Stop Loss Placement, ATR and Probability. What's the Math?

Trading Discussion
1

Hi,

There’s got to be a way to determine mathematically the odds of getting your stop loss hit whether it’s your initial stop, whether it’s moved to breakeven, or whether you’re trailing price with it.

Let’s use moving the stop loss to breakeven as an example. Here’s what I’ve come up with so far:

Please correct me if I’m wrong at any point. I’m sure that not only I, but many others, would like to get a good handle on this.

The ATR is the average range of a candle as calculated over a given number of periods. To simplify matters, let’s say that half the time during an ATR period the candle will be longer than the ATR, and half the time it will be shorter. Therefore, if I place my stop loss at breakeven when price is 2 ATRs away from it, I stand a 50% chance of being stopped out during that period - 2 ATRs, not 1, because, on the average, price will move either up or down 1 ATR during that period. Wrong? Let’s hear it, with an explanation, from someone good at this kind of visual thinking and math.

Anyway, here’s what Adam Lemon of Daily Forex has to say: “Every currency pair or cross has an average daily range of volatility. If your stop loss level is within half of that amount, it will probably be hit within the next day or two.” When to Move a Stop Loss to Break Even | DailyForex. This is the kind of thing I’m after, but with understanding. A formula for different ATR distances is the goal.

Here’s the million dollar question (Wouldn’t that be nice!):

What math formula may we use to determine the chance per cent of being stopped out based on the distance of stop loss from price?

For example, how would we determine what the chance percentage is of being stopped out if I place my stop 2 ATRs from price? 1.5 ATRs? Etc.

Please allow me: Let’s not discuss whether it’s good to move your stop at all or what the best way to do it is. Let’s stick to the question.

Thanks,
Norm

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[quote=“NormanA, post:1, topic:165943”]
There’s got to be a way to determine mathematically the odds of getting your stop loss hit whether it’s your initial stop, whether it’s moved to breakeven, or whether you’re trailing price with it.[/quote]

Hi @NormanA

A thread over on Forex Factory titled Trading Myths and Some Forex Math maybe of some interest.

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No offence, but i’m not in favor of giving a fixed odds for stop loss and target. Forex is too fluid and amphibious to be caged with simplified probability.

Depending on the period of assessment. The odds can varies between a wide spectrum of likelihood. It is unlike holdem where we can calculate the odds base on the number of cards leftover in the deck.

In forex, the are too many hidden and impromptu factors. Base on the fundamentals, we can only feel the directions and may not be right even, then when we get it wrong, we give excuse like the market have been priced in to explain the AFTERMATH. With technical analysis, we attempt to project targets and stop loss. End of the day, we are no different from fortune tellers.

Attaching fixed odds to stop loss based on ATR may lead to illusory foresight bias. When dealing with a forex market of such mercurial behaviour. We need to be just as mutable.

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Its a rational question Norm but I feel trying to increase precision on something like this is just illusory.

However, persuaded by arguments here and elsewhere I started using 2 x ATR20 as my SL this month. The sample size is too small to be conclusive but so far I have opened 17 trades on this SL basis - 6 are still running and in profit, while the 2ATR20 SL was hit 4 times.

Of the other 7, I closed them manually before the SL was hit, based on either TA weakness or adverse newsflow, 2 of the 7 closing for profits.

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Hi alphahavoc,

I must disagree. Fortune tellers have no clue. Odds and percentages of likelihood do give us a clue, and that is true with much of forex. For example, we’ve all heard the saying, “This is a low risk, high probability trade.” We’re not talking about certainties, merely probabilities, but probabilities are far better than nothing; and I think we can come up with some formula for probability based on ATR distance or something similar.

Thanks and take care,
Norm

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Hi tommor.

I’ve heard 2ATR, as well, from some very successful traders; and although the statistics you give are based on a very small sample, they are worth noting - but a probability formula or rule of thumb from someone would be outstanding!

Thanks,
Norm

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You’re right Norm. Just because there are two possible outcomes, it doesn’t mean they are each 50% probable.

