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Summary It is effective risk management that determines profitability rather than the incidence of wins to losses. The law of large numbers suggests that a larger number of trades with a positive reward to risk ratio will be more effective than a smaller number of trades. In this regard, it is possible for a trader to be “wrong” a majority of the time while continuing to remain profitable. “It’s not whether you’re right or wrong that’s important, but how much money you make when you’re right and how much you lose when you’re wrong.” – George Soros The entire dynamic of successful trading could probably be summed up in the above sentence. When I started out trading forex, I was overly concerned with getting the trades right. However, I have come to learn that the most successful traders are not the ones who are right all the time; rather they are the ones who know how to manage their risk most effectively . For instance, the odds that a plane will crash somewhere in the world are 1 in 11 million. Indeed, this is a very low probability. However, when one considers the vast number of flights that take off and land every day, it is sadly almost inevitable that there will be a plane crash at some point in the future. The odds of a golfer getting a hole in one are 5,000 to 1. However, across the world there are far more than 5,000 games of golf being played in a single day; it is therefore almost inevitable that a player somewhere in the world will manage to score a hole in one today. The above phenomenon is known as the law of large numbers ; where an event with a low probability of occurring on its own has a higher probability of occurring when subjected to a large number of trials. This has important implications for risk management, and moreover it demonstrates how a trader can still be wrong the majority of the time while continuing to be profitable. Let us take this as an example. Suppose that we have eight forex trades in a particular month, with a 1:3 risk-reward ratio, or a stop loss of 50 pips and a take profit of 150 pips. For each trade (discounting technical or fundamental factors), the odds are greater that we will make a loss rather than a profit. However, the profit on each trade far outweighs the potential loss. With a 1:3 risk-reward ratio, we have a 75 percent chance of the price hitting our stop loss with a 25 percent chance of it hitting our take profit ratio. However, this also means that only two of the eight trades need to be profitable for us to breakeven. Moreover, the law of large numbers dictates that at least two of our trades are indeed likely to be profitable. 1-(1-p)^number of trials where p is the probability of an event occurring In the above instance, we need at least three of our trades to hit the take profit point in order to be profitable. Given that we have a 0.25 probability of this happening, our probabilities are as follows: 1-(0.25)^1 = 0.25 1-(0.25)^2 = 0.4375 1-(0.25)^3 = 0.5781 1-(0.25)^4 = 0.6835 1-(0.25)^5 = 0.7626 1-(0.25)^6 = 0.8220 1-(0.25)^7 = 0.8665 1-(0.25)^8 = 0.8998 We see that with eight trades being placed, we have an 89 percent probability that at least one trade will hit our take profit point. Given that we need three trades to be profitable: 0.8998^3 = 72.85 percent probability of three trades being profitable In this regard, we see that the law of large numbers provides us with an attractive risk-reward set up in that it limits our downside while maximizing our upside. Moreover, we can be wrong more often than we are right and still remain profitable. One of the big reasons why most new traders fail is the inability to manage risk effectively. For instance, if we decided to set up trades with a high risk and low return, e.g. 150-pip stop loss and 50-pip profit, then even if we were right a majority of the time it would only take a couple of losing trades to wipe out our winnings. Ultimately, being a successful trader is not always about being right. It is about managing your risk effectively. As we can see, the law of large numbers plays a key role in doing so. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article. Scalper1 News
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