which severely limits its usefulness in trading.
Wrapping Up
The Kelly criterion is an aggressive position sizing method that serves to maximize your long-term returns, without taking drawdowns into consideration.
Statistics will vary for different strategies, but most traders will likely find the Kelly-induced drawdowns to be unbearable.
Together with its limited applicability to most trading strategies, I can only recommend the Kelly criterion if you’re taking part in a trading contest, or going for broke in the short-term.
The Kelly Criterion value itself can’t be used in trading because it assumes even distribution in the probability of results based on the presumed win rate. In other words, you could get a KC value of 33% risk with a 50% win rate and this of course can’t work because 3 trades would wipe you out. In this example, the KC assumes that if you lose one trade you WILL win the next one because of the presumed 50% win rate.
However, just because the value itself shouldn’t be used, doesn’t mean the math can’t be used to derive something useful. If you divide the KC value by a given number x, the result will be a value that has a probability distribution with a degree of x. So if a KC value of 25% is divided by 10, then 2.5% represents the optimum risk for a probability distribution that accounts for up to 10 consecutive losing trades.
Your solution does this to some degree by lowing the value to some thing more feasible. But if you were to take a derivative of the KC value, you can get an optimal risk according to how likely your system is to lose x trades in a row. So if you backtest your strategy for a long time and found that the max consecutive losses were 5, if you were being aggressive, you could divide the KC value by 5. However any strategy has the possibility to generate more losses in the future so I would divide by a value greater than 5 in order to have a value that is more stable. I generally divide the KC value by 10 only trade strategies with 7 max consecutive losses or less.
Hi Khari, fantastic points you raised there. To me, the Kelly criterion is a viable starting point for trading, as long as it’s tweaked to be more conservative.
Hi Wayne，
Could you elaborate on what you mean by more conservative?
Hi Benny, I would start by looking at the max historical drawdown. The Kelly criterion above produced a 71% max DD, which is likely too much for most people. If you really want to use it, perhaps take half (or even less) of whatever position size it proposes.