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Hey N, the problem with the math, is context. First whatever system you are using must have a positive expectancy. The problem with that, is that, positive expectancy. I was at a (comped) trading seminar and they did the coin toss thing, trying to prove that with proper money management you could run 50% losses and still survive. Well, guess what, it did not work, they were risking 2% per flip, after 20 flips, in the negative, well you can figure out the drawdown.

Now I think that getting 20 flips negative is an outlier, but it did happen, and can happen. Eventually the flips did get more of a slight +50% bias, but by then how long would it have taken to recover, who knows?

Also, if each flip is counted as a trade, and at one trade a day, that means you are 20 days in the hole. Now you could play with your size to keep the same stop, as far as size vs % of account. But even though you have drawn down maybe a half of a percent, you still have 20 negative trades in as many days on small size, which will take you quite some to recover.

I know the proceeding does not directly address your question, but I will in a moment. I believe the concept of being able to quantify/quantize (meaning giving it a number/value) to everything is, well, shall we say difficult. You first have to have the context of the trade, even the Quants do this, the context, news and reports etc are constantly updated in real time, it’s not just a matter of a plain set of numbers and then blindly following them.

This is why I always talk about PRICETIME, and not just price. There are time factors to consider, think about this, the longer you hold a trade the more risk there is, also there are random, emotional, mental, fundamental factors to bake into the mix also. So where does that leave us with ATR.

As with all indicators it can turn on a dime, also depending on what fractal you are trading in, your stop will be different, also the period setting of the ATR can make a difference, but 2x is the recommended number. The reality is if one is consistently on the wrong side, no matter what you do with the ATR, you will still lose more than make, I know you know this, I figured I would add it for new ones. Also ATR is not very good during news and unexpected events, you are better using your own discretion for a stop. I use it for stops and strength determination, it works well as an auxiliary indicator/filter. But I would not use it stand alone.

Don’t forget ATR tells you the range average, and if you have a lazy upward crawl, then you get a spike up followed by an immediate retracement, your ATR will be skewed, the bigger the spike and retracement the bigger the skew, so, while it is helpful, it is not a be all. As far as math, each system is different so you may have to come up with something custom that fits your (style).

The Ever Theorizing VIPER

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9

Great input, guys. You’re absolutely right. There are many factors that go into the mix, and there’s no way we can apprehend them all at any given moment, not even in a lifetime - the weather, the fluctuating price of bago’ong (a fermented fish dish or condiment in the Philippines), and who knows what else!

But the way I see it is this: Getting a rocket to the moon and bringing it back intact is not the product of one math formula, but of millions, perhaps, each affecting all the rest, including temperature, trajectory, acceleration rate, fuel consumption rate, stress tolerance of materials, etc., etc. That’s the way I see this elusive formula involving ATR and stop distance. It is one of many factors, but a very important factor worth apprehending.

What I’m about to offer is not the formula I’m trying to find, but it’s a very helpful principle. It’s the principle of inverse proportion. To quote an online dictionary, it’s the “relation between two quantities such that one increases in proportion as the other decreases.” Obviously, when distance between stop and price increases, the chance of the stop being hit in any given period of time decreases. That’s a no-brainer; but the math describing the rate of decrease is not.

If I remember my high school physics correctly - that’s a big “if” - if you’re talking to me from a distance of ten feet, I hear you at a certain volume; but if you move to twenty feet away, I’ll hear you at half the volume. Double the distance, half the volume. Triple the distance, one-third the volume. Perhaps it’s the same with stop distance: double the distance, half the chance of being hit in any given period of time; triple the distance, divide the chance by three, etc.

Is my math on the rate of decrease correct on this? Any thoughts? Here’s one: It would be great to quantify this, but I’d better get back to my charts or I’ll be dead in the water as far as making any money goes!

Looking forward to what you have to say.

Take care,
Norm

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Thanks Norman, you got me to re-look at ATR again. Will give some input after i digest my understanding on ATR & ADX and its application.

Here’s 4 video to bridge the gap regarding ATR and ADX .

How to Use ADX Indicator to Identify Trend Strength

Using the ATR to Help You Stop Chasing Entries

How to Use the Average True Range (ATR) To Set Stops

How to Use the Average True Range Indicator (ATR)

Sidetrack a bit, i thought this is quite useful, just want to share.
Why CandleStick Wicks Are So Important!

gu.jpg1919×851 355 KB

atradx.tpl (45.4 KB)
(courtesy of Alphahavoc)

Advanced_ADX.ex4 (6.4 KB)
(just search google, literally everywhere, i can’t remember where i download it from)

Atr&CandleLength.ex4 (11.7 KB)
(source of Atr&CandleLength indicator, forexfactory)

Here’s my observation of the chart using ATR and ADX versus the Time price chart

  1. ADX sloping upwards show trend continuation, Green means bullish, Red means bearish
  2. ADX sloping downwards show pullback phase (sometimes choppy) and possible reversal
  3. ATR long red histogram bar shows more than 200% ATR, normally trend continuation, breakout candlestick high buy, breakout candlestick low sell.
  4. ATR short red histogram bar shows less than 50% ATR, compression awaiting breakout, my gut feel is market’s attempt for reversal.

ADX below 20, lack of volatility, uncertain times, stay out of market.
ADX above 20, good volatility, challenge the market.

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The thing about using linear/ univariatate /bivariate (use as many variables as you want) math to figure out stop losses is that they are examining single points in time using data from recent history, and although past prices might influence future prices, the market is a reflexive process, able to influence itself. Unlike any process in the natural world (like gravity or thrust/acceleration in your going to the moon example) the market will adapt as new developments arise, continually thwarting any attempt at accurate pattern-based analysis.

So you can use ADR/ATR as a starting point to gauge volatility, but eventually multifractal time will shoot you an outlier (or a series of them) that will cause one or more of
a) stops that are too conservative
b) stops that are too lenient
c) stops that are completely ignored due to market chaos

That doesn’t mean that ADR/ATR isn’t useful, but I suspect any mathematical theory based on it is doomed to be ~50% accurate in the long run. I would love to be proved wrong about this. Hopefully you can tweak this a bit more using carefully chosen rules and that will be your edge, but is it a mathematical/quantitative solution?

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Hi alphahavoc,

Thanks for sending me those links. Fact is, I’ve studied ATR and ADX, and have a pretty good handle on the differences, on how many traders use ATR to set stops, etc.; but I was looking for something like a mathematical rule of thumb.

Happy trading,
Norm

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Hi clemmo,

Thank you for your reply. Believe it or not, I understood everything you said! But as I implied, an inverse relationship must exist as concerns stop distance, e.g., twice the distance, half the chance of being hit; three times the distance, one-third the chance, etc. - which brings to mind a related matter; but instead of pulling this thread too far afield, I think I’ll write you privately.

Thank you, and happy trading,
Norm

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It seems that you already know the answer. And the implication is, if you never set a stop loss, you will never get hit, provided you have enough margin for drawdown.

Why don’t you turn the table around and think about hitting targets , instead of thinking about hitting stop loss? So long the trend determination is correct , position sizing is safe, PROBABILITY of stop loss doesn’t really matter, isn’t it? When the trend determination is wrong, market conditions for the initial sentiments are no longer valid, position needs to be CLOSE immediately, stop loss is just for insurance.

Perhaps, the need to determine probability of stop loss, arise from the conventional view that we need to know where our stop is prior to entering a position, so that we can calculate the Risk : Reward ratio? I really don’t know man. Personally, Risk : Reward ratio feels like a fluke to me. I think what really matters are profit factor and accuracy. Just some fruits for thoughts, it is not my intention to thwart your enthusiasm in your search on the probability of stop loss using ATR.

On a personal note, if i have a position rollovered to the next day, i re-assess the conditions for my current position and adjust my stop loss accordingly, base on daily high low, taking into consideration of S/R zone, as well as accomodating levels for averaging, and if i average my position, will i be taking on too much risk … etc.

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Hi Alpha,

I “know the answer,” as much of it as I do know, to a great extent because of the thought processes involved in discussing it with you and others. In addition to pondering stops, I’ve already been on the other side of the “table” for quite some time, as well, thinking about the best way to squeeze the last bit of juice out of each trade. It’s never been one “instead” of the other.

