How to Place Stop Losses and Take Profits Using a Maximal Strategy

 When entering a trade, how do you choose the point of the stop loss and take profit? Clearly, this decision will have an impact on how profitable your trades are. However, did you know that the placement of your exit levels can actually have more of a bearing on your profitability than the decision on which direction to trade?

 
How to choose stop loss and take profit

In the volatile forex market, it is actually true. Given how important this decision is, it is surprising how little thought many traders give to this component of their trade.
In this article, I want to explain a quantitative strategy that will help you select stops and take profit levels for maximum profit. I also want to debunk some of the common misunderstanding around risk-reward setups, and show how following poor advice can ruin a potentially good trading system.
If you just want to try the stop loss/take profit calculator, and are not interested in the theory, please click here.

Why Guessing Stop Losses and Take Profits is a Plan for Failure

A trading position will normally exit at one of two points. After entering the trade, either:

• The price reaches the take profit (TP), and the trade finishes in profit
• The price reaches the stop loss (SL), and the trade winds up with a loss

When deciding trade exits, it is sometimes tempting to make an educated guess. Some traders use technical features such as chart candles, trends, resistances and supports. Others simply choose a fixed ratio of profit target to stop loss.
While this is very common, there are several drawbacks:

• It is error prone. When you guess the exit levels for a trade it is very easy to either overestimate or underestimate price movements.
• It is not repeatable and that makes it very difficult to analyze or improve performance. When there is no logic or methodology behind placements of exit points, you never know if a failure was due to a miscalculated TP/SL combination or because your strategy is not working.
• Traders will often move stops up or down on subsequent trades based on trial and error trying to find a “sweet spot”.
• It is very difficult to automate methods that rely on gut instinct or other subjective decisions.

There is nothing wrong with using technical analysis as a guide for timing the trade entry, nor for judging how far the price might move. Rather, the method I describe below is used alongside both charting and fundamental analysis.

The Fallacy of Using SL/TP as Proxy Risk-Reward

Forex trading forums are full of well meaning, yet rather misguided advice about risk-reward setups and how to set your stop losses. Unfortunately, many of these people fail to understand the true meaning of risk or reward.
The idea that simply setting your stop loss smaller than your take profits will achieve a certain risk reward is complete nonsense.
Using risk/reward to set your trade entry and exits does not make any sense unless you know the probability of outcomes in a given trade.
Take this simple example. Suppose there is a lottery costing $1 to enter. The prize is $1m. By the definition of the naïve trader, this gives:
Risk: $1
Reward: $1m
Reward/Risk ratio: 1,000,000
By that definition, this would seem a fantastic game to play. However, suppose we know that two million people enter the lottery. This makes the odds of winning 1:2,000,000 (one in two million). Now we know the odds, we can calculate the true risk reward:
True risk: p(loss) x E(loss) = (1- 1/2000000) x ($1)
True reward: p(win) x E(win) = (1/2000000) x ($1,000,000)
True reward/risk ratio: 0.5
In other words, for every $1 you put into this lottery, you’d expect to get 50 cents back. Most would now agree this is not a very good game. Even though on the naïve trader’s reckoning, it had a reward to risk ratio of one million.
This example highlights the fallacy of using stops and take profits as a measure of your risk/reward.
In a trade, we have the real risk/reward defined by:
Reward: p(win) x E(win)
Risk: p(lose) x E(lose)
Reward/Risk ratio: p(win) x E(win) / p(lose) x E(lose)

E(win) is the expected payoff in the trade, namely your take profit amount. E(lose) is your stop loss amount.

The Risk-Reward Relationship

The first thing to realize about setting trade exit points is that the amount of profit you want to make on a trade is directly proportional to the risk you will need to take to capture that profit.
This is not a supposition, but rather a mathematical fact.
Take the following trading scenario. Say for example that a trader sees an upward trend on the hourly chart for USD/JPY (see chart below). The trend has been in place for around one day, so the trader thinks there is a good opportunity for profit.
He decides on the following setup:
Entry: Buy USD/JPY@ 109.70
Stop: 109.50 (20 pips)
Take profit: 110.40 (70 pips)
Now let’s analyze this trade setup in more detail. The first thing to notice is the trader wants to capture a profit of 70 pips on the trade.
So what is wrong with this setup?
Based on recent price data for this currency pair, we can calculate that USD/JPY has an hourly volatility of 26.4 pips. That means, on average, the movement of the price over one hour is 26.4 pips. Sometimes more, sometimes less but this is the average.

