I generated the following trials using a trading simulator with the following parameters:
10000 trials, each trial having 386 trades, with 1 to 2 Risk/Reward ratio.
Variable winning percentage.

The number of trials is set at 10000. This seemed like a large enough number to ensure robustness after monkeying around with the simulator for a bit. Setting the higher number of trials would not affect the results in a substantial way, so 10000 is sufficient.

Each trial has 386 trades. This is the simulator limit. While not huge, it is sufficient for our purpose.

The risk reward ratio is chosen as 1:2 because most trading materials / maxims recommend having larger winners than losers (and I generally believe in that maxim so it seemed like a good case study, though a similar point could be made with a different ratio).

Case 1: 33% Winning (Random)

We'll start with the random expectation percentage, 33%. If you have 1:2 risk/reward, randomly, you'd expect to win 33% of the time.

No surprise. After 386 trades, we could up or down substantially. However, because of overhead cost, we cannot hope to be profitable winning 33% of the time at 1:2 RR.

Case 2: 35% Winning (Slightly Improved)

Suppose we improve our trading little bit past random. The results are surprising.

Only a slight improvement in our winning percentage (2%) resulted in substantial profitability increase, not just a small one. The maximum positive and negative excursions are no longer roughly equal. The positive one is about the double of the negative one. There are many more trials that finish in the upper half than the bottom half.

Trading at 35% at 1:2 RR means that one is likely a breakeven trader. We win more than we lose... but the transaction costs will likely eat it up. While we're much better off than random by improving mere 2%, 35% is not good enough.

Case 3: 40% Winning (Improved)

Suppose we enhance our trading 'mere' 5%.

By improving our winning percentage from 35% to 40%, we moved out of being break-even to clearly winning. Winning 40% will cover our overhead, and then some.

Consider the ratio of maximum positive to maximum negative excursion.
For 33% winning, the ratio is about 1 - roughly same positive and negative.
For 35% winning, the ratio is about 2 - the scale has tipped in our favor, but not enough.
For 40% winning, the ratio is about 5 - strong enough for profitability.

By improving just 7% over random trading, one has become profitable. The edges in trading are small, and any 'tiny' improvement has large impact.

Suppose we bat 45%.

Case 4: 45% Winning (Expert)

If we can bat 45% at 1:2, we are not merely profitable. One has become an expert. This step is likely to take a long time.

For 45% winning, the ratio is about 7 - expertise combined with experience.

Note that for the first time, none of 10000 trails ended below the start point. The edge is huge and the chance of ending up a loser is less than 0.01%.

But some traders evolve even further, to master status.

Case 5: 50% Winning(Master)

If one can reach 50% winning rate at 1:2, one is indeed a master.

For 50% winning, the ratio is about 15 - absolute mastery of mind, method, and money, combined with experience.

However, there is another level.... this level is called LIAR.

Case 6: 60% Winning (Liar)

For 60% winning at 1:2, the ratio is about 39 - absolute mastery of mind, method, and money, combined with experience. I AM THE MARKET. Monstrous edge of a trading mystic.

I'm not sure 60% at 1:2 RR is attainable... but you never know. Until I see somebody's trading records, I'm calling this the LIAR level (if you exist, speak up!).

Summary

This brief study is not meant as a 'proof', but rather a demonstration of the fact that the difference between success and failure in trading is a single digit percentage. The edges in trading are small, and even tiny improvements make a large difference, especially over extended periods of time.
Tracking one's percentages and using a trading trial simulation can be a valuable tool in determining process goals and orienting oneself on the ladder of success.

Happy Trading!

PS Thanks to @Big Mike for making this forum possible.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 59 users say Thank You to Anagami for this post:

Interesting analysis. From my own testing I've found that edges become relatively stronger the higher the timeframe (and holding time) of the trade. The more often you trade, the greater the vig and the more difficult it is to obtain an edge. So why trade short-term?

Undercapitalized
Bored

But also you learn a heck of a lot faster and you can execute a smaller edge over many more trades. Which smooths your equity curve substantially.

The following 4 users say Thank You to eudamonia for this post:

I have found that statement to be quite true. Get above the traders into swings or higher, and you can find and hone better edges. I wore myself out trying to find edges at the lower time frames, yet all my results points towards taking longer term trades at a minimum being willing to hold overnight. ~4 days is now my holding period.

Pic is of bot results "In Testing Sample" and "Out of Testing Sample". Obviously there are not as many trades out of sample yet, but looking at the numbers I would consider them statistically equivalent even though I have not actually done a stat test. The Out of Sample is a back-test, but I assure you that the results are equivalent in live trading. Just thought it might give you some additional real data for testing.

The following user says Thank You to Luger for this post:

Why is it you think a 60% win rate would mean you are a liar, exactly?

I think you have crunched some interesting numbers but to conclude someone with a 60% win rate is a liar is a stretch IMO.

The 1:2 r:r is also somewhat misleading in my opinion because in my experience, traders don't necessarily set and forget arbitrary targets. Trades need to be managed, not left with a hard risk:reward ratio.

I regularly open trades with a 4 tick stop on the ES. It is not unusual for me to get 6+ points on my last portion. That doesn't mean I have a 1:6 R:R. It means I scale out & manage the trade. Same on the downside I might get out at -1 tick, usually when market moves against me but comes back to give me a better exit.

What would be interesting would be to see the impact of better trade management. Not sure how that would be done.

The following 7 users say Thank You to Jigsaw Trading for this post:

At 1:2 RR, 40% winning rate overcomes vig (that's not to say that vig isn't important. It is.)

Yes, edges are stronger on higher timeframe, but there's much less opportunity.

Suppose one goes from trading 5 min charts to daily charts. You have just reduced your opportunity by a factor of 81!! (There's 81 bars every day on 5 min chart).

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

Simple R:R calculations are just one piece of the story. Trade /money management has to included to justify any potential stategy.

Since there were 4 consecutive losses ,why no set them up at the beginning of the exercise and see what kind of drawdown it would be? How often were there 4 consecutive losses.?

In real time, how would the "5th" trade be handled?

Trader

The following user says Thank You to Family Trader for this post:

60% with a 1:2 RR is a very nice edge I would not call it monstrous. It is doable for long stretches of time.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

Endless debate about putting trading records up. I for one will not do it because they are private and can be fabricated on a message board like this anyway. So it is moot.

This is definite doable and I think mistake to overlay your own experience onto what others have done and can do. I will say key though is to setup system that needs much less than 60% to survive and make money.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following user says Thank You to liquidcci for this post:

Maybe even 66% is possible at 1:2 RR if one is very, very selective in setups. I have not achieved that and have not seen others do it, so it's in the "maybe, but unlikely" category.

Yes, it misses the point of the thread entirely, so I'm not sure why people keep bringing it up. For some strange reason, people are riled up to defend something.

More trials to come, with 1:1 RR and 1:0.5 RR (scalper targets).

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

I like your thread and find it interesting. Not trying to miss point of thread but threads tend to take on a life of their own and I think 60% at 1:2 RR is within the scope of discussion. It does take being selective in setups to get that win percentage with that ratio but is doable was my only point. Being selective is part of the game but it is possible to be to selective.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

The point of the thread is to explore the question: what percentage do I need to improve over randomness to be profitable?

With respect to 1:2 RR, that percentage seems to be 7 (or the ballpark is somewhere there).

60% at 1:2 RR is virtually a license to print money. Since that is a huge edge and since over 90% of people in this business are losers and probably the same percentage of people are full of it, I am quite skeptical.

Just because it's doable doesn't mean it's doable for very many people out there. Some people go to Olympics and some receive the Noble prize. I personally have not met either.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 3 users say Thank You to Anagami for this post:

I suspect that for the majority of people out there, their entries (and probably trade management) is worse than random. They are below the random 33% category at 1:2 RR (meaning they are trapped more often than a random trader would be).

The public loses more than it's entitled to, as Bacon famously notes.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

I understand being skeptical. Reality most people are not even profitable thus the high failure rate. I am speaking from own experience I can get 60% with 1:2 risk to reward ratio. But to not be as selective I tend to get around 55% consistently at a 1:2 ratio. I am still selective and setup my system to limit trades with purpose. Quality trades with good money management to scale trades is a license to print money.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

As stated above if this edge is executed regularly this is a very strong edge indeed. However, I do want to note again that holding time matters a great deal. It is not that difficult to design a method that has an average of a 1:2 ratio and 55-60% win ratio if that system is taking 5 trades a month. Certainly to design such a system is not within the realm of "liar". Translating that into a system that can take 5 trades a week and keep the same statistics is a whole nother ball of wax.

