The Mathematically most Profitable Money Management Method

The Mathematically most Profitable Money Management Method

24 June 2016, 18:57
Sherif Hasan
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In this article, we will review and evaluate the traditional money management method in terms of the percent of our account we should be risking on each trade. Then, we will learn a money management formula that is capable of maximizing our trading system profits. We will finally give some serious considerations to be taken into account before applying this formula.

The forex traditional money management method

successful trading system must has a clear-cut rules for entries and exits, which include rules for exiting at profit targets and rules for exiting at loss targets.

When planning our trade ahead, the risk management process passes the following steps:

  1. Defining a predetermined point of exiting a losing trade according to our system rules (e.g., a stop loss under a support level 50 pips far from the entry price).
  2. Defining A predetermined portion or ratio of our account we are willing to risk on a trade. That portion varies from 1% up to an aggressive 10% (e.g., 2%).
  3. After deciding the stop loss size (50 pips) and the risk ratio (2%), we finally calculate the appropriate position size.
  • In this example if we trade a 10000$ account buying EUR/USD :
  • 2% risked ratio = 200$ (10000$*2/100)
  • If 200$ loss = the loss of 50 pip , then 1 pip value = 4$
  • Since a standard lot pip value = 10$, the appropriate trade size is 0.4 standard lot..

That is how we protect our account against some inevitably losing trades. That is how we cut our losses adopting the motto "Be able to live to trade another day!."

Criticism of the traditional method of money management

If I am to criticize the traditional method of money management, and I do, I will say that the predetermined ratio of the account we are willing to risk on a trade (usually from 1% up to 10%) is determined based on the trader personal risk appetite and tolerance, and whether he is conservative or aggressive, fearful or greedy. It doesn't relate to profit maximization which is trading all about. So, for a certain trading system, we don't know exactly which risk ratio is most profitable (e.g., 5% or 10%) , and by the way, for a profitable trading system, risking only 5% may be more profitable than risking 10% of the account on a trade ,and we will know about this later in the article.

Now you may be asking "how do I know the most profitable risk ratio for a certain trading system?", so let me introduce another money management method!

The mathematically most profitable money management method

In this method, the risked ratio is not subjectively chosen by the trader, rather it depends objectively on the trading system qualities and performance.

In his book "Forex conquered" john l. Person explained briefly what is called "the Kelly Formula", its history, and its application in the financial markets.

To apply this method for a certain trading system we follow these simple steps:

  1. We list this system's last 50-60 trades. Either from a live account, demo account, or from backtesting the system.
  2. We calculate "W", the winning probability. To do this, we divide the number of positive (profitable) trades by the total number of trades (positive and negative). This number is better as it gets closer to one. Any number above 0.50 is good.
  3. We calculate "R," the win/loss ratio. To do this we divide the average pips gained in the positive trades by the average pips lost in the negative trades. We should have a number greater than 1 if average gains are greater than average losses. A result less than one is manageable as long as the number of losing trades remains small and the winning probability is high.
  4. We input these numbers into Kelly's formula:
  • K% = W – [(1 – W) / R]
  • where
  • K = Kelly ratio percent value which represents the exact percent of the account we should risk on each trade.
  • W = Winning probability
  • R = Win/loss ratio

Example:

We analyzed the last 50 trades for a system and found the following:

  • 26 trades were positive ( profitable ) with a total gain of 780 pips
  • 24 trades were negative with a total loss of 600 pips

To get the Kelly ratio:

  • W = 26/50=0.52
  • R = (780/26)/ (600/24) =1.2
  • K% = W – [(1 – W) / R]
  • K% = 0.52- [(1 – 0.52) / 1.2]
  • K% = 12%

This means that to maximize the total returns trading this system, we should risk ideally 12% of our account on each trade. If we risked another higher or lower ratio, total profits will decrease.

The Kelly ratio also help us comparing different trading systems. . For example, assume “System 1” wins a lot of the time; but when it loses, it loses big. Whereas “System 2” doesn’t win very often; but when it wins, it makes big money. The Kelly ratio algorithmically combines both the winning percentages and the payout ratio to come up with a single number that may be used to “compare” the effectiveness of different systems. In order to make that determination, we look for the system that has the highest Kelly ratio.

If we are to diversify our account by trading more than one system or even trading a number of varied financial instruments in different markets (e.g. Forex, Options, Stock...etc.) , the Kelly ratio answers the simple question of " how much money should we put in each trade?".

The Kelly ratio usage considerations

So why not everyone is using this most profitable money management method?

  1. Since the Kelly ratio works from a purely statistical perspective, this method implies that the past performance of the trading system will remain the same in future and doesn't change. It assumes that the investor is able to maintain his promising results.
  2. Most people would agree that the Kelly ratio provides high risk. After all we are not machines. Maybe we cannot emotionally tolerate the high risk. It may affect our trading decisions and results. High risk may fit better the automated systems with stable results. For this purpose; so possibly cutting the Kelly ratio in half might get us closer to a more reasonable risk level.
  3. The Kelly ratio addresses the issue of maximizing profits, but it does not take into account some other factors that a trader might deem important when analyzing a trading strategy , such as the maximum drawdown (MDD),

Conclusion

Money management itself doesn't generate profits. We must first of all have a profitable trading system. Then, we are to choose a proper more fitting money management method. The Kelly formula is one tool that can help us in variety of ways. Using it we can intelligently fine tune our risk, compare different trading systems, and diversify our account or portfolio.

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