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# Mathematics of Stops: Choose Your Desired Win Rate

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I want to share a technique that can help you to choose your desired winning frequency before you enter into a trade. I would guess a larger number of retail traders don't lose because they are wrong but because they use stops improperly and lose money even when they're right.

Assume for these purposes that the market is mostly random, if true then that means that an X point move up or down has little value in determining what the market will do next because, of course, if it did have value then we could use that predict it. Now, it is true that I predict the market but I will agree that the market is mostly random to most people most of the time. This implies we can determine our win frequency before entering a trade simply by choosing a stop and target of the appropriate size. The expected profit must be zero.

The formula is:

WIN AMOUNT * WIN FREQUENCY – LOSS AMOUNT * LOSS FREQUENCY = 0

Examples:

+5 and -5 point target and stop will win 50% by random chance

+5 and -15 point target and stop will win 75% by random chance

+5 and -20 point target and stop will win 80% by random chance

Formula examples:

5*W-5*(1-W) = 0

5W – 5 + 5W = 0

10W = 5, W = ½, W = .5

5*W-20(1-W) =0

5W -20 + 20W =0

25W = 20

W = 20/25 = .8

If these are challenging, you can use the equation solver at

http://www.algebrahelp.com/calculators/equation/

You can choose any winning ratio that you desire using this method. I personally would feel quite comfortable with 65% to 80% win ratio. Of course, your profit expectation is still going to be zero unless you have an edge. My point is that many people may have a slight 2% to 5% edge but ruin it with poor stops. It is very easy to erode such a small edge with a poor stop. The goal is to use the mathematics of randomness to prevent that. While the expectation is the true measure of a system, if one chooses a system with a very low win rate then by random chance they could experience a very long streak of losers. Psychologically this will be difficult for many to work through. I have, also found that when win rates drop below around 55% that the resultant equity curves become rather unstable.

It is worth to consider the assumptions in which choosing a higher win rate would work better then not. If our model is such that we can predict that the market will move in a given direction more times then not then choosing a higher win rate should be beneficial. However, if our ability is more about predicting the larger movements then we may want to choose a lower risk and a higher reward payoff.

This is an updated authorized partial excerpt from My Favorite Edges Bonus. Chapter "Choose Your Win Rate".

----

Curtis

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Where can I get a copy of your book "My favorite edges bonus" ?

Ed

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Hi predictor

And just to make sure I understand it............

In a random market,

To achieve an 80% win rate,

To win \$5 , you need a stop of \$20.

The risk looks a bit lop sided?

Correct?

regards

bobc

PS

If my understanding is correct, my next question is....... Who worked this out?

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if you have to use an extra W-I-D-E stop loss in a day trade to improve your win rate,

you don't know what you are doing.

one of these days, the market will take your stop loss,

and you will give back 100 days of profit.

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have you actually coded this as you describe with random entries? i just did and it doesn't work out as a profitable system or at least i don't see how it can. i used risk:reward ratios of 1:2, 1:1.5, 1:2,1:3 and 2:1, 2.5:1, 3:1. none of those were profitable. in fact, they were horribly unprofitable which is exactly what i figured they would be. Also, i used a renko brick that accounts for the full range that price goes to form the brick. using renko creates a uniformand bounded view of the market and as long i choose stops and target beyond the range of the brick, i don't have to worry about intrabar wiggel as opposed to other bar types. that is why i chose the renko for this exercise.

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In the example of 5pt target and -20pt stop, you're saying an 80% win rate.

So, for every 10 trades, 8 will work, 2 will fail.

This means:

8 wins x 5pts = 40 pts

2 losses x 20 pts = -40 pts

Net = 0pts

Still not making money, right? (losing, if you count commissions) This is why you need to have your reward greater than your risk... even if only slightly. This is how casinos make money, even if the odds are only slightly in the house's favor. You have to be the house.

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In the example of 5pt target and -20pt stop, you're saying an 80% win rate.

So, for every 10 trades, 8 will work, 2 will fail.

This means:

8 wins x 5pts = 40 pts

2 losses x 20 pts = -40 pts

Net = 0pts

Still not making money, right? (losing, if you count commissions) This is why you need to have your reward greater than your risk... even if only slightly. This is how casinos make money, even if the odds are only slightly in the house's favor. You have to be the house.

True, but as I understand it, the thesis is that although gross expectancy is 0 in a 'random' market, your edge will slant the odds in your favour, or to put it another way, add a skew to the random outcomes.