Personally, I find a system that can get about 5 trades per week with a mere 50% win ratio and 1:1.5 average is more than enough license to print money.

The following 2 users say Thank You to eudamonia for this post:

Can I ask where you get that from? The edge that 99% of prop firms teach is trading off the order book, which is arguably the lowest timeframe of them all.

As for reducing your opportunity by 81 - how did you calculate this? Surely opportunity is measured by what comes along and not by a mathematical formula...

The following 2 users say Thank You to Jigsaw Trading for this post:

The thread is not about higher timeframes or even about edges on lower timeframes.

The thread is about the percentage of improvement that is necessary for profitability. (though you are welcome to discuss other issues as you choose, but that doesn't mean I'm terribly interested in them. ).

Daily chart - 1 bar a day.
5 min chart - 81 bars a day.

Therefore, there is theoretically 81 times more opportunity.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

Not sure what your gripe is, but it doesn't seem like you took your meds this morning. I would strongly suggest you don't trade in this mood.

I provided nothing but solid simulation data to show the point of this thread: the difference between failure and success in trading can be as 'little' as 7%. But it does not seem you are capable of grasping that.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

When you say "Yes, edges are stronger on higher timeframe", I think it is fair to investigate that and discuss why you think this is the case.

This is a discussion forum and I like to discuss. I would like to know why you think edges are stronger on a higher timeframe. It may be obvious to you but to me, it is not obvious.

You brought this fact to the discussion, you could at least show the courtesy to discuss the point you made.

I don't care either way to be honest, I just like to explore other people's opinions.

The following 2 users say Thank You to Jigsaw Trading for this post:

I primarily trade intraday because of overnight risk. The shorter time frame you are exposed to the market the less risk.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following user says Thank You to liquidcci for this post:

The smaller your holding time the smaller your targets. If a "price swing", whatever way you define it is an average of 50 points when holding for several weeks it might only be 5 points or even 5 ticks when holding smaller time frames (such as 2 hours or perhaps even 2 minutes).

As these targets become smaller your commissions and spread do not diminish. Therefore, the vig becomes a more substantial portion of your net profit. It is not uncommon that a swing trading method that has a 5% vig taking 5 trades per month would encounter a 25-30% vig taking 5 trades per day.

Therefore, your net profit and edge per trade goes way down the smaller your holding time. Of course, your opportunities go up.

Lastly, the purpose of a "prop firm" would be for that firm to make money. They make money when you take trades. Not when you are profitable. So it makes a good deal of sense to them that they teach a high trade frequency method. But that doesn't necessarily have anything to do with making good traders.

The following 3 users say Thank You to eudamonia for this post:

Continuing after being so rudely interrupted by an obnoxious vendor with his own agenda , let us look at 1:1 RR. This is an extremely common ratio. Many traders and algos take profits (usually at least partial) at the point where their gain equals their initial risk. Thus 1:1 RR makes for an interesting study.

The parameters are the same as previously, except the RR is 1:1.

Case 1: 50% Winning (Random)

Not terribly interesting, but a good starting point. Evenly distributed trials as expected.... the cost of trading will sink you though, need to improve the winning percentage.

Case 2: 55% Winning (Improved)

Say we improve our winning % by 5 percent. Profitable or not?

Looking at the results, one is more likely to be, but not strongly so. Because of vig, much more likely to be break even at 1:1 RR at 55%.

Case 3: 60% Winning (Profitable)

At 60%, we encounter a much healthier picture.

Notice that for the first time, none of the trials finished below the starting point, meaning the odds of being in the negative after 386 trades are less than 0.01%.

Case 4: 70% (Expert)

We take a very significant jump here out of being 'merely' profitable to being proficiently so.

Achieving 70% at 1:1 RR is difficult (though attainable as I'm sure some members will remind me).

Case 5: 80% (Master)

Master level would require having an incredible insight and very high level of selectivity (i.e. a-hole the size of a decimal point ).

Now, let's look at the ratios of the maximum positive trial (MAX VALUE) to the maximum negative trials (MIN VALUE).

At 1:1 RR, at 50% Winning Rate, the ratio is about: 1.
At 1:1 RR, at 55% Winning Rate, the ratio is about: 2.
At 1:1 RR, at 60% Winning Rate, the ratio is about: 6.
At 1:1 RR, at 70% Winning Rate, the ratio is about: 17.
At 1:1 RR, at 80% Winning Rate, the ratio is about: 42.
Recall from the first post that for 1:2 RR, at 40% (minimum ballpark level determined for profitability), the ratio was 5.

Important Question: Which is easier to achieve? Which one should the trader strive for?

I can't say which is easier to achieve like you said many factors. But I would rather be profitable with the lower winning %. Gives you more room to absorb outlier type draw downs. I think is bad idea to trade a strategy that needs those high percentages to make money.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

The expectancy of the two alternatives is identical, the answer lies elsewhere. You will find it in the thread on the risk of ruin. To show this, we need to make some assumptions on the way we trade and on risk tolerance.

Assumptions:

-> I start with an account size of 100.000 USD
-> My target account is 400.000 USD
-> I will definitely stop trading after a drawdown of 50% (ruin)
-> My tolerared risk level for that drawdown is 1%
-> I am following a fixed-fractional approach for position sizing, that is I will increase my position size if my account gorws or decrease it after a loss
-> I use a model for YM, which includes slippage and commission

The results are shown below:

(1) The trend following model with the higher R-multiple and the lower win rate requires 450 trades to reach the target.

(2) The model with the lower R-multiple requires only 218 trades to achieve the same target.

The reason here is that the second model produces far lower drawdowns. Although both systems have the same expectancy, the second model has a higher Optimal F - in the example below 12.09% compared to 5.76% for the first model. This means that for equal drawdown risk the second model trades twice as many contracts and it comes out the clear winner.

@Anagami: Your analysis was right, the second model beats the first. You have just given an excellent example for the application of a Monte Carlo analysis. You can also use Monte-Carlo Analysis for fixed fractional betting, the difference between the two systems will even be more impressive.

@liquidcci: You got it wrong, the second model is better because it produces lower drawdowns and therefore allows for higher leverage. But I agree that the result is counter-intuitive.

The following 31 users say Thank You to Fat Tails for this post:

Fat tails I was not using draw down and did not see it in the examples given. Maybe I am reading to fast. I always include drawdown in factoring anything I personally do. My system depends on low draw downs.

I think even if one has better draw down over the other you still have to consider the potential of what depending on a high winning percentage can do to you in a bad run situation outside of a systems norm. I was more looking at how robust the system is or is not. If I can breakeven at 35% and make money handover fist at 60% I stay in a good mood.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

As far as my understanding goes, @Anagami has presented Monte Carlo Simulations. The worst path on the chart allows for an estimation of the maximal drawdown.

Bad runs are accounted for in that simulation, as the order of the trades is different for every path. The point I am trying to make - and this is understood by very few traders - that the second system, the one with the high win rate and the 1:1 average win to average loss is the better option because

-> it produces smaller drawdowns (your intuition here is false!)
-> can support a higher leverage with equal risk (in particular in a bad run situation)

Both the model that I use and the Monte Carlo Simulation by Anagami have confirmed this with a completely different approach (one is theoretical the other experimental). Ralph Vince has written this again and again, but nobody seems to understand the mathematics.

Of course an edge is an edge, but look at the pictures of the simulation and you should understand. Two systems having the same expectancy, but the second has the better Optimal F!

The following 11 users say Thank You to Fat Tails for this post:

Fat tails not sure what you mean by my "intuition". I am not using intuition I was looking at a limited set of facts and not including draw down in my response. So I was not looking at the way you are looking at it when I posted my response. I was making a very narrow specific point about using a system that needs a high win ratio to be profitable.

I understand the math and use fixed ratio in my trading. 90% of my profits come increasing my contracts thus I need low draw downs. I shoot for systems that are robust that need fairly low winning percentage and can take a beating. I must have low draw downs so I can leverage.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 3 users say Thank You to liquidcci for this post:

I liked that risk of ruin thread and the realization that the winning percentage had a larger impact. Thinking of it simply: Would you rather have to deal with a 1x draw down 60% of the time(40% winners) or 40% of the time(60% winners)? 40% of the time sounds better to me because statistically there are going to be smaller strings of 1x losses put together compared to 60% of the time. Thus lower potential for draw down.

The following user says Thank You to Luger for this post:

I was astonished as well the first time that I realized that the winning percentage prevails over the R-multiple, but in the end it is just mathematics.