As concerns stops and targets, I’ve been having a love affair with Heiken-Ashi. H-A is a bit tricky to work with because its levels do not always coincide with the levels of traditional candles, which are much easier to read; but because of the math involved in their construction, one can afford to have a much tighter stop with them, and they help keep you in the trade much longer by overriding much of the “noise.” Traditional Japanese candles, though, are as clear as a bell; and to keep things clear for me when working with H-A I view the same time frame and pair on the two different types of charts, switching from one to the other. Traditional candles for clarity, H-A for shorter stops and staying with trends longer. It’s working well for me. I have one MT4 for traditional candles, and one for H-A.

The very best article I’ve read on H-A is by Dale Woods, the Forex Guy: Your Ultimate Guide to Trading with Heikin Ashi Candles.

Happy trading,
Norm

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@NormanA - I like the HA candles as well but found they seemed clunky in MT4. My solution has been regular candles and using a HA oscillator. This has worked well as I continue to develop my price action skills.

FR&L

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Thanks FR,

I’m using stochastics and RSIOMA on HA and traditional candles. Still deciding between the oscillators, but they are both good!

As for RSIOMA, I took a tip from a trader in another thread and changed the default input RSIOMA to 8, and the default Ma_RSIOMA to 12. It is working GREAT on the daily!

Happy Trading,
Norm

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Hey Tommor,

How’re ya doing? Nice to be knocking on your door again.

Do you have anything further to report on your 2 ATR trials? Have you used it for trailing stops also? If so, how’s that working out?

Thanks,
Norm

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Hi Norm.

I have found 2ATR20 too tight for long-term trend-following Keep getting shaken out and missing good moves due to volatility. Although in theory getting out too early with a profit is not an issue, sometimes in practice the pullback and resumption of trend are so fast I don’t even see them occur.

I have seen some occasional reference to 5ATR20 as a stop-loss indication but am currently using 3ATR20.

Trailing stops for me are as ever a 50/50 gamble. I only kick them in when the original trade makes a profit equivalent to the original risk. Which is so often no way to terminate a good trade - original trade breaks even and the pyramid trade makes a small loss. So right now I am taking profits at r:r of 1:1 and looking to re-enter asap after. So far so better.

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Hey Tommor,

Thanks for all your responses. Just thought I’d turn you on what looks outstanding to me, which I’m sure you’re no stranger to, but I thought I’d show you my tweak on it. It’s PSAR, found on perhaps all trading platforms.

J. Welles-Wilder, if I remember correctly, designed it specifically for stops and trailing stops. John Bollinger, whom you must know invented the very useful Bollinger Bands as well as a host of indicators, does not recommend any of his indicators for trailing stop use (to my knowledge), but in his book, Bollinger on Bollinger Bands, recommends Wilder’s PSAR for trailing stops.

The usual method of using it is to simply move your stop loss behind each new dot after it forms.

Investopedia, in
How is the Parabolic SAR used in trading?, says, “In a sustained trend, the parabolic SAR is usually far enough removed from price to prevent a trader from being stopped out of a position on temporary retracements.” “Usually” is the grabber. It’s not bad, but I’m trying to improve on it.

Chris Capre, Trailing Stop Forex | Forex Trailing Stop Strategy | 2ndSkiesForex, suggests not manually exiting if the dots flip from uptrend to downtrend or downtrend to uptrend, but to hang tight because trend might reverse again back to the one we’re trading.

So to combine the usual method (behind the last dot), the “usually” of Investopedia and the hang tight of Capre, I’ve settled on this: As the dots progress, place your stop loss just ahead of the next to last one, or at least part of the way between the last and next to last.

It’s GOT to be good. I haven’t tested it yet, but it looks great on the charts. To explode all of our brain cells for the perfect placement is futile. As you know, what works on one trade doesn’t work on another. However, I think I’ve settled on the method that, as far as I can tell, squeezes the most juice out of all trends I’ll trade, in the big picture. Of course, one must temper whatever method one chooses with Price Action, support and resistance, etc; but I’ll let math brain Welles-Wilder do my math for me! What I’ve come to thus far after exploding most of my brain cells is “just ahead of the next to last PSAR dot.”

Thanks again for your well thought out communications, and hopefully this will at least give you some food for thought and not explode too many of your brain cells.

Blessings,
Norm

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