Although I think Tams was correct in what he said about stop placement, but Predictor is on the right track I think in terms of a starting point - especially for someone going down the algo/mechanical route

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In the example of 5pt target and -20pt stop, you're saying an 80% win rate.

So, for every 10 trades, 8 will work, 2 will fail.

This means:

8 wins x 5pts = 40 pts

2 losses x 20 pts = -40 pts

Net = 0pts

Still not making money, right? (losing, if you count commissions) This is why you need to have your reward greater than your risk... even if only slightly. This is how casinos make money, even if the odds are only slightly in the house's favor. You have to be the house.

Net = 0pts ONLY if there is no transaction cost and no slippage.

the reality will be much uglier.

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In the example of 5pt target and -20pt stop, you're saying an 80% win rate.

So, for every 10 trades, 8 will work, 2 will fail.

This means:

8 wins x 5pts = 40 pts

2 losses x 20 pts = -40 pts

Net = 0pts

Still not making money, right? (losing, if you count commissions) This is why you need to have your reward greater than your risk... even if only slightly. This is how casinos make money, even if the odds are only slightly in the house's favor. You have to be the house.

You don't need to have your reward greater than your risk to make money...

The only think you need is a edge AND an adequate money management.

I use to do scalping (1 tick only) in a prop trading firm and no one had a reward > risk, you will often risk 2/3 ticks to win 1, but because we had an edge, our % win was very high and we end up being positive.

Also look at insurance companies, they have very bad risk (paying you in case something happens) /reward (the annuity you pay) ratio but still make money because they have an edge (knowing the probability that you will have an accident).

The point predictor is trying to make is that if you have an edge (like you good at drawing trendlines) but don't know where to stop and exit, using a fix ratio as described can eventually help you.

Now you need your edge to be good enough to compensate for slippage and commissions.

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.....your edge will slant the odds in your favour, or to put it another way, add a skew to the random outcomes.

I assume you mean a good entry pattern/reason. ?

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So let me get this straight....To summarise the Original Post...

If you have an usable edge, and win more than you loose you can afford to use wider stops. Thus giving you more opportunity for your edge to work.

Not only this, we've been supplied an algebraic formula to demonstrate the amount profitable minus the amount loss returns a figure of our expected return.

Sounds to me like a Taleb distribution.

Taleb distribution - Wikipedia, the free encyclopedia

And there is a whole chapter in a book dedicated to this???

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I appreciate that this topic generated a lot of consideration. There are many ways to look at it and many lessons/implications that can be derived from this simple article. One thing that really stuck with me though was that I made a system that bought the SP 500 at the open on random days and sold at the close. This system was basically break even over a long period of time. I ran the same test with a 20 point stop. The system that used the stop lost 100% of capital.

I build a lot of trading systems. I find that on the systems I've been able to test that using stops hurts the performance in almost every case. The worst combination has been the tight stop and large target combination in my testing. Perhaps, it is not surprising that this is the favorite combination favored by most traders.

There are a lot of take-aways One take-away should be obvious that the concept of risk/reward if defined by a static risk and reward is irrelevant and not meaningful. When a trader says he only takes 2x reward/risk opportunities then his E is also going to be zero. It is much more useful to think in terms of probabilities. This introduces such concept but again not in the ultimate form that is most useful but certainly it introduces it.

Another way to view this is that if you choose to use an equal stop/target combination that you have a 50% probability of getting stopped out just by random chance. On the other hand, if you set it higher to something where you win 80% by random chance then you know there was only a 20% chance that you were stopped out due to random chance.

As the article clearly states, this is not an edge in itself. Think about a system without stops that wins 10% more then it loses. That's a bigger edge then many casinos have. But, it is still relatively small, it is only winning 1 extra trade out of 10 more then a random system. Adding a tight stop is very likely to erode that edge. Logic reveals why. We know that any identification system will have false positives. The implication is that improper usage of stops can basically erode a significant edge.

It is worth to consider what type of edge one thinks one has. If the edge is more about predicting big movements, i.e trends or tail risk events, then one might be better to use options. If the edge is more about saying we are more likely to go up or down then this should work well. The usage of a tight stop with large target implies one can both predict tail risk type events and also the path followed. Of course, these are concepts for the beginner trader. Even so, experienced traders may improve their results when considering these implications.

I should stress these are concepts. In my tape reading course, I share methods for managing risk that goes beyond the use of stops. I will also add that stops don't work the opposite of trading targets. One would think they would but form my testing, they don't. One reason is that true protection would work more like an option, it would pay out a certain amount when you win and limit your risk when you lose. Stops don't really do that though. This is why it is important when appropriate to be aggressive on re-entering after stop outs when one uses a tighter stop loss.

url removed

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I knew it... it is a SPAM promotion for your website.