The concept for Optimal F points you into that direction, although the model is only valid for Bernoulli distributions.

A Monte Carlo simulation - let us say an experiment - confirms the finding for a more general case. So you know that the risk adjusted returns of the strategy with a low R multiple but a high winning percentage are better. This allows you to use a higher leverage and in the end you will attain your goal with only half the trades.

This is really astonshing and I cannot easily grasp it with my mind, but then I don't have to, the model states it and the simulation of the experiment confirms it.

The following 10 users say Thank You to Fat Tails for this post:

I'm currently trading above 60% win rate and going into each trade with a 1:1 mindset, though each is managed uniquely as the trade evolves. I tried for a long time to think in 2:1 terms, but the question is does the market make this easily available. I think not. If every trader in the market is trying to achieve 2:1 how does it add up. The fastest of the HFT are definitely going to get these opportunities if when and where they exist. Perhaps the best game you can actually get from the market is 1:1, makes more sense. I do not trade forex but had a look at some webinars from one very successful trading room with a long and profitable track record for scalp trades. There they have a negative risk reward and go for the 70% plus winning rate. Their mantra is that the market does not give a better than 1:1 to anyone. Anyways, getting base hits and keeping that win rate high will give you far more confidence which will give you the real edge each time you step up to the plate, staying cool and in the trade and not worrying about where your back ratio'd stop is supposed to be...

Being an empiricist and more of a visual thinker, I took the Monte Carlo path... and I am surprised that the traditional maxim of "let your winners run" and "your winners must be bigger than your losers" is not necessarily the best... The 60% winner at 1:1 is better because of lower drawdowns... which allows one to crank up the leverage (which ought to be a big consideration because we can reach our goal faster). I should also add that 60% win rate makes trading a more psychologically enjoyable experience.

Later today, we'll look at a third alternative, scalping, with 1:0.5 RR.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 8 users say Thank You to Anagami for this post:

There is one last possibility to explore, and that's scalping. I define scalping as a trading style where one is playing for gains smaller than risks. For the purpose of this particular experiment, we will consider scalping to be trading with the RR 1:0.5. In other words, the profit size is only 50% that of losses.

This is an inversion of classical trading advice such as "let your profits run"...etc. (Notable exception among classical 'market wizards' being Mark Cook, who trades with this ratio.)

Case 1: 66% Winning (Random)

Again, we start with Random. We need to improve to have a chance.

Case 2: 70% Winning (Slightly Improved)

If we improve by 3%, the result is noticeable but not strongly so. Hitting 70% at a scalping RR won't do the trick. It's not good enough, and vig will eat us alive.

Case 3: 75% Winning (Profitable)

If we improve only 5% more, things get interesting.

We are definitely profitable now. There are almost no trials finishing below the starting point, and about 90% of the graph is in the upper area. We can beat vig now and then some. The ratio of MAX VAL to MIN VAL is now 5, indicating that we have reached a profitable point. We will come back to this case later for comparison purposes.

Suppose we improve further. Instead of winning 3/4, what if we win 4/5?

Case 4: 80% Winning (Expert)

Improving additional 5% has a tremendous impact on the performance.

We not only finish above the starting point in every trial, but quite a bit so. The MAX VAL/MIN VAL ratio has now risen to a very impressive 12. We are expert scalpers and sky's the limit... well, until the next level.

Case 5: 85% (Master)

Steep curve with a MAX/MIN ratio of 18. The problem now is not how to make money. It's how to spend it.

Is this possible? Perhaps for a master scalper, picky, experienced, and patient.

Summary

What interests me most at this point is the performance at the 75% winning level with RR 1:0.5. Previous we discussed 40% at 1:2 RR and 60% at 1:1 RR. Let's look at the charts together:

1. 40% at 1:2 RR

2. 60% at 1:1 RR

3. 75% at 1:0.5 RR

I'm not sure where the optimal f is for #3 (Harry, could you calculate it please? (@Fat Tails)), but here is my reasoning:

#2 and #3 seem very comparable to me visually.
#2 has greater MAX and MIN excursions, but the ratio is higher than the ratio for #3.
#3 can have nasty drawdowns when losses bunch because of its loss size relative to gain, but these should happen quite infrequently (impact on leveraging??).

For me, the overriding factor for deciding between these two would be a psychological one.

It's much more enjoyable experiencing 75% winning trades than 60% winning trades (even if winners are half). I like to create a positive psychological feedback loop: the more I win, the better I am inclined to trade. Other traders may have a different preference, but I feel this is probably true for most of us.

I did not discuss how the drawdowns would affect the leverage (and therefore profitability), as I am not certain about the optimal f of #2 vs. #3.

But in the end, I seem to be making a case for scalping.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 12 users say Thank You to Anagami for this post:

@Anagami: If you talk about optimal f, the results will be terrible for scalping, once you include

-> the spread as created by using stop market orders (stop loss) and limit orders (profit target)
-> slippage
-> commissions

You cannot make any case for scalping if you use any realistic mathematical model. Below is an example which shows two systems, both with a winning probability of 60% and a R-multiple of 1. The first system uses a target and a stop loss of 10 points, the second system uses a target and a stop of 20 points.

The results are appalling. The 10 point system requires 6302 trades to achieve the target of doubling the account, the 20 point system only 218 trades. Even if you take into account that the 10 point system will generate about 4 times as many trades than the 20 point system, it will only have generated 872 trades out of 6302, when the 20 point system is already done.

Spread, slippage and commissions have a huge impact on scalping systems, this is the reason I never will do scalping with my retail account.

The following 16 users say Thank You to Fat Tails for this post:

Thanks. These are very interesting results @Fat Tails, and they do give me a pause.

HOWEVER,

notice that I did not define scalping as trading on a very short timeframe where spread, slippage, and commissions are such a huge factor that they eat you up.

I defined scalping merely as a 1:0.5 RR. You can use this ratio while trading a longer timeframe where those things are not such huge factors.

What do you think?

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 2 users say Thank You to Anagami for this post:

You cannot define something, which is already defined. Scalping is

(1) a legitimate method of arbitrage of small price gaps created by the bid-ask spread.
(2) a fraudulent form of market manipulation
(3) a legitimate method of trading based on quick momentum trades triggered by order flow reading setups

We were referring to 3, quick momentum trades. The main characteristics of a scalp trade is the shorter timeframe, not the win ratio.

The following 4 users say Thank You to Fat Tails for this post:

Platform: CTS/T4 (realtime); RT Investor (DTN-MA); POP.calculator (my own prop front end)

Broker: DDT (Crosslands) / Cunnigham - CTS T4

Trading: E6

Posts: 28 since Jan 2012

Thanks: 22 given,
21
received

I assume by "vig" you mean "vigorish":

[I]Vigorish, or simply the vig, also known as juice, the cut or the take, is the amount charged by a bookmaker, or bookie, for his services[/I]

And to clarify, would maximum draw down represent the MIN values as a percentage of the 100 unit base that you use to start the calculations; or does it refer to the minimum value encountered at the end of the 386 trades?

Thanks, Anagami for your work here and also thanks to Fat Tails for his contribution.

The following 2 users say Thank You to tpbyyc for this post:

Yes, that's the common definition. That's why I was crystal clear that I don't mean a specific timeframe, but a specific ratio. Those are 2 different issues.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

It is the MIN Value at the end. If MIN is say 60, then we consider max drawdown 40 (100-60). This may obviously not be the maximum drawdown per se, but it is the maximum drawdown from the starting value of 100.

You're welcome, it's been quite interesting... not over yet.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following user says Thank You to Anagami for this post:

While taking a shower this morning (), it occurred to me that your comparison of a 10 point and a 20 point system is useful in some aspects but quite misleading in others.

The # of trades that it takes to reach a target is useful as a comparison benchmark only if the systems are taking the same trades or if the same number of trades occurs in the same time period.

1) Are both systems in your example taking the same trades? Not at at all! A trade that is 60% certain using the 10/10 system is not necessarily 60% using the 20/20 system. The latter is a much rarer occurrence.

2) Is the same number of trades occurring in the same time period? No. Same problem as number one. The 20/20 system simply cannot take the same # of trades at 60% as the 10/10 in the same time period.

You're comparing apples and oranges.

Consider:
Say both systems have been trading for some time period which we shall call X.
Say at the end of X, the 10/10 system completed 20 trades.
Where is the 20/20 system? How many trades has it completed?

The 20/20 system has completed many times less trades (maybe 5, maybe 7...etc.) than the 10/10 system in the same time period (X).

