Kelly criterion – calculating the risk per trade
Hello gentlemen traders! Have you ever wondered how to calculate exactly what percentage of your account balance should be in order to take risks in a given trade? For example, you are about to open a trade, but you are not sure what is the optimal volume / lot size. On the one hand, you do not want to risk too much if the market goes against you, but on the other hand, you also do not want to risk too little, suddenly you find yourself at the beginning of a trend and miss the opportunity to make good money. Sounds familiar? Today we will introduce you to a unique money management tool – the Kelly criterion. With it, you can effectively calculate your trading risks as well as the long-term profitability of your strategy.
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Favorable coin toss
Let’s imagine we are playing a game: you bet $ 1 on a coin toss. The rules are as follows:
- If it comes up “tails”, then you get $ 2;
- If heads come out, then you lose $ 1.
Mathematically, the expected value (EV) of this investment can be calculated as:
EV = $ 2 × 0.5 – $ 1 × 0.5 = $ 0.50.
A positive EV indicates a profitable opportunity. This means that in the end, if you average all the tosses, you will be making an average of 50 cents per coin toss.
This coin tossing game is a great analogy for a profitable trading strategy, for example, where TakeProfit = 2 × StopLoss and the frequency of winning and losing trades is about the same. Obviously this is a great trading strategy!
But actually, no. It turns out that you can lose even in such a profitable game as this one.
Improper money management
Let’s say you only have $ 100 to play this game. And because this is such a great opportunity, you decide that at any given time, you will be wagering 75% of your funds. Let’s see what happens in the end.
You bet 75% × 100 = $ 75. It comes up tails and you just made $ 150. Your balance is now $ 250.
You bet 75% × 250 = $ 187.50. The heads up, you just lost $ 187.5. Your balance is now $ 62.5.
So now you see that after two shots you are already in the red. And since heads and tails come at roughly the same frequency, eventually this pattern will continue and you will lose all your money!
What is the reason for the failure? Improper money management, overestimation of risk.
Note. The sequence of “heads” and “tails” does not matter, check it out for yourself.
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What is the Kelly criterion?
Let’s see what happens to your account balance if you decide to put a different percentage of risk per trade (you can check these numbers):
- 10% -> 108 $
- 20% -> 112 $
- 30% -> 112 $
- 40% -> 108 $
- 50% -> 100 $ (breakeven point)
- 60% -> 88 $
- 70% -> 72 $
- 80% -> 52 $
- 90% -> 28 $
- 100% -> 0 $
Thus, you can see that the maximum profit is somewhere between 20% and 30% of the risk.
Here’s where Kelly’s formula comes into play:
K = (P × B – (1 – P)) / B,
K is the optimal percentage of risk;
P – odds of winning;
B – payout at stake.
This formula determines the optimal percentage of your account that you can bet on in order to get the most profitable result in the long term. Let’s calculate the Kelly criterion for our scenario:
- B = 2 (payout 2: 1);
- P = 0.5 (50% chance of winning).
K = (0.5 × 2 – (1 – 0.5)) / 2 = 0.5 / 2 = 0.25%.
Thus, the best long-term outcome is achieved by betting 25% of your account on every coin toss!
25% -> 112.50 $ (after one “tails” and one “heads”).
Indeed, this result is better than anything we calculated earlier.
Note. This percentage is called one Kelly, and the exact value may be different for each trading strategy.
The Kelly Criterion is a good start, but it is not the complete picture. If you visualize the relationship between the growth of the balance and the percentage of risk, it looks like this:
We can observe the same pattern we noticed earlier – to the left of one Kelly, the recoil increases as the risk increases. Then the return drops to zero at 2K. After 2K, you will inevitably lose your investment in the long run.
The best part is that this chart is suitable for any strategy!
If you have calculated the Kelly criterion correctly, you can create such a chart for your specific case and understand how your investment will behave in the long term depending on the selected risk. Let’s talk about this in more detail.