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Has anyone else noticed an increasing number of threads that are Q & A sessions for Vendors, Disguised as a discussion.

oh by the way....

Trading is tough, if you have an edge over time you could create enough wealth to by a

2008 MASERATI GRANTURISMO 4.2 V8 [400 BHP] AUTOMATIC BIG SPEC + WARRANTY 44k ono. PM me if interested.*

*not genuine add,just making a point

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Why is it that all these people who are vendors can post here without giving away their nature? This one is marked "not a vendor" in his profile but the oil still smells of snake.

I've complained about a few of them including umbloomer who repeatedly denied his true nature only to come out in a post a few months back and admit he was selling shit. What's the story?

:deal:

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Why is it that all these people who are vendors can post here without giving away their nature? This one is marked "not a vendor" in his profile but the oil still smells of snake.

I've complained about a few of them including umbloomer who repeatedly denied his true nature only to come out in a post a few months back and admit he was selling shit. What's the story?

:deal:

Thanks for the heads up ... user tagged appropriately as a vendor now.

regards,

MMS

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Dear MMS

How much does it cost to place a small advert on TL?

kind regards

bobc

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.......... the concept of risk/reward if defined by a static risk and reward is irrelevant and not meaningful. When a trader says he only takes 2x reward/risk opportunities then his E is also going to be zero.

.......... that stops don't work the opposite of trading targets. One would think they would but form my testing, they don't. One reason is that true protection would work more like an option, it would pay out a certain amount when you win and limit your risk when you lose. Stops don't really do that though.

.........This is why it is important when appropriate to be aggressive on re-entering after stop outs when one uses a tighter stop loss.

I think you miss the point of options and letting things run. They do have unlimited upside. There is not a cap on the upside, and so they are just like a stop when buying them...limited downside, unlimited upside.

If you want to put caps on with taking profits then you change the situation.

Personally.....the last things has me scratching my head.....how do you re-enter, after a stop out if using tight stops when you dont use stops, or what if the stop is large, is the next stop tighter or larger.

The major problem with what I think you are saying (and while there may be some interesting ideas for thought) is that while you might have a 90% win rate, it is the 10% of the losers that will wipe you out. It is one of the major flaws (recently discovered by many risk managers even though it seemed obvious at the time) with Value at risk models.

You have a 99% chance of loosing \$x dollars as a maximum today......however what they dont tell you is that they have no idea of how much you will loose in that 1% when its bigger.

There are some models that work aggressively, work fantastically for a while, but ultimately are impossible for the average person to trade over the long run....and you do so at your own peril.

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First, I think it is only fair to provide a discreet link to where people can go to find more of my material if they like it. I mean, I guess, you rather me post my material under an anonymous handle with no link to my work? I had other free articles I had planned to post but will not do so until I'm assured that I can provide references to my material.

SIUYA: This is the problem with stops no matter how they are used. If you use a tighter stop then you're going to be stopped out more often and if E is zero then you're going to lose even more/faster. Experienced traders know that one has to be more aggressive when using tighter stops. It should make sense due to the false positives. I was going to post another more in-depth article about knowing WHEN to use big vs small stops but I'm going to wait for an official word from the moderators about if they will accept a link to my website.

Options are different then stops because the price can go lower then your stop out level and come back. Stops are PATH DEPENDENT whereas options are sensitive to the END POINT. Likewise, options have time decay whereas holding the underlying doesn't. These are much different trading vehicles.

I think you miss the point of options and letting things run. They do have unlimited upside. There is not a cap on the upside, and so they are just like a stop when buying them...limited downside, unlimited upside.

If you want to put caps on with taking profits then you change the situation.

Personally.....the last things has me scratching my head.....how do you re-enter, after a stop out if using tight stops when you dont use stops, or what if the stop is large, is the next stop tighter or larger.

The major problem with what I think you are saying (and while there may be some interesting ideas for thought) is that while you might have a 90% win rate, it is the 10% of the losers that will wipe you out. It is one of the major flaws (recently discovered by many risk managers even though it seemed obvious at the time) with Value at risk models.

You have a 99% chance of loosing \$x dollars as a maximum today......however what they dont tell you is that they have no idea of how much you will loose in that 1% when its bigger.

There are some models that work aggressively, work fantastically for a while, but ultimately are impossible for the average person to trade over the long run....and you do so at your own peril.