Which is ahead at this point in time (X)? Not the 20/20 system.

To say that the 20/20 system gets to the target much faster because it requires less trades is misleading because it takes many less trades than the 10/10 system in the same time period.

The 20/20 system gets to the target faster in terms of the # of trades, but it is slower in terms of time.

Your example is an oversimplification that fails to model this crucial aspect of trading.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 9 users say Thank You to Anagami for this post:

The 20/20 system cannot take the same number of trades over the same time period, but I had already taken it into account! Based on the square root relationship between volatility and time, I had made an estimation that the 20/20 system will be able to enter only one trade, while the 10/10 system enters 4 trades. This assumption is realistic, you can compare the average true range from N-minute bars with the average true range from 4xN-minute bars, and will find that it is approximately the double.

If you read my post attentively you will also understand that I have not directly compared the 6302 trades needed by the 10/10 system with the 218 trades of the 20/20 system, but I have used the above approximation to state that the 10/10 system will be able to take about 872 trades while the 20 /20 system takes 218 trades.

But even after 872 trades (4-times as many as the 20 point system) the 10/10 system is far from reaching the target. I will take about 7 times (!) as long to achieve its target, as it has to generate 28 times as many trades.

The 20/20 system needs 28 times fewer trades (218 versus 6302), and will reach its target about 7 times faster. It is therefore both faster in terms of trades and in terms of time.

Have added the 15 min charts of ES 06-12 from last Friday with the ATR(256) calculated from the primary bars (red) and the ATR(25) calculated from 60 minutes bars (blue)=. The approximation which I have used postulates that the
ATR from the secondary bars should be about twice the size as the ATR from the primary bars, and this is indeed the case, as 3.16 is about the double of 1.64.

The following 5 users say Thank You to Fat Tails for this post:

Platform: Abacus, Slide Rule, HP-65, Metastock, TOS, NT

Trading: Futures

Posts: 3,424 since Aug 2010

Thanks: 1,057 given,
5,840
received

Not trying to defend any side, but I don't see what is so personal if someone put up trading records and remove personal info, i.e. name, account number. @Anagami presented results for combinations of R/R and profitability expectation, he did some homework. Just throwing hands in the air without substantiating a disagreement with real data or some sort of statistical analyses is not a credible argument.

The following 2 users say Thank You to aligator for this post:

For the same reason I would not blot all my personal info on my tax returns then mail it to all my neighbors.

But really it is a waste of time. I could quite easily create a fake statement and make every one oooh and ahhh. Point being any statement posted here by anyone cannot be proven to be real. So there is no reason to make effort to do so or request anyone else to do so.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

Platform: Abacus, Slide Rule, HP-65, Metastock, TOS, NT

Trading: Futures

Posts: 3,424 since Aug 2010

Thanks: 1,057 given,
5,840
received

I don't think @Anagami or @Fat Tails wasted time by posting some good studies. It does not have to be a broker's summary. It could be stats on let's say a year of trading or a few hundred trades or some kind of mathematical demonstration. It's usually obvious if the stats are bogus or real. People tend to believe what they see (religion aside).

Otherwise, it's like this guy who is selling his fakebars for $199 a month and has been telling the followers I can't legally give you stats (although he is not licensed in anything), but if you don't believe me go do your own stats (he used to post stats that showed miserable results, then he stopped doing that).

The following 3 users say Thank You to aligator for this post:

Aligator I never said what Anagami or Fat tails posted was a waste of time. What they posted is very different from someone being asked to post a brokerage statement as proof of results. It is a waste because it cannot be verified as being true. Even if a brokerage statement could be verified to be true it helps no one on board unless the method that goes with it is revealed as well. I am not selling anything here so it is moot.

However, I am going to bow out of this conversation because it is really not the intent of Anagami's thread and this just clutters up the original intent.

"The day I became a winning trader was the day it became boring. Daily losses no longer bother me and daily wins no longer excited me. Took years of pain and busting a few accounts before finally got my mind right. I survived the darkness within and now just chillax and let my black box do the work."

The following 2 users say Thank You to liquidcci for this post:

Thank you for your detailed and elucidating post, Harry (@Fat Tails).

Yes, 4 times the # of trades (10/10 system) for every 1 trade (20/20 system) is a reasonable modelling.

As a good empiricist, I plan to write some quick Java code to duplicate your results (not sure what sim you are using? Prop?).

Before that, however, maybe you can help me understand the formula for the Adjusted Win Loss Ratio in your simulation (I think you mean Loss / Win Ratio?). I tried factoring in commission and slippage but was unable to come up with the same ratios (0.83 and 0.69).

Thanks!

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 2 users say Thank You to Anagami for this post:

The excel model is just from the thread "Risk of Ruin". You can actually read through the stuff and download the excel model from post #65, as per link below:

Thanks again, Harry! (@Fat Tails) Much appreciated. You help me (and I'm sure many others) to correct certain distortions that have been ball and chain in our trading.

Just crunching some numbers with respect to the 20/20 and 10/10 system. Let's calculate trade expectations after factoring in vig (slippage and commission) as well as time (10/10 trades 4 times more often).

10/10 System @ 60% Winning
(0.6)(8.2) - (0.4)(11.8) = 4.92 - 4.72 = 0.2 points.
Because this system trades 4 times more often, for the same time window, we get 0.2 * 4 = 0.8 points

Wow. The 20/20 has almost 3 times higher expectancy (even though 10/10 trades 4 times more often), because the vig is much less of a drag. This ratio is amplified with % position sizing. Essentially, the 20/20 gets ahead, stays ahead, and increases the lead more and more because it is dragged down less on every turn.

Now, does this effect continue? In other words, what happens if we create a 40/40 system (60% Winning)? Will it perform better than 20/20, just as 20/20 performed better than 10/10?

NO! It breaks down somewhere...

Let's take a look at math and then do a simulation.

The expectation for 20/20 system was 2.2. Keeping that same assumption about the number of trades when we double, the system at 20/20 level would be taking 4 times as many trades.
So, for the purposes of comparison, we get 2.2 * 4 = 8.8

20/20 has better theoretical expectancy than 40/40!! Why??

Let's look at the simulation.

Ouch! It doesn't perform better anymore than the previous step up. Why not? 20/20 was better than 10/10.
But 40/40 is not better than 20/20.

It took us less trades at 40/40 (112), BUT by the time we get to 112, the 20/20 system already finished (remember, it takes 4 times as many trades. So by the time 40/40 finished 112 trades, 20/20 would have completed 448 trades... but it finished in only 218).

I think the answer lies in the fact that once vig (commission/slippage) has become sufficiently small (how do we calculate this without going through every case?), what becomes more important is the number of trades taken at 60% winning.

It seems there's a 'saddle' transition point somewhere. Vig becomes relatively small, and leveraged compounding multiple times within a fixed timeframe becomes more paramount.

Any thoughts? Harry?

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 8 users say Thank You to Anagami for this post:

Now that thanks to Harry I have access to a quick and dirty simulator , I want to go back to the original question. Which is the best:
1) 40% @ 1:2 RR ('trend model')
2) 60% @ 1:1 RR ('low R-multiple model')
or
3) 75% @ 1:0.5 RR ('scalping')

As Harry already posted simulations for the first two, here's a simulation for scalping.

75% @ 1:0.5 RR

UGLY. It took us 991 trades to reach the target.

75% @ 1:0.5RR seems worse than 60% @ 1:1 RR.

What if we improve by 'only' 5%?

80% @ 1:0.5 RR

Surprising!! Improving from 75% to 80%, the time to reach our target was reduced by a factor of 10!!! This confirms my initial thesis, that trading edges are small, and 'small' improvements have very large consequences.

All of a sudden, MUCH better than 60% at 1:1 RR!! It took us only 99 trades instead of 218 (or 450 or 991). And optimal f is significantly higher than any of the other simulations.

So, scalping seems like a great choice at 1:0.5 RR, BUT you must bat 80% (on a reasonable timeframe where your vig is 10% or less of your SL).

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 5 users say Thank You to Anagami for this post:

@Anagami: First of all, I agree with your findings. The 40/40 system only requires 112 trades as compared with 218 trades of the 20/20 system. Based on volatility expectations, however the 20/20 system should still achieve its target first. This suggests that there is an optmimum size, as

-> commissions and slippage destroy any system that has too narrow stops and targets
-> the trade frequency is low and drawdowns are high for systems which have wide stops and targets

In this case the risk adjusted Optimal F is slightly higher for the 40/40 system (4.22% versus 3.14%), but as your stop is wider, you are only allowed to trade 20 contracts with the 40/40 system, while you may trade 29 contracts with the 20/20 system - a 20 point stop on 29 contracts equals $ 2,900 and is less than a 40 point stop on 20 contracts, which equals $ 4,000.