Figure 1: Trading example, wrong placement of stops/take profits

This means the trader is trying to profit by 70 pips. In reality, he is actually betting against the market because he is relying on the fact that the price will not descend more than 20 pips from the open price during the life of the trade. That could be up to 30 hours if the current trend continues (from Figure 1).
Given the hourly volatility in USD/JPY is currently over 26 pips, this much stability in price would be highly unlikely. While the trade has a very low maximum loss (20 pips), which might seem like a plus, the chances of it finishing in profit are extremely low.
If we know on average that the price of USD/JPY moves up or down by 26.4 pips every hour, why would it do anything different for this particular trade? The answer is that it would not and the trade would probably strike the stop loss for that reason.
Due to the volatility in FX, this is true even if the predicted trend continues.
The basic problem with the setup was that trader was trying to capture too much profit without accounting for volatility.
Remember that in forex, volatility is not something you can avoid by careful trade picking or a clever strategy. It is an absolute certainty.
That’s why it is far better to make volatility work for you rather than against you.
The question then is when setting up a trade, how do you know where to place the exit points other than just taking a wild guess? The following will explain how to do this.

Calculating Stop Losses and Take Profits Using Maximals

The method I prefer to use is based on a technique known as maximals. What this does is give a precise formula to work out the probability of the price moving a certain distance from the open during a given time.
This model gives a complete distribution of price moves for a given volatility. This method works for any timeframe, minutes hours or even months. It also works equally well with either historical (past) or implied (future) volatility.
In deciding trade exit points, there are three things to consider:

• The expected timeframe of the trade (related to profit target)
• The market trending behavior
• The profit target

Let’s take a look at each of these.

Step 1: The Time Frame

The type of trader you are will have a bearing on the time that your trades need to stay open to reach your profit target.
A day trader or a scalper would hold a position for hours, minutes or even seconds. At the other extreme, a carry trader holds positions for weeks, or months. For the carry trader, capital gain on the trade is usually less important. The goal is to hold the position open for as long as possible to accumulate interest.
Clearly then, profit and time are linked. So in setting your trade exit points, the first step is know precisely how far the price is likely to move in a given timeframe. Once you know this, you will be able to decide a realistic profit target.
Take the following example. Figure 2 below shows EUR/USD over five minute intervals (M5). The chart spans a 24-hour period.

Figure 2: EUR/USD 5 Minute Chart (M5) – 24 hour period

The first thing I do is calculate the volatility over my chosen period. From the open/close data, I calculate that to be just over 10 pips per 5-minute period.
Once I know how volatile the market is, I can project the price forwards to work out the probability of a certain move x hours (defined by 5-minute intervals) into the future.
To do this, I need to calculate what are known as maximal curves (see box for an explanation). Briefly, taking the volatility as input these curves will tell me the probability of a maximum price (either up or down) being reached.
Figure 3 below shows the maximal curves calculated for 1 hour to 24 hours ahead for the EUR/USD chart.

Figure 3: Maximal curves for EUR/USD (M5) - Pip Movement vs Probability

For example, looking at the maximal curve for 24 hours (top line), I know the price has a 76.8% probability of moving 62 pips within a 24-hour period. Whereas it has a 40% probability of moving more than 141 pips in that same time frame.

The Random Walk

I only give a brief description here of what are rather complex calculations. The best market model we have for forex is the random step process or random walk.
This just means that in every interval, the market moves by a random step value. The price can slant towards an uptrend or a downtrend with a drift parameter.

Yt = Yt-1 + α

Using a discrete unitary step function to model these price moves, the probability that price reaches a certain maximum at any time can be found as

We then transform the price Z, using the volatility into a standard unit variable for comparison against the step process. From this we create a set of curves for different timeframes. In essence, the longer the time interval and the greater the volatility, the further the price can move from the existing level.
From these we can calculate the probability of a price change over any length of time.

Hedge funds and professional traders often use maximal curves or some variant thereof. The reason they are so important is that they allow you to setup your trade accurately in terms of time and profit capture. The curve tells you if the amount of profit you want to make is reasonable in terms of the time span.
For example, I know if I wanted to capture a 300-pip movement, I would likely be waiting roughly ten-days based on the current volatility level. This is because from the curve, there is only a 10% chance of the price moving 300 pips in any 24-hour period.

Step 2: The Market

If the market is flat, or trending in a certain direction this will have a strong bearing on where you place your stops and profits. In terms of the model, it means that we have an asymmetric distribution of price movements.
There are several ways to allow for this, but the simplest and the one I prefer is to use a different volatility for the upside and downside price model.
The statistical skew is useful here because it tells you how asymmetric the volatility distribution is and allows you to add an upwards/downwards drift.
Market
Random walk – not trending
Trend up – positive drift
Trend down – negative drift
With the random walk, up and down price moves are equally likely. When trending, two different sets of maximal curves are needed, one for up moves and another for down.

