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## What is the Kelly Criterion?

The Kelly standard or Kelly formula for the gambling world in general and the traders, in particular, is nothing new. However, it is still very new to some beginner traders, so we will introduce to you a classic formula for Capital Management skills. Through this, we can somewhat improve our money management skills. As traders, most of us understand that a good trading system is not as equal as an effective money management skill.

We usually hear about the importance of diversifying our portfolio, but speaking is easy. How much will we spend on each transaction? When will we use the Buy or Sell order? All these questions are all solved by a Capital Management system. One of the effective Capital Management techniques we need to know is the Kelly Criterion.

## The history of the Kelly Criterion

This standard was named after its creator, John L. Kelly Jr., who works for AT&T Bell’s Laboratory. He developed the Kelly Criterion to assist AT&T in the problem of long-distance phone interference. Shortly afterward, this method was published widely as “A New Interpretation Of Information Rate” (1956). However, the gambling world has begun to notice it and realize its potential as an optimal betting system, starting with horse racing. It allows the gamblers to place a greater bet (up to a certain limit which does not cross the fine line between profit and loss) in a long time. Today, many people use it as a Capital Management system.

## Basic Kelly Criterion

There are two basic elements to build up the Kelly standard:

Win ratio (W): the probability of winning in total transaction.
Reward: Risk ratio (R): number of profit pips/loss pips.

We have the following formula:

Kelly% = W – [(1 – W) / R]

## How to use the Kelly Criterion?

Kelly system can be used by following these steps:

1. First, there must be a history of 50 – 60 orders. You review your history and then statistical or backtest the system if you do not have any histories.

2. Calculate the “W” number. For example, if you trade 50 orders, you win 20 orders then W = 20/50 = 0.4. The closer this number is to 1, the better it is, usually above 0.5 is ok.

3. Calculate the “R” number. Everyone knows the Reward: Risk ratio. If this number is greater than 1, it is fine, which means your profit is enough to offset or overcome the risks that you have to take.

4. Add the number to the formula, calculate K%.

## Interpret the Kelly standard results

The percentage K% (always a number less than 1) will indicate the optimal volume you should enter the order. For example, if K% = 0.05, you should only spend 5% of your account to bear the risk for each trade. This system basically tells you how to balance your portfolio.

But you have to remember one significant rule is no matter what K% result, it must be no more than 20-25% of the account for each trade. If it was more, it would be a risk.

A perfect capital management system does not exist. Even this system will help you to diversify your portfolio effectively by allocating capital appropriately for each trade order, each currency pair or each stock for optimal optimization, there are many things it cannot do. It is not able to choose which pair is suitable for you to trade or forecast a sudden market decline, but it may reduce your risk.

Have you ever wondered how to calculate exactly how much you have to spend (what percentage of your account) for an order?

Let’s pretend that you are going to enter an order that you expect it is going to be a good opportunity, but you are not sure how many lots, how many contracts, how many stocks, etc. go against your expectation. On the other hand, you are also afraid of not receiving many profits by risking too little. Sound familiar?

What we are going to find out now – exactly what percentage of your account that you will spend to maximize profits and minimize risk. Let’s play a game!

## Coin toss game

Imagine you are playing a game and betting \$ 1. The rule is as follows:

+ The heads is 2 \$

+ The tails only costs you 1 \$.

From a mathematical standpoint, the Expected Value (EV) of this investment is calculated as follows:

EV = \$2 * 0.5 – \$1 * 0.5 = \$0.5

(Explain: the ratio of winning \$ 2 and losing \$ 1 are equal to 0.5 – 0.5, minus profit, we still have \$0.5)

The EV result shows this is a good opportunity. The number \$0.5 also means that when you toss a lot of turns, you will earn an average of 50 cents per coin toss.

The coin toss game is exactly like an effective trading strategy. For example: take profit = two times stop-loss and the rate of loss is almost the same. It is obvious that you have a fine strategy, you cannot lose.

That is the common way of thinking, but the truth is not like that. You can lose everything in an easy game like tossing coins above. Why?

## Wrong money management strategy

Let’s pretend you only have \$100 to play this game. And due to a great opportunity this time, you decide to bet 75% of the money on the heads of the coin.

First turn:

+ You bet 75% x \$ 100 = \$ 75

+ The result is the heads – you earn 2 x \$ 75 = \$ 150

+ Now you have \$ 250

Second turn:

+ You bet 75% x \$ 250 = \$ 187.5

+ The result is the tails – you pay back \$ 187.5

+ Now you have only \$ 62.5 left

It is still the same rule, the same winning 2 and losing 1, and the same ratio of 50-50, but you can see you have a loss after two tosses of a coin. And if you keep on playing, you will completely lose your \$ 100.

The reason is betting too much.

## Applying Kelly formula

Look what happens to your account if you choose different odds (you can verify these numbers):

+ 10% -> \$ 108
+ 20% -> \$ 112
+ 30% -> \$ 112
+ 40% -> \$ 108
+ 50% -> \$ 100 (equity)
+ 60% -> \$ 88
+ 70% -> \$ 72
+ 80% -> \$ 52
+ 90% -> \$ 28
+ 100% -> \$ 0

What do you see? From 10% to 100%, the profits increase and decrease and eventually become negative. The optimal ratio we see here is in the range of 20% – 30% (the highest profit). But what is the specific number?

K = (P x B – (1 – P)) / B

Therein:

+ K: optimal bet (risk) ratio

+ P: Winning rate

+ B: loss / win ratio (win 2, lose 1 then B = 2: 1 = 2)

This formula determines the percentage you need to bet how much to maximize your profit. Apply to the previous game:

+ B = 2

+ P = 0.5 (50% chance of winning)

K = (0.5 * 2 – (1 – 0.5)) / 2 = 0.5 / 2 = 0.25

Therefore, to maximize profit when tossing a coin multiple times, you should bet 25% of your account for each toss.

Then we will get 25% -> \$ 112.50 (after 1 win and 1 lose).

Indeed, profits will come when we know how to calculate first.

Note: this ratio is called One Kelly (to distinguish it from Half Kelly) and depending on the trading strategy, the exact value can be different.

## How efficient is the Kelly ratio?

Kelly formula is a head start, but it cannot reflect the full picture. The correlation between account growth and risk can be interpreted as such:

This is the same figure as seen from above – from left to K point (Kelly ratio point), profit maximized and then sank below zero at 2K. Profit is of negative value after reaching 2K.

As long as you can calculate Kelly ratio successfully, a chart like such applied for your own case and a suitable investment approach is achievable.

Just some notion concerning this topic:

## Sub-optimal point

According to popular belief, the most ideal approach you can have is placing your bet on the Kelly ratio. However, there’s nothing such as certainty in this world. One way or another, you can get there by understanding the effect of Sub-optimal point can have on your decision process.

Let’s divide the Kelly chart into 4 fragments:

+ Yellow: from 0 to ½ Kelly is a conservative risk area

+ Orange: ½ Kelly to 1 Kelly is the aggressive risk area

+ Red: 1 Kelly to 2 Kelly is the over-aggressive risk area

+ Black: without any argument, this is the death area

## Conservative risk area

Half-Kelly is truly an attractive number. Sometimes Kelly formula can give you fairly high value, for example, 25% of your account risk. Although the theory is that this ratio is optimal, it is too high in practice.

The reasons include things like the possibility of a series of ongoing losses and factors that make account volatility as well. These are all factors outside the Kelly formula. In short, there are good reasons to think Kelly’s rate gives you a number that is too high. Then move on to Half-Kelly.

The main reason why Half-Kelly is the solution is that it halves your risk, while the long-term profit is only down 25%. You can look at the graph. The other reasons include reducing account volatility by more than 50% and giving us a large margin of safety in our estimated risk.

It is quite safe if you trade with Half-Kelly. This is probably suitable for traders who don’t like risk a lot or have to manage a large account in which risk reduction is a top issue.

## Aggressive risk area

Anything between Half-Kelly and One Kelly is considered a risky area.

Your profits are really higher, but not that much high. Take the example of coin toss again: the risk of 20% (4/5 Kelly) of your account is \$ 112, the risk of 25% (Full Kelly) also only gives us \$ 112.5.

Obviously, we get 0.5% more profit (50 cents for \$ 100), but we have to take 5% more risk (25% -20%). Is it worth it? That is why we call this is a risky area.

## Over-aggressive risk area

Have you ever placed your risk in the red zone and why?

If you enter a single order, of course, the higher the risk, the higher the profit. However, what we see here is a trading list where you trade lots of pairs at once or in turn. And the Kelly formula is used for a long period of time and counting for a portfolio, not a single pair.

Thus, this over-aggressive risk area tells us that, if you trade long-term with this risk ratio, your account will only decrease, not increase. You can only revive profits if you know how to reduce the risk of the Kelly ratio.

The questions like: “What if I don’t have an effective trading system? What if each of my orders is different?

Can the Kelly formula work? ”

## Death area

The name tells you everything. If you have been in this area, get out of there urgently. Only one way for you is the margin call.

A good example of a death zone is the first example of this article when you bet 75% of your account for a coin toss. After applying Kelly formula twice, you only get up to 50%. Therefore, you are in the death zone and witnessing your account being run out every time you toss a coin.

## How to apply for Forex and Crypto?

Very simple. But first, you must have your own system first. If your system is equipped with stop-loss and take profits, then you are fine. You will easily calculate B (Reward: Risk). If not, you have to calculate and average.

When you have B number, now calculating P. It is also necessary to trade a certain number of orders to statistic win / lose ratio. The ratio of the main win is P. Then adding B and P numbers to the formula is finish.

## My Kelly result is negative, what does it mean?

If the result is negative, it means your system is too bad and have to change to another system.

For example:

Pair EURUSD, system has win rate = 70%. SL = 40, TP = 20 (spread included)

Attached to the formula, we have:

K = (P x B – (1 – P)) / B

-> K = (0.7 x 0.5 – (1–0.7)) / 0.5 = 0.1

K = 10% means the maximum you can only bet is 10% of the account.

If you are more careful, you can use Half-Kelly = 5%.

If you place more than 10% on a trade, you will have your account decreased.

## Summary

+ The coin toss game is an interesting example of the Kelly method.

+ Profits can be calculated when we know how to adjust our trading volume.

+ Kelly graph gives us an idea of the risk levels when we use different trading volumes.

+ The Half-Kelly criterion is more optimal is that it halves the risk compared to the Kelly standard, but the profit in the long term only decreases by 1/4 (Risk management is a top priority in trading).

+ It is necessary to have a complete system (with entry, exit, stop-loss, money management, tactics, etc.) and a backtest of at least 50 commands to apply the Kelly standard.

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