The narrow stop of the 20/20 system allows you to trade more contracts, but at a lower value for Optimal F with the same risk of ruin.

Your conclusion is correct, there is an optimum size which of course relies on all the dubious assumptions, such as the relationship between time and volatility, slippage and commissions, and the model parameters such as the 1:1 win/los ratio. The model tell us that the optimum size to trade is 18/18, that is a profit target of and a stop loss of 18 points.

But it is only a model based on a Bernoulli Distribution.... so do not take this as the ultimate wisdom.

The following 5 users say Thank You to Fat Tails for this post:

@Anagami: Very dangerous conclusion: You have a nice system and you hope to make a win rate of 80%. If the win rate drops by 10% to 72%, your expectancy drops to zero.

The problem is that the model calculates the fixed fractional amount based on the assumption that you have a known edge. This would hold true for card games, at least over the period during which the rules of those games are not changed. Trading is a game with ever changing rules, so there is an additional risk that the backtested or assumed edge does not exist.

No model covers the model risk, and here the model risk is huge, as it includes the assumption of a known and stable edge. Also there is an operational risk. Would you feel happy if you ran a position of 64 contracts of YM with an account of $ 100,000? The favorable results with the win rate of 80% heavily rely on leverage. The leverage is suggested by the Optimal F model, because it ignores model and operational risks.

Models simplify, so they should not be applied to reality without care. If I was to trade anything like this, I would rather rely on a Monte Carlo Simulation of a backtest and a forward test then a model. The model should only be used for understanding the basic mechanisms, for example it is certainly interesting if a model postulates that there could be an optimum size for trades.

The following 11 users say Thank You to Fat Tails for this post:

If the win rate in the 60% 1:1 RR model drops by 10%, then one's expectancy is much worse than zero.

Thinking about it, I have to agree with you. Yes, the results with the 80% scalping do rely heavily on leverage, and no, I would not be comfortable with 64 cars of YM with a 100K account.

There seem to be much greater unstated risks in the 80% 1:0.5 RR model (scalping) than in the 60% 1:1 RR model (low R-multiple).

You make a strong case against scalping, one that I cannot argue with.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 3 users say Thank You to Anagami for this post:

The case against scalping is a case based on commissions, slippage and the spread. There is no argument against scalping if

-> you do not pay retail commissions, but have an exchange seat and lower rates
-> you trade a highly liquid instrument, where you do not experience slippage
-> you enter via limit orders in order to avoid to pay the bid-ask spread (market maker strategies)

But being a retail trader and paying the commissions that I have mentioned, I am not in this game for good.

The following 4 users say Thank You to Fat Tails for this post:

The thread discussion got me more interested in analysis. Found a great resource for Free Stats Software.

As the market gives me plenty of time between my setups, this is something I plan to get more into. I spent my time in the stats class in university chatting up the pretty honey next to me... but I'm back, it's an interesting field.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 4 users say Thank You to Anagami for this post:

Here's a curve ball. What about blending strategies sequentially to adjust overall potential?

For example, trade a 1:1 60% accuracy system to grind out a weekly (or daily, or monthly or whatever) target and then switch to a much a higher risk:reward system with a trailing stop on the weekly gains to limit downside exposure.

This is a type of 'barbell' approach where you can (in theory) get exposure to asymetrical payoffs.

Thoughts?

The following user says Thank You to mokodo for this post:

I am not seeing any advantage of following this path. I would continue to trade the system with the R-Multiple of 1 and the win rate of 60%.

The only reason to trade two different systems in parallel (not sequentially!) would be a negative correlation of their returns. In that case drawdowns should be reduced allowing for a higher leverage.

The only problem with this approach is that the negative correlation often turns positive in a flight-to-safety scenario, and the higher leverage does not make things better either. See the demise of Long Term Capital Management. I think that they traded non-correlated or weakly correlated strategies, which turned out to be positively correlated when the flight-to-safety event (Russia defaulting on bonds) occurred.

The following user says Thank You to Fat Tails for this post:

I guess my 'angle' on this is not purely maths based, but practical in how I can use it to trade better and that in my case incorporates my psychology. I do employ such a 'barbell' approach which panders to my split trading personality. Very safe most the time and then - after a line in the sand is crossed - very risky.

I think Paul Tudor Jones has said that after you have grinded out a 30 or 40% year you have earned the right to go for it and perhaps book a 100%+ year. From a psychological perspective this makes sense (or at least it does to me), as you will probably have needed to trade well to get to that level in the first place and will be well tunded in when you drop the hammer and increase risk and/or the targets.

So not to divert the OP's intention of the thread, I'll bow out.

The following 2 users say Thank You to mokodo for this post:

I understand your position from a psychological point of view. George Soros called this going for the jugular .... What they probably meant is that once your have been profitable, it makes sense to increase size or to include trading strategies that may expose you to larger draw downs.

I do not think that this means necessarily switching to a different type of trade. You might simply build your position by pyramiding, once you have gained confidence, because the market has validated your strategy.

The following 3 users say Thank You to Fat Tails for this post:

Trading short-term allows you to place more bets. Provided your strategy comes with an intrinsic edge (let's denote this with some fixed value called the expected mean of returns), Bernoulli's theorem states that the larger the number of bets, the closer the sample mean of returns approaches the expected mean. As such, you should experience a smaller deviation of the sample mean from the expected value for every fixed unit interval of time while your strategy is run. In more concrete wording, the more the number of bets, the smaller the deviation of your realized daily returns from the expected mean of daily returns that you should experience, and hence higher Sharpe ratio. It can be estimated that the maximum compounded growth rate attainable with your strategy varies with the square of your Sharpe ratio, an order of magnitude faster than losses from transaction costs. By this reasoning, quite the contrary, there is actually an absolute advantage in shorter time frames.

The following 2 users say Thank You to artemiso for this post:

@artemiso: Brilliant post, you hit the nail on the head.

However, there is one minor glitch. Transaction costs do matter. If you trade ever smaller timeframes, transaction costs will outgrow the intrinsic edge, and you strategy will be making losses.

That said from your statement above and the knowledge that transaction costs will overcome the edge for very small timeframes, you may conclude that there is an OPTIMUM timeframe to trade.

Under optimum I understand the timeframe that allows you to attain the maximum compounded growth rate.

I have tried to give an example for the optimum frequency / targets in the thread "Risk of Ruin". You will probably like these posts:

I wanted to respond more in depth to this but I confess I need to go back to school and understand Kelly, Opt F from first principals before I can do so. But thanks for clarifying my guesswork there.

- System with 2,000 trades, and net expectancy after commission and slippage of $5 per trade.
- System with 200 trades, and net expectancy after commission and slippage of $50 per trade.

I tend to always …

The key is understanding that the variance of return matters, and that you more easily achieve a better variance with a high win rate than with a high R-Multiple.

The following 7 users say Thank You to Fat Tails for this post:

I've not much to add, I absolutely agree with the idea of an optimal frequency and that the function of transaction costs do not necessarily increase in a way which leaves higher frequency trading possible.

The following 2 users say Thank You to artemiso for this post:

Great thread....just wanna say thanks to everyone who's contributed.

Couple of thoughts, and I apologize as I'm no math genius or fancy programmer, and lots of questions going thru my head.

I personally have not found success in "simulating" real trading, much less mathematical formulations or probabilities.

The one thing I 100% completely agree on is that small edges can have a huge impact, and it only takes 1 or 2 jackass trades to knock you back a few weeks or months.

Without trying to go off subject, I've found the most success in adding the 'picky' filter to my trades. I'm not going to take every trade my 'system' produces, so that upfront filters out profitable and (hopefully mostly) losing trades...is there a way to factor that in for simulations or is it already there?

Also, is there a way to calculate 'mixed profit targets'? What I mean is, that if I don't feel the trade, I'm out...so suddenly I'm changing from say 1:1 to breaking even or losing a few ticks.....and the same for profit targets? If I normally trade 1:1, but I see major buying or selling, I'm gonna let the market tell me when to get out.

And on the same note, say if a trader mixes his trading 'styles' for market moods....say trading 1:1 for choppy days or when the trend is in, trading 1:4 or more....

just a few thoughts....

Now to continue with the ideas from the basis of the thread, I'd be interested in figuring out some mixes....