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i dont have an issue with you being a vendor....though I do understand the issue

regardless of how aggressive you want to be, and how small or large a stop you want to use, your method IMHO is likely to cause issues with blowups, due to sequencing of events/stops/trades/

While it might be used to help modify to try and get an optimal stop level for future trades that give you your desired trade off between win/loss ratios and the like.

however, I look forward to seeing other more detailed ideas.

when it comes to options - if they are different why bring them up?

Plus they are exactly the same in the way you describe them.....they might expire and then become profitable, or the decay might not be enough to cover the gain over the time period, even though the direction is right.....same end result, you loose but then you are right.

Options I assume you mean are sensitive to THEIR end point, if you buy them in that they both have an expiry and set amount that can be lost (with no slippage)

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As a simplification, each time I look at the market, I ask, where is it going and how well is it getting there, and what do I need to do to take money from it, and can I do it without hurting my account.

There are times in markets where and when a high risk, low reward, high probability trade makes sense if done right. And there are times when a low probability, high reward, and low risk strategy makes more sense to me, and there are times when neither make sense. In poker parlance, sometimes it makes sense to play rags and sometimes you have to dump Aces.

Under all circumstances I do not turn a blind eye to risk or ROR. I dial up or down the number of contracts I trade to bring the dollar risk into line with my account. The max risk is really all that matters to me. I am not a "stop or target" trader. I believe that it is foolish to impose overly rigid rules on a dynamic system. The markets encourage arrogance.

Other times, when I can't figure out the 4 questions I stay away completely. Without question, there are times, many times, when I do not get the answers right. Generally, that means that market conditions are changing. Hopefully, at that point, I am not on tilt and too stubborn to realize the change.

I have certainly have had bad days trading a high risk, low reward, high probability strategy, wishing I had stayed out, but I have had bad days with a low risk, low probability, high reward trade strategy too. On the other hand, I have also had insanely profitable days trading either or both.

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I want to share a technique that can help you to choose your desired winning frequency before you enter into a trade. I would guess a larger number of retail traders don't lose because they are wrong but because they use stops improperly and lose money even when they're right.

Assume for these purposes that the market is mostly random, if true then that means that an X point move up or down has little value in determining what the market will do next because, of course, if it did have value then we could use that predict it. Now, it is true that I predict the market but I will agree that the market is mostly random to most people most of the time. This implies we can determine our win frequency before entering a trade simply by choosing a stop and target of the appropriate size. The expected profit must be zero.

The formula is:

WIN AMOUNT * WIN FREQUENCY – LOSS AMOUNT * LOSS FREQUENCY = 0

Examples:

+5 and -5 point target and stop will win 50% by random chance

+5 and -15 point target and stop will win 75% by random chance

+5 and -20 point target and stop will win 80% by random chance

Formula examples:

5*W-5*(1-W) = 0

5W – 5 + 5W = 0

10W = 5, W = ½, W = .5

5*W-20(1-W) =0

5W -20 + 20W =0

25W = 20

W = 20/25 = .8

If these are challenging, you can use the equation solver at

Equation Calculator & Solver -- Algebra.help

You can choose any winning ratio that you desire using this method. I personally would feel quite comfortable with 65% to 80% win ratio. Of course, your profit expectation is still going to be zero unless you have an edge. My point is that many people may have a slight 2% to 5% edge but ruin it with poor stops. It is very easy to erode such a small edge with a poor stop. The goal is to use the mathematics of randomness to prevent that. While the expectation is the true measure of a system, if one chooses a system with a very low win rate then by random chance they could experience a very long streak of losers. Psychologically this will be difficult for many to work through. I have, also found that when win rates drop below around 55% that the resultant equity curves become rather unstable.

It is worth to consider the assumptions in which choosing a higher win rate would work better then not. If our model is such that we can predict that the market will move in a given direction more times then not then choosing a higher win rate should be beneficial. However, if our ability is more about predicting the larger movements then we may want to choose a lower risk and a higher reward payoff.

This is an updated authorized partial excerpt from My Favorite Edges Bonus. Chapter "Choose Your Win Rate".

----

Curtis

WOW!!! This sounds exactly like my idea! What a coincidence.... NOT!

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if you have to use an extra W-I-D-E stop loss in a day trade to improve your win rate, you don't know what you are doing.

One of these days, the market will take your stop loss and you will give back 100 days of profit.

:crap: OUCH!! Thanks for the painful reminder, Tams. I got bit using the wide S-L in my early quest and it was a very cold bucket of water lesson learned.

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Dear MMS

How much does it cost to place a small advert on TL?

kind regards

bobc

Here's one for tagging too. At least he's honest enough to pay for his forthcoming ad/post....

(only kidding Bob )

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