# The trader's equation: Should I take this trade?

By Al Brooks

When you consider a trade, you ask yourself: "Will I make money on this trade?" The decision is based on an assessment of the mathematics of the setup. Although the trader’s equation may not come to mind explicity, it is always the basis for the decision. You will take the trade if you believe the chance of success times the reward is significantly greater than the chance of failure times the risk.

There are three variables in the trader’s equation, and we can control two of them and estimate the third. The risk is based on the protective stop. If the stop is two points from entry, then the risk is two points. The reward is based on the profit-taking limit order. If the target is two points from the entry, then the reward is two points.

Most traders should not take trades when the reward is less than the risk because an unrealistically high winning percentage is necessary to be profitable over time. For example, if a trader risks three points to make a one-point scalp, he has to win about 80% of his trades just to break even (and the goal should never be to just break even). To make a living trading this risk/reward profile, the trader would have to win about 90% of the time. And this level of performance would have to be maintained month after month, year after year. If this trader took 10 trades using a one-point profit target and a three-point stop and won on seven and lost on three, he would make a total of seven points and lose a total of nine. Even though he won on 70% of his trades, he still would have a net loss of two points.

You also have to allow for commissions, slippage and the occasional mistake.

### The third variable

As a general rule, do not take a trade unless the reward is at least as great as the risk. As such, the trading decision always should begin with an assessment of risk. Risk is defined by the distance of the stop. If two points are risked in the E-mini on the five-minute chart, the trade only should be taken if two points of reward reasonably can be achieved. Risking two points to make two points needs, realistically, a 60% winning percentage to provide profits over and above commissions, slippage and mistakes.

Is that realistic? If the trader carefully picks setups, it can be. Alternatively, if only the best two or three trades a day are taken with a four-point profit target and a two-point stop, a 40% success rate may be viable.

For example, if four points each were made on four trades and two points were lost on the other six, 16 points would have been gained and 12 would have been lost, for a net of 4 points or 0.4 points per trade. After commissions, this is about \$20 per trade per contract in the E-mini. A 60% win rate would increase profit per trade to 1.6 points, or \$70 per trade after commissions. At two trades a day, 10 contracts at a time, this is \$1,400 a day and more than \$250,000 per year. Bottom line: If reward is at least as large as risk and if the win percentage is more than 50%, a trader is in a position to make money.

Improving the third variable — probability — can go a long way toward increasing profit. Probability never can be known with certainty because countless factors affect it. Even with careful testing, a trader might be only 90% certain that a setup has a 60% chance of success. Most traders should not take trades when they believe that they probably will lose. Can a trader make money on a trade where the chance of success is only 20%? Of course, because the trader’s equation has three variables and if the profit target is 16 ticks and the stop is only two ticks, he could make money.

But is a two-tick protective stop ever realistic? Not often, but sometimes it is. If a trader thinks a pullback should not fall below a prior low, a limit order to buy one tick above that prior low with a one-tick stop loss below it might work. If the order gets filled, there may be about a 30% chance of the market forming a double bottom and reaching the profit target without the stop being hit. Finding low risk/high reward opportunities is the key to success.

At the other extreme, is there ever a situation where the chance of success is 95%? Yes. However, that does not mean that the trade is worth taking. For example, if the market is in a strong bull trend and is breaking out of a bull flag, there could be a 95% chance that it will go one tick higher before it falls to below the bottom of the flag. If a trader bought at the market and placed a limit order to exit with a one-tick profit and had a protective stop below the bottom of the flag, maybe 20 ticks away, the chance of success would be extremely high. However, if the trader took the setup 20 times, he would have 19 ticks in winnings but the one 20-tick loser would erase all of those winnings.

### Probability analysis

It is useful to think about directional probability. For example, what is the chance that the market will rally X points before falling Y points? If you look at a situation where your risk equals your reward, then you are considering the directional probability of an equidistant move.

Most of the time, it is about 50%. That means that during most of the day, the E-mini has a 50% chance of falling two points before rallying two points or rallying two points before falling two points. As long as you are considering moves that reasonably can be expected, given the average daily range, this is a reliable rule.

There are times when the directional probability may be skewed, and these are the times traders might have an edge. Indeed, there are situations when the directional probability of an equidistant move is 60% or higher. Then there are times when the probability is 60% or higher that the market will go four or more points in one direction before going two in the opposite direction. When traders learn to spot these setups, they have a great mathematical edge and a profitable trader’s equation.

Two common setups occur in strong trends and another in trading ranges.

### Directional edge

If the market is in a strong bull trend, such as in "Power up" (below), 80% of reversal attempts will fail. That means that about 80% of the pullbacks will result in a test of the high of the trend.

If a trader bought a small two-legged pullback to the moving average and there was a bull signal bar, it is reasonable to assume that there would be a 60% chance of making two points before losing two points. Also, if the trend began with a strong bull spike composed of two or more consecutive bull trend bars with large bodies and small tails, the chance of making two points on a long before losing two points is probably at least 60%. If the trend is strong enough, and the trader swings the trade, he might discover that his average win is five points while risking just two points and his winning percentage might be greater than 60%.

If the trader took this setup 10 times and won two points on his six winners, he would make 12 points while losing a total of eight points on his four losers, for an average profit of 0.4 points per trade. The reality is that the probability is likely 70% or more in a strong trend, the risk is often six or seven ticks instead of eight, and the reward is often four or more points, so the setup is even stronger. With a 70% chance of making four points before losing two points, the average profit per trade is 2.2 points, or more than \$100, which is great for a day trade.

When the market is in a trading range, it spends most of its time in the middle where the directional probability of an equidistant move is 50% (see "Middle man"). The middle of the trading range is where uncertainty is greatest, and that means the probability of the market going up one point before dropping one point is about 50%.

However, about 80% of the attempts to break out of a trading range fail (depending on how you define: trading range, breakout attempt and failure). That means that looking to short near the top of the range might have an 80% chance of success, depending on your risk/reward, and it is reasonable to assume that it has at least a 60% chance of success. Likewise, looking to buy near the bottom of the range to scalp an up move probably has at least a 60% chance of success.

If the range is large enough, a trader often can set a profit target that is twice as far away as the stop. For example, the trader might sometimes be able to risk just six ticks and have a good chance to make three points, and have at least a 60% chance of success. If he takes this setup 10 times, he will make 18 points on his winners and lose 24 ticks, or six points, on his losers and averages 1.2 points of profit per trade.

With any trade, it is distracting to spend too much time assessing the exact probability. A reasonable alternative is to limit the decision to just two choices. If a trader cannot convince himself that a trade likely will be successful, he should assume that the probability is 50%. If he thinks that he has a good chance of making money on the trade, he should assume that the probability is 60%.

On the 50-50 trades, the trader needs to have a reward that is at least twice the size of the risk to make the trade worth taking; this does not occur often with 50-50 setups. Instead, traders should focus on setups that they believe will have at least a 60% chance of success. In all cases, the trader should choose a profit goal that is at least as large as the risk. This approach is a good foundation upon which a trader can build, and once he develops the ability to read charts well and the discipline to follow his rules, he has a good chance of success.

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