Say trading 3 equal unit sizes, 1:1, 1:2, 1:3 or maybe 1:.5 1:1, 1:2....and even smaller differences....1:.6, 1:.8, 1:1

The idea of using fixed risk/reward is interesting, in taking out the 'emotional' element to some extent.....See the trade, put the order in, once hit, have the stop and profit target in and then go for a walk....that way you're not scared out at break even or on a stop run.....

def. cool stuff....one thing I do like about this forum is the general attitude of traders helping open each others eyes to ways of more profitable trading.....much better than those 'elite' traders and such...

cheers!

The following user says Thank You to lsubeano for this post:

Just read a fantastic book related to topics discussed here, Fortune's Formula. Recommended reading.
Btw, Poundstone has other highly entertaining books out (philosophy, math, computer science...etc.). New favorite.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 4 users say Thank You to Anagami for this post:

Great thread, thank you for posting. I went to bed thinking about this last night and I have a question regards how the simulation is generating trade distributions based on the input figures Win%/RR. I've attached an image that shows two different distributions with resultant Win% and RR being the same. I created two graphs so that it's clear to see why they are different from each other.

When the simulations are being run - is the model generating type A, type B and all variations thereof or is it merely generating type B distributions and randomizing the sequence of events?

I'm trying to understand the application of the edge and its ramifications for the model as a whole. If I can understand it I'll try to draw it in, which might make it slightly more accessible. Sometimes I get a bit lost in the maths.

Cheers

1Lot

The following 6 users say Thank You to 1LotTrader for this post:

Before I start, there is a small glitch on the right chart, as the visual part shows 11 wining trades and 8 losing trades. However, the figures below are correct. Just the last and the third but the last bars are off.

You have selected two examples with the same win rate (50%) and the same R-Multiple (2.0). However, there are two differences that can be spotted

(1) The first example generates larger average returns, both positive and negative.

(2) The returns of the first example are dispersed, while the second example only has two outcomes.

Actually the second example represents a Bernoulli distribution, which is a discrete distribution with two outcomes a and b which occur with a probability p and (1-p). We have built a model for optimizing trade size of this type of distribution by considering the maximum acceptable risk of ruin (or the probability admitted for a predefined drawdown) in the thread of risk of ruin. You cam compare with the cases listed here as well:

Now let us play a little with the Excel application and compare three different trading systems that have exactly the same expectancy per trade!

System 1:

- Average Win : 30 points
- Average Loss : 10 points
- Winning Percentage: 40%

Expectancy per …

Larger Average Returns Have no Impact on the Risk Profile

(1) The fact that average returns are larger, just means that you will experience larger profits, larger losses and larger drawdowns. To understand the impact of the larger returns, let me add a third model to your two cases. The third modell is a system that produces returns of + 13.8 points for 50% of all trades and - 6.9 points for the other 50% of all trades. So it is a Bernoulli distribution of returns as model 2, just with larger outcomes. As both models 2 and 3 are Bernoulli, I can use the spreadsheet below to study the risk adjusted outcome.

Bascially the two models are identical. Except for some small differences which are a consequence of the non-possibility of trading fractional futures contracts, the model 2 can be leveraged up to match model 3. So with predefined risk characterstics, you could trade model 2 with 33 contracts and model 3 with 9 contracts for the same acceptable drawdown, and they would both require 43 respectively 45 trades to reach the target.

A Larger Dispersion of Returns as Measured By The Variance Leads to a Less Favourable Risk Profile

(2) This case can no longer be analyzed with our simple model, which only works for Bernoulli distributions.
The trade returns for model 1 are dispersed around the average return.

If I compare your model 1 to the newly created model 3 (Bernoulli distribution of with returns of + 13.8 points and -6.9 points) I know that the two models produce

- the same average win rate
- the same R multiple
- the same expectancy

The only difference is the risk profile, which can be determined by calculating the probability for a maximum acceptable drawdown.

(2a) If you have real trade-data you can do this with a Monte-Carlo simulation and determine the percentile corresponding to your draw down.

(2b) Before even starting any calculations, we already have a feeling that the dispersion of returns is nothing good and will negatively affect drawdowns. The average return does not help us to confirm that bad feeling, but there are other statistical tools that do, for example the variance/standard deviation of the sample (division by N-1) becomes

For obtaining the standard deviation, we simply calculate the square root, which returns

model 3: standard deviation = 11.2
model 1: standard deviation = 12.7

The suspicion has been confirmed, the dispersion leads to a higher standard deviation, which is probably bad.

Comparing Drawdowns

(3) To better understand the risk profile of the trades, we will have a look at the probability that a maximum acceptable drawdown is generated by 3 successive trades. Just for demonstration purposes I will look at the possibility of a drawdown of 25 points

The model 3 only generates a win of 13.8 points, or a loss of 6.9 points, so it cannot produce a drawdown of 25 points with three successive trades, the probability is therefore 0.

The model 1 can produce 20 different outcomes for each run, that leaves us with 20 x 20 x 20 possible outcomes for three consecutive trades. Out of these the combinations the folowing 39 produce drawdowns of more than 25 points: (-11,-11,-11), (-11,-11,-10), (-11, -11, -7), (-11,-11,-5), (-11,-11,-4), (-11,-10,-11), (11,-10,-10), (-11,-10,-7), (-11,-10,-5), (-11,-10,-4), (-11,-7,-11), (-11,-7,-10), (-11,-7,-7), (-11, -5, -11), (-11, -5, -10), (-10,-11,-11), (-10,-11,-10), (-10,-11,-7), (-10,-11,-5), (-10,-11,-4), (-10,-10,-11), (-10,-10,-10), (-10,-10,-7), (-10,-10,-5), (-10,-7,-11), (-10,-7,-10), (-10,-5,-11), (-10,-5,-10), (-10,-4,-11), (-7, -11, -11), (-7, -11, -10), (-7,-11,-7), (-7,-10,-11), (-7, -10, -10), (-7, -7, -11), (-5, -11, -11), (-5, -11, -10), (-5, -10, -11), (-5, -10, -10).

The probability of a drawdown of 25 points or more is therefore 208 / 8000 = 2.60 %.

This simple calculation (don't beat me up, if there is a numerical error in that calculation, just made it quickly) shows that the risk profile of the two models is different, and that indeed model 1 cannot be traded with the same leverage for the same risk appetite.

A Monte Carlo simulation on both in-sample and out-of-sample data will show the impact on position sizing and aggregate returns.

The following 7 users say Thank You to Fat Tails for this post:

After reading your post 4x I actually understood everything you said

From my own very long hours of testing data sets and live trading I knew that Sample A would have a different risk profile to Sample B and the effect of a position sizing algorithm on top of it would only serve to increase that uncertainty. We know the expectancy is the same for both sets but we also know that the curve in A could potentially be far more volatile. So I garnered that from your post as well as how one would go about calculating that mathematically which I didn't know how to do before.

Unless I have misread something and the answer actually lies in there I'm still kind of wondering about how the simulation on page 1 is generating its curves. All I can see in the input parameters is the Win/Loss and Win Probability. So how is it simulating the trade distribution that we see in set A?, Is it the case that the simulator automatically assumes a Gaussian distribution and then generates random trade sets based on that profile. (if so then how are we defining the domain since it's not being based of an initial trade set?).

I know this is the realm of a Monte Carlo simulator but if it isn't a Monte Carlo Sim then what is it that we are we looking at?

Apologies if my questions are a bit basic, as I mentioned I'm not a statistics wizard.

Cheers
1Lot

The following user says Thank You to 1LotTrader for this post:

It is a Monte Carlo simulator. This is what a Monte Carlo Simulator does:

Let us assume for simplicity that you have a sample strategie which produced 100 trades during a backtest. Now you watch your equity curve and find out that it is pointing up. Nice. But if you run the same strategy again in the future, what is going to happen, will you observe the same drawdown?

To continue your analysis you now assume that the outcome of each trade is stochastically independent from the outcome of all prior trades. This is one of the typical assumptions made by financial mathematicians, because it facilitates model building. Of course this is never true, but if you don't make that assumption, things become too complicated. Reminds you probably that the Black-Scholes model also assumes lognormally distributed prices and we actually know that they are not.

Now, assuming that stochastic independence holds, you could take all the hundred trades, rearrange them in all possible orders and then draw the equity curves. If you do this you wil have a chart with exactly

100 x 99 x 98 x 97 x ............ x 5 x 4 x 3 x 2 x 1 equity curves

Now you switch on your PC, and in about hundred years your great-grand-son will see a black cloud on the chart.

