Using the Kelly Criterion in actual trading

Position sizing methods like Kelly Criterion have an optimal leverage to 'apply' to a specific trade. The way I currently understand it, it is the percentage of your account that you should 'apply' to that trade. But how do you apply it?

When I make a forex trade I look at 3 things:

1. Risk = Price-Per-Pip x Stoploss Pips
2. Notional Value = Volume x Price
3. Margin = Notional Value / Broker Account Leverage

Does Kelly tell me how much money I should risk? or how much margin I throw in? or the notional value of the trade?

According to this post:
https://www.forexfactory.com/thread/...ptimizing-risk

Kelly determines the optimal % of account to RISK.
But assuming this is right, I still dont understand how to accurately calculate the Kelly Criterion.

Here is the equation that Ernie Chan uses in his books:

Assuming your using a systematic trading strategy, you need the historic returns of that strategy to plug into the equation.
But the returns depend on the position size of each individual trade taken by the strategy.
And these position sizes presumably depend on the % of your account you should risk.
If the position sizes did not depend on this %, then why use this kelly optimization in the first place?
Its a chicken and egg problem!

Hi,
You can argue the finer details of the mathematics of the Kelly Criterion forever but in practical terms it's perhaps better to stick to some common sense understanding. Remember the Kelly Criterion gives you the optimal bet size, i.e. the biggest bet size that maximises return for the numbers you plug into it for your system. If you go a little too large and/or your system doesn't in reality work quite as well as the numbers you plug in, you run a high risk of falling over the edge of taking too much risk with disastrous potential consequences.

The below chart shows simplistically what happens to returns (blue line) and volatility of returns (red line) as you increase the Kelly %. The optimal % is right at the top of the blue dome; get that slightly wrong by betting just a bit too big and returns start quickly collapsing due to excess risk assumed. In the meantime, volatility goes up steadily as the Kelly % increases.



If you bet half the optimal Kelly amount you get about 75% of the maximum return with about half the volatility. This is much more comfortable to trade in practice for most traders and you are not sitting right on the precipice at the top of the dome.

Overall, then, I wouldn't worry too much about what your precise Kelly % might or might not be. Understand what ballpark it is in and then bet around half that at the most. It will make for a much more relaxed trading experience and you'll still make good money if your system works as you think it should. Too many traders bet way too big for their account and eventually get wiped out by a huge loss along the line. Focus instead on trying not to let it happen to you.

There is an interesting article that talks about that volatility and maximal Drawdown : https://elliotnoma.wordpress.com/201...-max-drawdown/

The article demonstrated that even if you use fractional Kelly, the more you trade, the more there is a risk of a catastrophic drawdown. And for Kelly users, there is another factor to take into consideration: withdrawals. As traders can't just let the capital grow without consuming it, they make regular withdrawals to enjoy the profit they made. However, withdrawals can be seen by the Kelly formula as an unexpected loss, which can amplify the effect of drawdown in the fractional Kelly. The question is how to avoid that? What is the optimal strategy to maximize the growth of the bankroll while also maximizing the expected withdrawals?

I was inspired by Kelly's approach into solving that problem mathematically. I found this formula (which I've dubbed "The Just Criterion"):


Where :
- The fraction of the bankroll you should risk is f.
- The fraction of the profit you should withdraw if you win is w. If you lose, you don't withdraw anything.
- The probability of winning is p.
- The profit/loss ratio is b.

For example, if your initial bankroll is $100 and the probability of winning is 60%, with a 1:1 profit/loss ratio, then p=0.6 and b=1. The formula gives us f = 11% and w = 18%. So you risk 11% of the bankroll, which is $11. If it's a win and the odds are 1:1, you get $11 as profit. Then you withdraw 18% of that $11 profit, which is $2, and put the rest back into the capital. Now you will have $109 and $2 on the withdrawals. And then you repeat the same process with the capital $109. And obviously if it was a loss, you lose $11. There will be no withdrawal and you will have $89.

I made a simulation with an Excel spreadsheet for 1000 trades (the spreadsheet file is attached if you want to try it):


The blue area represents the capital in the broker, and the orange area represents the total withdrawals. With this system, only the blue area is kept in the broker. If the broker closes your account after big profits, you have already withdrawn all the orange. And no matter what happens to the capital, you either withdraw profit or don't withdraw, so the total withdrawals always increase when you are profitable, and don't increase when you are not. This makes it extremely resistant to catastrophic drawdowns.

Look at this drawdown (you can get it if you refresh the spreadsheet simulation multiple times):


The Just formula did well but look how Kelly performed:



Kelly crashed from 1000 USD to 1 USD, a -99.9% DD, while the formula got -35% DD in that period and kept more balance than Kelly. This is because, with Kelly, you risk it all when you have a streak of losses, while with the formula, you only risk a fraction of it. The formula is not just for avoiding big DDs. It also helps you withdraw profit regularly without affecting your capital too much. With this system, you can risk more and grow your capital faster, while still protecting yourself from a big drawdown.

The formula can also be used to calculate the optimal amount to withdraw from a winning trade, based on the percentage of your capital that you're willing to risk. From this simple relation :

If you risk 2% of your capital in a trade and your overall probability of winning is 50%, in a lucky trade you won five times the amount risked. The formula indicates that the optimal amount to withdraw would be 2% divided by 50% which is 4% of that profit. So even if you find the fraction from the formula too much to risk, and risked less, it still can give you the optimal fraction to withdraw in a wining trade.

I'm currently building a bot with Python and Metatrader 5 API that will use a simple Bollinger Band and RSI trading strategy incorporating this formula. I'll be testing how it performs in a demo account. I will keep you updated.

Hi JsLc, I just came across your post where you describe your Just Criterion and accompanying spreadsheet. It looks very interesting and I was wondering if there has been any further research done on your proposed method by either yourself or other third parties?

Regards

Duke226

Hello Duke,

I've been continuing to work on my Python bot since my last message in October. I've been backtesting the RSI+BB strategy and testing it on a demo account. I've recently decided to put it into action on a real account starting this Monday. I plan to let it gather statistics on the most profitable hours of the day before applying the formula.

I've also been working on a new, more complicated formula in the form of a differential equation. The goal is to maximize exponential growth of both capital and withdrawals. This new formula provides a dynamic balance between the aggressiveness of Kelly and the conservatism of the first Just Criterion. It minimizes maximal drawdown and time spent in a drawdown. I haven't decided whether to share this formula yet, but I'll keep you updated on my bot's progress.

Best Regards, Justus

Congratulations on this excellent work.

Kelly Criterion works much better in systems where there is an average of positive dependence streaks: winning trades will be followed by winning trades and losing trades will be followed by losing trades.



With the formula:
N: Total trades number
R: Number of streaks in the series
P: 2*W*L

With an example: N:36 R:10 P:616 z-score: -2.75. It´s a Possitive dependence




Attached below is a partially translated Excel Z-Score for reference.

New implementations so far in the Just Criterion; testing good?

I find your formula really interesting. However, I'm still a bit confused about how exactly to apply the Z-score in trading strategies. The provided Excel spreadsheet is in a different language and doesn't seem to explain its usage in detail. For example, after 30 trades, my Z-Score is -2.5 what should I do?

In terms of my progress, I've been doing a lot of research to find a trading strategy that consistently generates profits or at least has a positive expected value. I've tried out many strategies and tested them on demo and real accounts, but unfortunately, they all ended up losing money in the long run. In fact, I lost almost $1,000 USD on my real account, some due to coding mistakes, some simply the strategy isn't profitable. But I haven't given up and I'm still determined to find a way to make the formula into a profitable strategy.

Through this long journey I explored many things from high frequency to machine learning to genetic algorithm to AI. Right now with the help of ChatGPT, I'm exploring the use of deep neural networks with Python and TensorFlow to build a trading model. The idea is to train the model using a large dataset of collected trades and their outcomes as either wins or losses. Then, based on this training, the model should be able to accurately predict the probability of a winning trade. If I can get the model to provide reliable probabilities with a positive expected value, I can apply my formula to risk the minimum and grow the capital optimally. However, I'm still in the early stages of this research, and need to gather a substantial amount of trade data to train and test the model's predictive abilities.

I will keep you update it if there is any new findings.

How we can use them in trading if we don't know exact probabilities?

I was delighted to be able to analyze the Z-Score in your Just Criterion system, albeit manually because so far I would not have been able to implement the streak count in all the T.P/S.L cells. But what I have been able to obtain, attending to the distribution in the sequence of results when they mark a positive Z-Score, is simply excellent, being even more consistent in terms of profit and keeping away in losses when the Z-Score is with positive dependence along the 1000 results of a randomization in the excel results sheet. When a system has a minimum acceptable probability of profit and its profit/loss ratio is equally of an acceptable value, the Z-Score establishes a more positive risk/return management when applying the Kelly Criterion.
However, I have not yet applied this content to Forex trading systems but I am thinking carefully about it and how to do it, since I currently use the Ninjatrader 8 platform for Futures, and there, Kelly's Criterion is practically impossible to sustain, because it is not possible to make partial use of lots, there are no decimals or fractional amount for the capital.

What has gone wrong in the long run? Because your Just Criterion Excel barely yields negative results if we start from the basic criteria of systems with acceptable profit probability and profit/loss ratio. Yes, you can blow up the account, but the fact of withdrawing 2% of each positive result, exposes that the capital withdrawn is higher than the lost one. What are we missing? On the other hand, my best encouragement for your research on deep neural networks for trading models.
Next I want to show the result of a high reliability backtest for a trading strategy, totally logical, viable results, without alterations or false resistances, and a backtest generated by ticks, but in the Ninjatrader 8 platform. What I want to show is that in a long term system, 1.5 years, a fixed micro lot trade size, a large number of trades (343,182), an average time in market: 2.93 mins, 60.85% profitable, 1.06 profit factor and usually ending with positive results, maintains for at least 10 months a loss difficult to assume. This picture can be understood as a distribution of disparate streaks in long-term systems, and that a broad set of results can be subjected to the Z-Score test and, in our case, we can also apply the Kelly Criterion to obtain better results.



As a quantitative traders we look at Z-score as an statistical measurement that describes a value's relationship to the mean of a group of values in terms of standard deviations from the mean. USING THE Z SCORE TO DETERMINE TRADE SIZE AND BOOST PERFORMANCE:
https://www.forextraders.com/forex-e...ne-trade-size/
Please feel free to use MT5 EA example with a positive Z-score optimization implemented:
https://www.earnforex.com/guides/z-s...f_Forex_system

Don't use the full of Kelly, just a fraction.

I would like more content like this in this forum, congratulations. I am a systematic trader and have created several grid / martingale bots, I want to try to introduce this formula. Will show the differences in the backtest if you are interested!

I think the most obvious way is optimizing betting size based on it.

imagine you have a distribution, and when you look at it was a whole, it’s completely normal. 50% of outcomes are wins, 50% of outcomes are losses and the average size of each is the same.

BUT

the z score is 3 indicating the wins and losses cluster around each other… This in and of itself would be an edge. Each trade relative to all of the trades in a sample is 50/50 but if the last trade was a win, the probability the next one would be a win would theoretically be higher than 50/50. Once a loss occurs, the likely hood of the next trade losing would be higher than 50/50.

You can give a try to the attached kelly coded formula, it worked for me. Implement this with any improvements, for example, if you can include Z-Score, that would be a good implementation.

About the Z-Score code, please note that this code is taken out of context, so you may need to adapt it to your specific trading environment to implement it. It is designed to be executed either when closing an order or inside the deinit() function, utilizing OrdersHistoryTotal(). wit the entire formula:

Z=(N*(R-0.5)-P)/((P*(P-N))/(N-1))^(1/2)
where:
N - total amount of trades in a series;
R - total amount of series of profitable and losing trades;
P = 2*W*L;
W - total amount of profitable trades in the series;
L - total amount of losing trades in the series.


What I'm looking for now is how to handle a % blocked part of the profit from profit operations, to honor Just Criterion Formula and keep testing. If anyone knows, it is appreciated.

Sure, I will be interested in the backtest. The formula needs only one thing, and that thing is a trading strategy with a positive expectancy. If the grid has a positive expected value, then it would work. Like Kelly, if the expectancy is negative, it will simply output negative numbers.

About my experience, I tried my best on the forex with an automatic bot on backtest, but it's no use. Since October, which is around 10 months of coding and backtesting, the commissions eat into every single one of the potential edges. Hedge funds' high-frequency bots have all the edge with direct access, almost no commission, and no spread. I cannot compete with them as a retail trader. I plan to change the market to manual trading crypto. I started paper trading manually just recently, and until I naturally develop a strategy and skills to gain an edge, then I can apply my formula.

Oh the "Kelly criterion", one of those things that looks fine on paper vs reality in live trading

In this activity is useless and while you should have a game plan for drawdowns, is equally (even more i would say) important to have a strategy for growing the account! and no, using a fixed % per trade wont get you anywhere you want or like

practically every "money management" approach on the internet is based on fear, on trying to achieve "little" drawdown and leave the profits and growing the capital in the backburner.. Hell, they never talk about withdraw targets ever too

Think about it, how can you protect your capital on a loss streak? and how can you grow drastically your account with the winners?

As weird as it sound, both must be different and They are not connected =)

Golden

please check my msg in your inbox. Wanted to reconnect please.

It's been a long time since I posted here. I'm back to announce that I made some great discoveries beyond the simple Just Criterion formula that I first shared (which I now call the Tax Criterion and the level after that the Just Criterion), and I decided it is now worth sharing with the world. So, I wrote a 47-page paper around those discoveries with the help of ChatGPT. It's my first paper with the help of an AI, so expect some expression mistakes.

Beyond the Kelly Criterion, Justus L. Ludovic
https://zenodo.org/records/10681498

Meanwhile, while working on the paper, I also developed a single page JavaScript calculator that follows my criterion . I named it the Just Calculator; The link is on the paper. But first give a general look at the paper to have a general idea how the calculator works.

The calculator still need some final code refinement and extensive testing of all trading scenario, so expect bugs in it.

interesting, i will read it later, thanks