Step 3: The Profit Target

Having decided on a timeframe and on the trending characteristics, I can now choose an appropriate profit target that will give my trade a high win probability.
Say I’ve checked the chart, and decided to buy at the current market level, and I decide my target will be +40 pips and my cut off will be -100 pips.
The table below gives the probability of my exit points being reached in each of the three market conditions.

	Take profit @ +40 pips			Stop loss @ -100 pips
Hour	Flat	Trend+	Trend-	Flat	Trend+	Trend-
24	82%	66%	88%	57%	70%	27%
18	79%	61%	86%	51%	65%	20%
12	75%	53%	83%	42%	58%	12%
6	65%	38%	76%	25%	44%	3%
4	58%	28%	70%	16%	34%	1%
2	44%	13%	59%	5%	18%	.01%
1	28%	3%	46%	.4%	6%	0%

Copyright © 2015 Forexop.com

Trend+: Trend in same direction
Trend– : Trend reverses direction
Flat: Sideways market
My trade setup is then:
Take profit +40 pips   82% probability of reaching TP within 24 hours
Stop loss -100 pips   57% probability of reaching SL within 24 hours
Entry price: Buy 1.1290
Take profit: 1.1330 (+40 pips)
Stop: 1.1190 (-100 pips)
What this analysis tells me is that EUR/USD has a certain chance of reaching the TP/SL levels within my trade timeframe. But it doesn’t tell me which is reached first.
What I would also like to see is the probability of the trade actually making a profit or loss. The price could reach the stop first, and then the take profit. In that case, my trade would finish with a loss. It could alternatively reach the take profit first, in which case it wins. Alternatively, it may neither reach the stop nor take profit level in which case the trade remains open.
Based on this analysis I can use standard probability theory to work out each outcome for the trade:

Outcome	Flat	Trend+	Trend-
p(win)	63%	42%	82%
p(lose)	29%	47%	9%
p(open)	8%	10%	9%
Win ratio	68%	47%	90%

My best outcome happens if the short-term trend reverses, that is if the market rises and makes my buy profitable. The worst outcome happens if the trend continues in the same direction (trend+). In that case, I have a 42% chance of the trade ending in profit, and a 47% chance of it ending in a loss.
When I set the trade up what I am looking for is the chance of the take profit being reached, to be at least 1.5x the chance of the stop being reached. This will give a win ratio of around 70% or higher.
Also, remember that if you move the stop loss or take profit while the trade is open that gives you an entirely different set of outcomes.

Analyzing the Trade

To see how the stop and take profit levels shift for different trading timeframes, I can work out an envelope, which will give me a fixed win ratio. The graph below in Figure 4 shows this plotted out for my example trade.
From this, I can see that if I were trading over a 12-hour period, I could choose to set:
SL = -67.3 / TP= +26.9
That would achieve the same win ratio. It would also give a lower profit of just +26.9 pips.

Figure 4: TP/SL envelope for fixed trade win ratio

With my 24-hour timeframe, I can also see how the possible outcomes will change over time.
The chart below (Figure 5) shows the probability of a win, a loss, or the trade remaining open over 24 hours – the expected lifetime of my trade.
From the chart, I can see it has the highest chance of closing in profit within the first 90 minutes of being opened. Thereafter, the chance of a loss rises significantly.

Figure 5: EUR/USD Trade outcome probability over 24 hour period

This is because the maximal curves become flatter for longer periods. If you check Figure 3 again, you will see that the curves for 24-hours and 18 hours are quite similar, whereas there is a big difference between the 1 hour and 6-hour curves. The highest differential is in the first few intervals where the curves are steepest.

Money Management

As shown above, your stop distances have to work in terms of your profit target and the volatility levels.
New traders often place stop losses too tight, thinking they are reducing risk. The usual reason for this is that they are using far too much leverage and try to reduce exposure by placing limits on individual trades. It is better to manage risk through trade size (exposure) than to use stop losses which don’t make sense.
Suppose you see a trading opportunity, and the potential drawdown needs to be 300 pips to capture that profit. If 300 pips is not an acceptable loss, then it is better to reduce leverage and adjust your trade size downwards to give you more flexibility.
Instead of trading one lot, consider trading in one tenth of a lot units or lower.
What is most important is that a potential loss (or drawdown amount) on a trade should be manageable within your account. This should be part of an overall money management strategy so that you know your loss limits and those losses, even in succession will not cause a margin call or bankrupt your account.
Remember, over-leverage is the #1 killer of new forex traders.
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Stop Loss Calculator

I provide the Excel spreadsheet with all calculations here so that you can download it and try this system out for yourself.

For instructions on how to use the sheet, please see here. The spreadsheet does not have the live price feed which I use, but you can manually paste in historical price data from MetaTrader to work out optimum take profit and stop losses in the same way I’ve explained.
We also have a MetaTrader expert, which does the same calculations in real time. This calculator will be available to download on the website shortly.

source:forexop