This is not feasible, so instead of anaylzing all the combinations, you just select a few of them with the help of a random generator. After having selected about 100 different paths you draw the equity curves and look at the behaviour of drawdowns.

Variations of Monte Carlo Analysis:

Urn model without replacement: This is just a reshuffling of all trades. All equity paths will lead to the same final result, as each of the trades is drawn once and used for the equity curve.

Urn model with replacement: One trade can be drawn several times, some trades will not be used at all for the equity curve. For example you can see that the Monte Carlo Simulation on page #1 used this model, as the equity curves do not converge to a single point at the end of the back test.

The second question is what you use for your Monte-Carlo Method. You can use

- the numerical result of each trade
- or the returns of each trade

The appropriate method depends on how you determine your position size. If you use a constant position size over the backtest, then you should reshuffle / redraw the numerical result for each trade. In this case the equity path is calculated by adding or subtracting the result of each selected trade to the equity.

If you use a fixed-fractional approach to position sizing in order to obtain maximum geometric growth, then you need to calculate the equity path by multiplying the equity with the growth factor calculated from the return of the last trade.

Both approaches are possible, as - lucky enough - both addition and multiplication are commutative.

The Monte Carlo Simulation shown in post #1

I think that this simulation is limited to Bernoulli Distributions, that is trades with two possible outcomes. These can be entirely defined via the win rate (probability of a favourable outcome) and the R-Multiple (ratio obtained by dividing the winning trade by the losing trade). The simulation use an urn model without replacement, because the equity curves diverge. It use an approach of constant position sizing, as other wise the equity curves would not show linear but exponential growth.

For Bernoulli-Distributions, a Monte-Carlo Simulator is not needed, as you can determine the optimal position size with a simple calculation. The Monte-Caro Simulator is superior, when you cannot build a simple model to describe the behaviour of a statistical series. In that case it can be used to get an approximation for real probabilities, although the model is built on the false hypothesis of stochastic independence.

The following 5 users say Thank You to Fat Tails for this post:

Thank you Fat Tails for taking the time to help me reason this out and validate my initial thought. I've done quite a bit of work with different position sizing algorithms, so I am familiar with the way in which they randomize the trade sequences in order to analyse the effects of leverage on the different sequences that are possible in a normal random distribution. However, I have always done it by running a simulation on top of an existing trade set as opposed to generating it off such a simple set of inputs. This is what led me to suspect in the beginning that the only way this simulation could do this is by generating a simple two type outcome model.

As we know the market is not a Bernoulli distribution, if I'm not mistaken, the only way to actually create one is to implement a system on top of it that creates one through rigid trading rules. Having thought this through thoroughly I think it would be presumptuous for Anagami to assume that every trader or a large amount of them at least are using a Bernoulli distribution. To be quite frank in my 4.5 years trading I can't actually remember having met one that does.

My thought is that the reason a small edge is generating such magnificent returns is because of the consistency of the Bernoulli distribution itself. The risk profile as we previously talked about is in no way the same as the risk profile in type A. If we are then using fixed fractional sizing on top of it, we magnify this edge tenfold since the strength of most position sizing algorithms rely heavily on the consistency of the underlying distribution.

So are we really looking at "Why 7% is the Difference between Failure and Success in Trading?" or are we looking at "Why 7% is the Difference between Failure and Success in a Bernoulli Distribution?"

Thoughts?

1Lot

The following user says Thank You to 1LotTrader for this post:

The Bernoulli distribution is a special case, which can be used to build a simple model. The simple model is very useful as you can already show a lot of things, for example

- that departing from an identical expectancy, a trading system with a high win rate produces lower drawdowns and gets you better risk-adjusted returns then a trading system with a high R-multiple and a low win-rate,
- that an input is needed from the trader selecting maximum permissible drawdown (= ruin) and the maximum acceptable probability (= risk of ruin) that this drawdown will actually occur during the trading period.

This is very useful, as it allows for understanding some of the basics.

Now if you have a system with a proven edge (proven means that the system worked for the in-sample period), then the question of position sizing is quintessential. In real life, you will not be able to build a model that reflects your backtest, so it is better to do some simulations. And that is where Monte-Carlo kicks in. I agree that it should be run on the real or backtested set of trades and not on a model. This will get you an estimate (not an exact value, as you assumed a Gauss distribution of returns and use a random generator to select the trades) of the likelyhood of the maximum permissible drawdown.

Then you can adjust position size to stay within the limits that reflect your risk appetite.

The following 2 users say Thank You to Fat Tails for this post:

I have always like this thread, and the recent discussion got me thinking about it again. Looking for some reasonable, if not statistically sound way to apply the metrics to generate results for non-Bernoulli distributions by combining Monte-Carlo with the Risk Adjusted Optimal F template.

Would it not make sense to find out the statistics of the low performance on a Monte-Carlo and then run those numbers in the Risk adjusted optimal F?

While writing this post I have spent too much time implementing my idea to see if it was worthwhile...lol.

I used the results of the bot that I have been running this year as my starting point.

Take the win loss ratio from the Low PnL on the Monte-Carlo simulator, then apply that to the Risk Adjusted Optimal F template. With my example, the accuracy went from 63% to 48.5%. Granted you have only taken care of one variable, accuracy, with the win/loss ratio still potentially in flux.

W/L changes are much more subjective. I adjusted average win down by the same percentage as average loss, basically reducing my W/L ratio at current accuracy until the profit reached the Low PnL on the Monte-Carlo simulator. Again with my example, W/L ratio went from 1.65 to 0.95.

I then have 2 points that I can use for sensitivity analysis. One if I have adjustments in my system accuracy, the other for W/L ratio changes.

I made 2 copies of the Optimal F sheet. Put data tables below where I could feed in "Low Accuracy" and current W/L ratio to the model for one sheet and current accuracy and "Low W/L ratio" on the other. I can then evaluate impacts to accuracy given the "Low W/L" and impacts to the W/L assuming "Low Accuracy". Basically, conducting a sensitivity analysis on each variable given the "worst" situation for the other variable.

To me this seemed a decent way to check system risk. In the end, my position sizing on the bot match my analysis results. @Fat Tails is welcome to tell me how statistically unsound this is, so that I know how much statistical risk I have remaining.

The following 2 users say Thank You to Luger for this post:

First of all I want to thank @Anagami for creating this thread and for @Fat Tails for adding so much context and understanding to it.

In trying to take the content from the world of theory down to "how do I apply this?" I thought about some considerations I have, and would like to discuss them here.

Do all of the simulations here all assume a mechanical approach, where the stop and target are always fixed? My assumption is yes but I may be incorrect.

My issue with the mathematical content in this thread, besides the fact that my limited brain power prohibits me from fully grasping it after only one brief read, is that it assumes that we are trading a "system" and that we have a definite signal, and that we take every one, and that we are trading a system that implies the market is essentially the same at all times and days (at least that's what I think it assumes).

But as a day trader trading ES, with the trades I normally take, a 1:1 would absolutely kill me. I would have to modify my approach drastically to obtain the optimal F that FT is touting. My trades are based around the structure of the typical ES day, and taking the trade off simply at 1R when I know that it will yield more profit seems a bit unusual to me. In other words, I would be trading a system, and not the market.

I apologize for taking this from a great mathematical discussion to the gray areas of practicality and for being less than eloquent with my words. But at the end of the day, we are still humans (though I think FT may be an android in disguise), and human behavior is not always a case of "optimal F".... if humans were driven by mathematics, there would be no such things as credit card debt and we would not have the sovereign debt problems we see on such a grand scale. What fool would spend more than he takes in? It's possibly the most simple math on the planet, yet, humans fail to obey even that. So, I think there is more to making money with a discretionary approach than accepting a 1:1 as optimal.

The following 4 users say Thank You to josh for this post:

I trade a very mechanical system with a fixed 2:1 risk/reward. I generally take an average between 10 and 15 trades per day. At the end of every day I review all my signals and determine how the method would have done if I traded with a various risk/reward ratios. The 1:1 ratio generally always has more winners, but is also almost always less profitable. I have been doing this exercise for years just out of habit. I don't know how that fits in with the theoretical findings here, but this has been my experience with a real world mechanical method.

The following 5 users say Thank You to monpere for this post:

For the Risk Adjusted Optimal F spreadsheet, your assumption is correct. Only 2 outcomes to a trade, win "x" or lose "y". Giving you ratio x:y. Basically, you enter a trade and put on an ATM with a fixed target and fixed stop loss and walk way.