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Calculating the risk per trade
We already know that in an ideal scenario, you would be best suited to bet on only one Kelly. However, the world is not always perfect, so now we will analyze the Kelly chart and understand the consequences of sub-optimal bets (that is, not one Kelly).
Typically, a Kelly chart is split into four parts:
- Yellow: from zero to 1/2 Kelly – area of conservative risk;
- Orange: 1/2 Kelly to 1 Kelly – aggressive risk zone;
- Red: from 1 to 2 Kelly – a zone of increased aggressiveness;
- Black: Anything above 2 Kelly is in the insane risk zone.
Sometimes Kelly’s formula for calculating a position can give you quite high values, for example, 25% risk. While in theory this might be the optimal risk, in practice it might be too high.
Reasons include things like the possibility of a series of consecutive losses that don’t count in the Kelly criterion, and balance sheet volatility. In short, there are legitimate reasons why you might think your Kelly is too tall. That’s when we look at 1/2 Kelly.
The main reason 1/2 Kelly is so good is because it cuts your risk in half and your long-term income is only 25% lower. You can even see it on the graph. Other reasons include a decrease in balance sheet volatility by more than 50% and a greater margin of safety in your risk assessment.
If you trade below 1/2 Kelly then you are pretty conservative. Which can be useful for risk-averse investors or if you control a very large balance sheet.
Anything between 1/2 Kelly and 1 Kelly is considered aggressive risk. Your income is higher, but not much higher. Consider our example of a flip game: a 20% risk (4/5 Kelly) brought our balance to $ 112, and a 25% risk (1 Kelly) raised our balance to $ 112.5.
This is just a 0.5% extra return (50 cents per $ 100) for a 5% increase in risk. Is it really worth it? This is why we associate this area with aggressive risks.
Overly aggressive risk
If you are looking at one trade, then of course if you win, the more you risk, the greater your profit will be. However, what we’re looking at is a lot of deals – the Kelly criterion works in the long run.
Thus, the super-aggressive risk zone tells us that in the long term, there is no need to risk such a large percentage of your balance. You can achieve the same result with less risk.
Question: “What if I don’t have a systematic trading strategy? What if all my trades are different? In this case, the Kelly criterion does not apply? ”
Answer: choose one of the trading strategies or develop it yourself.
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How to Apply the Kelly Criterion in Forex?
Very simple. But for this you need to have a trading strategy. If your trading strategy has fixed stop loss and take profit , then you are in luck. For you, the B value is equal to TakeProfit / StopLoss (do not forget to subtract / add the spread if it is not included in your TP / SL).
Now that you have B, all you have to figure out is the value of your parameter P. To get P, you need to look at your trading history in similar market conditions. I recommend checking the last 100 trades to be sure.
See what percentage of trades are profitable. This will be your P.
Now that you have both B and P – plug them into Kelly’s formula and see what you get.
What if you have negative Kelly?
If your K is negative, then your trading strategy is unprofitable and you will lose in the long run. You need to find a new trading system.
Let’s take a look at the following example. Let’s say you have a EURUSD trading strategy that wins about 70% of the time. The stop loss in your strategy is 40 pips, and the take profit is 20 pips (the spread has already been taken into account).
This means that your parameters B and P are as follows:
- B = 20 pips / 40 pips = 0.5;
- P = 70% = 0.7.
Let’s put these values into Kelly’s formula and see what we get:
K = (0.7 × 0.5 – (1 – 0.7)) / 0.5 = 0.1.
This means that the optimal risk for this trading strategy, which will maximize your long-term profit, is 10%.
If you want to be a little more conservative then use 1/2 Kelly with 5%.
Whatever you do, don’t invest more than 10% per trade – it’s pointless.
If you invest more than 20%, you will turn this great strategy into a strategy that will lead to a loss of your capital.
Here’s how you can put the Kelly criterion into practice.