I don't think that anywhere it was said a pure 1:1 is best. The outcome that Fat Tails noted was that higher accuracy and lower W/L ratio allowed more leverage than low accuracy and high W/L ratio.

65% accurate and 1.5 : 1
50% accurate and 2.6 : 1

Those scenarios are almost equivalent in this fixed stop and fixed target world, with a slight edge going to the one with higher accuracy.

For a discretionary guy, I think the only real take-way is that a consistent trader should work on increasing accuracy before increasing W/L ratio to allow for an increase in leverage or a smoother equity curve. Really it is a balancing act between the two, trying to make sure you don't give up too much of one for the other.

The following 4 users say Thank You to Luger for this post:

@monpere Since you trading is directly applicable to this thread. When looking at the profitability of 1:1 or 2:1, have you considered the impact of being able to increase leverage on the 1:1 due to accuracy?

The following user says Thank You to Luger for this post:

If I was trading 1 contract on both methods, and I now double the contracts on the 1:1 and also double the contracts on the 2:1, wouldn't the 2:1 still come out ahead? or is there a piece of the puzzle I am missing?

The following user says Thank You to monpere for this post:

@Luger: I think that we are talking about two different things here ....

(a) the risk that the trading system is correctly represented by the sample
(b) the risk derived from the variance of the sample

How good is the sample?

The sample trades are those backtested over the in-sample period. The question whether the sample correctly represents the edge of the trading system is important. There is a systemic risk (a1) that the behaviour of the market participants has changed and the edge since evaporated, which cannot be easily estimated with statistical tools. And then there is a risk that

(a2) the sample size is too small and represents too favourable an outcome
(a3) the trading system has been curve fitted to the sample

Your approach deals with (a2), if you analyze the low point of the MonteCarlo simulation. My approach ignores that type of risk. I assume that my sample has a sufficient size and that it correctly represents the edge of the system. So I focus on the risk (b), which comes with the variance of the sample.

Adjusting position size to risk of ruin

Example: I have an account of $ 100,000. I do accept a risk of ruin of 1%. My definition of ruin is that the equity has dropped from $ 100,000 to $ 50,000. How many contracts should I trade to comply with the specified risk?

The risk of ruin is equivalent with a maximum drawdown and the probability that the maximum drawdown is reached or exceeded.

What do I now? I take the backtest of my trading system based on a single contract and do a Monte Carlo Analysis with 1,000 different equity graphs. Then I look at the maximum drawdown that occured during the in-sample period for each of them. I plot a distribution of the 1,000 drawdowns and take the lower 1 percentile value, which is the worst remaining occurence, once I have eliminated the worst 10 drawdowns of the Monte Carlo analysis.

Now let us assume that the worst remaining occurence produced a maximum drawdown of $ 12,500. Starting from my requirement that there be a risk of ruin of 1% of a drawdown to an equity value of $ 50,000, I can now leverage the system by trading 4 contracts.

I would not use the Optimal F sheet for other than Bernoulli distributions. I will have to check, whether Ralph Vince has developed a more universal approach that can be used to do that. The simple spreadsheet is probably not the best tool for position sizing in a real world.

The following 5 users say Thank You to Fat Tails for this post:

TS sucks for certain capabilities but for analysis like Monte Carlo, Walk Forward, etc...it's awesome.

TS's walk forward optimizer actually does a pretty good job and has built in rules for pass/fail for strategies. It rejects (fails) those that have a certain number of "runs" that aren't profitable or those that have an excessive drawdown, etc. It even gives you recommendations on the next optimization interval.

Interestingly, I wanted to discuss your comment about in sample.

I find a lot of misconception about in sample size. Contrary to popular belief, you can actually include TOO much data. If for instance, the market has recently shifted significantly (i.e. a margin increase crushes volatility), then going further back with your in sample analysis is simply muddying the water more.

Although it's helpful to try to find an in sample period that includes multiple market structures and conditions, why go back any further than a couple of years on lower time frame strategies? On CL for example, if you had data, you could try to go back 35 years and you'd find there was a decade in there when oil didn't move hardly at all. So obviously optimization or analysis including periods like that is going to affect/sway your results, possibly in the wrong direction.

I find that it's best to find a happy medium of enough data to give you a trade size that's statistically significant (and I don't accept the college textbook n=30 value) and features a couple of recent relevant market structures, but doesn't give me so much history that it favors out of date/obsolete conditions.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."

The following 4 users say Thank You to RM99 for this post:

The main purpose of the thread was not to promote 1:1 (or any other RR for that matter) or a mechanical approach. It was to simply see how trials and the capital curve emerge as one changes RR and the winning %. FT introduced position sizing into the picture, which is also paramount.

The Kelly formula assumes that the outcomes and probabilities are known, so it has certain inherent modelling limitations (particularly if we believe in 'let the profits run', as we cannot predict the outcome). In theory, it is actually impossible to fulfill the formula conditions, because the trade probabilities are never known with certainty.

However, you can still get a ballpark position sizing recommendation by averaging your winners, losers, and probabilities and plugging them in. It's not the same, but gives you some idea.

I should add that most people seem to prefer to position size less than Kelly suggests (say, half Kelly), as the capital curve can bit a bit too rocky for comfort (giving up some gain for smoothness and minimizing the impact of unaccounted-for risks).

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 2 users say Thank You to Anagami for this post:

I should nothing to add to your comment, as you have all said it.

If there is a shift in a market paradigm, then it does not make sense to include old data. As markets change all the time, a sample period, which is too long uses data which can no longer be exploited.

The following 3 users say Thank You to Fat Tails for this post:

I don't use dice for trading (though there were times when I would have done better if I did ).

The dice part refers to my addiction to backgammon.

While we're at it, it may be interesting to see what the success/failure distinction is in fields other than trading. What % separates losers, good players, and great players???

So let's take backgammon. There's an objective way to measure backgammon skill. The programs play at 'God' level or almost there, so their play / analysis is considered standard.

Here are the levels with error %s. They represent erroneous deviation from perfect play on each move.

Supernatural 0 to 5 %
World class 5 to 10 %
Expert 10 to 15 %
Advanced 15 to 20 %
Intermediate 20 to 25 %
Beginner 25 to 30 %

These are cumulative for each game. By that I mean, just because you play a perfect move, doesn't mean you play a perfect game. (Analogously, just because you make a perfect trade, doesn't mean you are a perfect trader). So an expert deviated 10 to 15% on all moves combined (effectively, maybe made 2-3 good but less than perfect plays).

As you can see, in backgammon, the differences between levels are about 5%.

From experience, I can play a game at the supernatural level occasionally, but certainly not consistently. If I average out my games, I perform somewhere between Advanced and Expert level in backgammon.

How much study and experience would it take to move into World Class?

A lot!! It's a not a linear curve.

I feel that roughly the same divisions are present in trading.

Advanced level is tough to achieve, but to go beyond that takes even more effort.

Same in other fields. You can get good at chess, but to became an Expert, Master, and Grandmaster presents progressively tougher strata of achievement, maybe exponentially so.

Some of my conclusions: 5% or 7% improvements are huge, and they are harder to achieve the higher you go.

"The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." - Milton

The following 9 users say Thank You to Anagami for this post:

You are right, I was taking into consideration the (a) category of system risk. However, I did feel that I was building a plan for the (a1) type of risk. Loss of an edge will show up in W/L ratio and accuracy. So why not understand the sensitivities so that you can leverage down if the system statistics are in a period of decline.

The (a2,a3) types were also on my mind as the number of trades in the back-test was not huge. That same sensitivity understanding and leverage management applies here as well.

For the (b) type of risk, in my system...what are the odds that the system enters a trade and the next 3 days move against it 10%? That is my unquantifiable risks of ruin. Everything else should be manageable. Having only time stops puts a lot of risk in the realm of what is possible in the market.

I will still run the same type of analysis you mentioned for (b) type risk to see what kind of results I get. I will likely use back-test and real trades for the bootstrap. If this method tells me to use more leverage than I am, then I may just stay sub-optimally levered.

Can you provide the link to the website you used for your testing? I used to use it quite a lot, but have misplaced the link. For some reason, I thought it had gone dead a year ago or so, so never updated my bookmarks.

@Bau250: He was referring to a win rate of 60% in combination with a R-Multiple of 2:1. This would mean that if your risk is R, out of ten trades you would have 6 winning trades of 2R and 4 losing trades of 1R. Your average trade would then yield (6*2R - 4R)/10 = 0.8 R for a risk of 1 R. This is indeed difficult to achieve, and if at all with a system that trades every when and now.

The following user says Thank You to Fat Tails for this post: