No registration required! (Why?)

Jim on 'fuzzy math'


I think there has been some misleading math being shown in this forum. I'm not saying anyone is purposefully misleading anyone, only that perhaps it's a case of having just enough mathematical knowledge to be dangerous. Here's an example. A common amount of an account to risk on a given trade is 0.5%. I saw a debate in here about risking 50% per trade. I know there may be some merit, for example purposes, to look at that example. But it can't be used in any way, shape or form to debate trading reality. If you actually bet 50% of your account per trade you're crazy (and I'm sure we all agree on that), end of story. 0.5% is a conservative amount. Now, if I traded three times per day, and I lost every single trade in a row, how many days would it take to draw my account down 99%, that is, to 1% of the original value? Well, it would take 918 losing trades in a row to do this, or about one and a quarter years of straight losses. First off, let me tell you that I am not too worried about that happening. Over a year and I haven't had a single winner (wow, quite a trading edge I must have had, huh?), and only now my account is down to 1%? Yep. (This assumes I can still open trades as the account value gets very low, which may not be possible in the real world, but it is an acceptable assumption for this example). But here's where it gets wild, as far as the math and the erroneous assumptions.

So, what does this imply as far as odds? If I trade for one and a quarter years I must blow out my account? No, that's silly. This is how many losers in a row I'd need to blow the account out. Let's say I'm no better than a coin flip in my winning percentages, 50/50. If I don't have an edge there would be no point to trading, so we must assume I have an edge as far as reward/risk goes, since I'm 50/50 on the winning percentages (but still, this is all irrelevant to the upcoming calculation, which is only going to look at percentage risked per trade and the case of the 918 losing trades in a row, and the odds of that happening). The argument I have seen isn't that it is impossible to have an edge, it is more that even with an edge, the random streaks that would naturally occur will necessarily blow your account out, every time. Money management decreases those odds to the point they can be much less than being struck by lightning. I still go outside even though in a given year my odds of being hit by lightning is about 1 in 600,000-700,000. What are the odds of being killed in a car accident, with perhaps almost 40,000 fatalities per year in the U.S.? But we still drive, and the small odds keep very few from driving. I contend the odds of blowing out an account, using the above parameters, based solely on a random streak of losing trades, is less than being struck by lightning or getting killed in a car accident.

See, here's where the wildly faulty and erroneous assumptions come in. If 918 losers in a row would draw the account down to 1% (I chose 1% for the example, but until you get down to a penny, you can keep going, and that would be a lot more than 1 in 918, but you need some minimum to make another trade, so let's say 1% and you are done), are my odds 1 in 918 that I'll go bust from this random drawdown, then? Nope, not even close. That's the erroneous assumption based on a misapplication of the mathematics. The talk is that if you take 918 traders who are risking 0.5% per trade, one will go bust in that one and a quarter years (I can tell right now all the traders in here are saying that's plenty good enough for me, you can stop right now). That's simply not correct. In fact, it's so far from correct that you won't even believe the 'real' mathematics here.

You see, in this 50/50 scenario, you have to figure out, as I showed Joe in the other thread, what .5^918 (one-half raised to the 918th power) is, and to calculate the odds, divide that into 1. The problem is, my calculator can't handle this. I know this will get a little boring, the math details, but I want to show them, in brief, anyway, so bear with me. I'll first do some rearranging, substituting 1/2 for 0.5, and ignoring that 1 to any power is still 1 (this is just some very basic algebra here), and we get this: 1/(2^918). Since we don't have any supercomputers handy, I'll do a little math shuffling to get an estimate. Since 2^3.32 is approximately equal to 10, we can say that 1/(2^918) is approximately equal to 1/(10^276), again using some very basic mathematical principals (2^918 = (2^3.32)^276 = 10^276). That is, the odds of actually blowing out the account with approximately three trades per day, in 918 trades total, with a 50/50 win loss ratio and a 0.5% risk per trade, based solely on a random drawdown, is approximately one in 1 x 10^276, or a 1 with 276 zeroes after it. Let's see what that looks like, assuming I counted my zeroes correctly:

1 in 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

Hmmm, looks like a lot less than my worries from lightning or a car accident, as I suspected (for perspective on 10^276, one estimate I saw said there are 10^85 atoms in the entire universe! ). So, that many traders would have to ply this approach before one would blow the account out from 'random effects' in the one and a quarter years? Yep, looks like it, if my math is correct. Well, I can say one thing, those odds are the least of my worries. You see the difference between betting 50% with winning percentage of 50% and betting 0.5% with the winning percentage 50%? Ah, the beauty of money management in trading. Most or all the examples given use figures for money management that are insane and would never, ever be used by any consistent trader who plans to stay in trading. Let's apply some real-world money management to our examples, then we can look at the results and argue if those are odds we realistically want to accept, or not. But don't tell me when the odds are like the above that I'd be insane to trade. I don't feel insane when I drive my car, and I'm not going to feel insane when I accept odds like the above in a trading plan. I'd like people to stop looking at unrealistic examples, and to use the math not to deceive but to enlighten.

P.S. For those that like to take 'big risks' of 2% per trade (something I would strongly recommend against, so I shouldn't even show it here, since it is getting away from what I think should be used for real trading), it would take 228 straight losing trades to draw the account down to 1% using the same assumptions as above, and the odds for that are about 1 in 10^68. Hmmm, maybe I have to rethink how much risk I am willing to take, as those odds don't sounds that bad :-)

P.S.S. Let me add another thought in here. If a trading plan is net negative outcome i.e. it loses money, then it will surely draw down over time until it is busted. That goes without saying, and isn't addressed here, and needn't be addressed in this thread. The sole purpose for this post is to see what it would take, what the odds were, that straight losers would happen to draw an account down to essentially zero, as was the example and basis for argument in another thread. Accounts can be drawn down with combinations of winners and losers, in all sorts of manners. None of those scenarios are addressed here, and the complexity of the calculations goes up with the complexity of the scenarios. All I wanted to show here was how small the odds of drawing an account straight down actually are using a reasonable per trade risk amount. All calculations are done for fun and educational purposes, and aren't to be taken as a recommendation of a trading style, or that any trading style must be profitable because of any calculations I have shown. The point was to show that of all the worries I may have about the viability of a trading plan, this type of random effect drawdown isn't one of my prime worries.
Just clarifying so I know how to write the program:

this is a coin-toss simulation, start out with a certain account balance, and bet .5% of that on each flip?

quote:
Originally posted by jimkane

So, run those simulations with the parameters I mentioned above and post those results in here and that will be worth discussing. But post all the results, not just some of them. Don't just post the maximum drawdown cases, show everything. And don't bother posting results for simulations that aren't listed above. If you want to do that, post them in your section. Let's keep this an area for what seems to be realistic trading parameters.

No, this is a trading simulation. Program it so it wins 50% of the time on one series, do another series winning 60%, and another doing 70% winners. Bet 0.5% per trade of the account balance. Make the reward 2 to 1 on each of the above, and 3 to 1 on each of the above. That would be six total runs. Once you create the program, you can just input the three key variables, which are % winners, reward/risk, and % of account bet. This simulates real trading results demonstrated by traders such as PT. Then run it for 40,000 iterations, or whatever you want, and see what happens. Look at the maximum drawdown. You'll be shocked by what you see, even after 100 million iterations. I know, because I've done it.

BTW, if you come back and say those results are not acheivable so you don't want to run the simulation, then we are done, and I'll run it and post it. But it will say a lot to everyone if you refuse to run it or post the results.
Now, speaking of number of runs, which seems to one of be the main issue in this discussion, let's look at that. The contention is all the 'poor slobs' who have traded for even ten years simply haven't done enough 'round turns', so it is likely luck, and not skill. It's just not statistically significant with a few thousand 'round turns', or so we keep hearing. Give me statistically a significant number of 'round turns' and then we can talk, I hear. So, if the results are overwhelmingly positive and the number of 'round turns' are statistically significant, then the conclusion is that it is not 'luck', it's skill, then? This seems to go without saying, right? Otherwise if it is all luck no matter what, there is no point to mention not enough 'round turns', since it is always luck. So, let's proceed with the idea that with enough 'round turns' we can reasonably eliminate the likelihood of luck being the primary reason for the success.

Let's look at Don Miller, who was recently mentioned in another thread. On his blog he shows how many round turns he does on a given day. The range I have seen has been between 1,000 and 9,000 per day. Let's say 5,000 is an average. For 250 trading days and five years, that would be, give or take, 6,250,000 round turns. Hmmm, over six million round turns and up over $2 million in real dollars in just the last year and change. Okay, so, is over 6 million round turns enough for statistical validity? For a series like this, you just find me any statistician that will say that's not enough. Good luck. So, we've ruled out 'luck'. But guess what I just saw. His results are due to luck.

There is zero point to continuing this discussion. It is getting ridiculous, and it is greatly detracting from the forum. I am going to wait on the simulation results just discussed above, and for those to be posted in this thread, and once that concludes, I will be locking this topic and quitting from this madness. I think continued interaction from anyone is just detracting from this forum. We have someone like TraderMom asking good, legitimate questions, and I can't contribute to that because I am too busy doing this. It's insanity. So, give me the results for the study as I laid it out, then we'll lock this topic down.
quote:
Originally posted by jimkane


Let's look at Don Miller, who was recently mentioned in another thread. On his blog he shows how many round turns he does on a given day. The range I have seen has been between 1,000 and 9,000 per day. Let's say 5,000 is an average.



Those aren't separate trades. That's the number of contracts. A single trade is something like several thousand contracts.
Actually I don't think he does trades that big, but I haven't asked him. I used 'round turns' because that is what you mentioned in yout post. Only the number of trades matters, but you said 'round turns' so I figured that was what was important to you. I will try to get an approximation on the average number of trades per day and post it. Even if he was doing 100 lots, which is huge size, he'd still have over 60,000 trades, which is way far beyond the number needed for statistical significance. But it's all academic, your mind is made up, I'm just waiting on you running those simulations and posting the results so I can shut this thread down.
The only way you can know what risk:reward ratio your trading method gives you is by simulating it on real price data over an extremely large number of iterations. Otherwise, you are simply guessing.

Where are you getting this 2:1 and 3:1 from? You're guessing. Your pulling a number out of a hat. You're basing it on:

a) a small number of trades
-or-
b) the naive assumption that if you set your stop at x1 and your take profit at x2, you will always be two steps ahead
-or-
c) it's got to be 2:1 or 3:1 because 50:1 is too much and 100:1 is too much

I repeat: the only way you can know your risk:reward ratio is to run your trading method through a very large number of iterations. Hopefully you do this in a simulated environment instead of using real money.

I won't bother asking you if you have done this - I already know the answer. If you had, you would realize the fallacy of your assumptions.

quote:
Originally posted by jimkane

No, this is a trading simulation. Program it so it wins 50% of the time on one series, do another series winning 60%, and another doing 70% winners. Bet 0.5% per trade of the account balance. Make the reward 2 to 1 on each of the above, and 3 to 1 on each of the above.

quote:
Originally posted by jimkane

Actually I don't think he does trades that big, but I haven't asked him.



Well, I did because talked to him on the phone.
quote:
Originally posted by mmartinez

The only way you can know what risk:reward ratio your trading method gives you is by simulating it on real price data over an extremely large number of iterations. Otherwise, you are simply guessing.

Where are you getting this 2:1 and 3:1 from? You're guessing. Your pulling a number out of a hat. You're basing it on:

a) a small number of trades
-or-
b) the naive assumption that if you set your stop at x1 and your take profit at x2, you will always be two steps ahead
-or-
c) it's got to be 2:1 or 3:1 because 50:1 is too much and 100:1 is too much

I repeat: the only way you can know your risk:reward ratio is to run your trading method through a very large number of iterations. Hopefully you do this in a simulated environment instead of using real money.

I won't bother asking you if you have done this - I already know the answer. If you had, you would realize the fallacy of your assumptions.

quote:
Originally posted by jimkane

No, this is a trading simulation. Program it so it wins 50% of the time on one series, do another series winning 60%, and another doing 70% winners. Bet 0.5% per trade of the account balance. Make the reward 2 to 1 on each of the above, and 3 to 1 on each of the above.



So, we are already at the squirming part where you won't run the simulation, and so you plan to disagree with the parameters, and argue they aren't realistic. You already know what they will show, and that they will blow your case out of the water, and so you have no intention to do the simulations. And everyone reading this already knew that was what you would do. I got plenty of e-mails saying this would be exactly what would happen.

Look, I don't care about iterations. My style is discretionary. It can't be run through any backtesting engine, period. So, there is no way I can ever 'verify' to anyone like you it is anything but luck, since my average might be 3-5 trades per day. If I traded forty years I'd do maybe 40,000 trades total at that rate. Since that would never be enough for you, my methodology is unverifiable. Big deal. I'm going to use it until the day I die. If I'm one of the handful of 'lucky ones', good for me. If I bust out, oh, well. I'll join Don Miller, and PT, and all the rest and we'll all have an old age party, sip some drinks on someone's porch, and laugh about how we all should have listened to mmartinez, who made it his mission in life to warn us, but we were all just too stupid to listen.

Look, we all knew you'd never run any simulations that wouldn't 'prove' your point, we all knew you'd never run this one, based off PT's numbers that he is doing week in and week out. Consider this thread done. You are not helping this forum or anyone here. Everyone has heard your story over and over. No one wants to discuss it with you anymore. Why don't you go back to Elite or wherever and let all us poor, ignorant traders get on with trying our best to create a good forum for traders.
quote:
Originally posted by mmartinez

The only way you can know what risk:reward ratio your trading method gives you is by simulating it on real price data over an extremely large number of iterations. Otherwise, you are simply guessing.



Any trading plan contains a number of assumptions. Determining the optimal reward:risk profile in real-time is a very difficult problem to solve. Any R:R strategy you choose, from the most basic (static) to advanced (dynamic), all presume upon the future. We simply cannot know in advance the future outcome for any individual event. This uncertainty factor is a constant we will always face.

Most new traders use a static bracket order strategy. For example, the strategy could be to risk 8 ticks in order to make 16 ticks of profit. This gives slightly less than a pure 2:1 reward:risk (due to broker commissions). You can give it 17 ticks of profit if you want to cover commmissions which will give you slightly more than 2:1 depending on your broker's fee structure. If you want to simulate 3:1 set your profit target to 24 or 25 ticks.

So for the sake of simplicity starting out, you could use the basic bracket order strategy against a win % of 40%-60%. I don't think 70% is a realistic expectation for most traders.
No squirming here. If you're going to live in a world of fantasy, why stop at 2:1. Let's just plug in a 500:1 reward/risk ratio.

who says 2:1 is realistic? Who says any positive reward:risk is realistic?

As I said before, you're pulling this number out of a hat. The reality is that there is no positive reward:risk over the long term.

In my other thread, I'll run the simulations on a fair coin toss using the "double-down" strategy the other poster was talking about, so that everyone can see it's an untenable strategy.

quote:
Originally posted by jimkane

So, we are already at the squirming part where you won't run the simulation, and so you plan to disagree with the parameters, and argue they aren't realistic.




quote:
Look, I don't care about iterations. My style is discretionary.



As I said before, this means there's no way you can know what reward:risk your trading method will give you over the long term.

quote:
It can't be run through any backtesting engine, period.



Yes it can. How do you think I arrived at my conclusions about trading?

quote:
So, there is no way I can ever 'verify' to anyone like you it is anything but luck,



nor is there any need for you to. At the end of your trading career, you will know what the true reward:risk ratio is. It will be your total lifetime P/L.

quote:

we all should have listened to mmartinez, who made it his mission in life to warn us, but we were all just too stupid to listen.



I've never said, implied, nor thought you guys are "stupid."

quote:
Look, we all knew you'd never run any simulations that wouldn't 'prove' your point, we all knew you'd never run this one,



You explain to me how you "know" your trading method gives you a 2:1 reward:risk. Once you've taken this number out of the realm of fantasy, then we'll talk. Otherwise, it's like telling somebody they've got a 100% chance of hitting the lottery as long as they follow some sort of unproven method of selecting numbers.

quote:

Consider this thread done. You are not helping this forum or anyone here.



I disagree.


quote:

Everyone has heard your story over and over. No one wants to discuss it with you anymore. Why don't you go back to Elite or wherever and let all us poor, ignorant traders get on with trying our best to create a good forum for traders.



Unless one lives under a dictatorship, a "good forum" for traders is one that gives all sides of the story.

It's disappointing to me that someone who is educated and a math teacher is unable to debate in a calm manner without getting upset and taking it so personally.
Sorry I wasn't clear on that PT, and it was good that you caught it, in the interest of accuracy for all the readers. I dig into this quite a bit in my Trade Management book (mentioned only for reference, not as a promotion, as I do none of that in this forum) for just the reason you mention, it is so rarely discussed anywhere. Seeing the net results as a function of the expected value, the combination of winning % and reward/risk, and seeing how they are inversely related and pretty much equal a constant (all other things being equal) is a really key concept. I love it when this forum provides great info for traders. That's why I'm here. That's why most of us are here. It's great when it works :-)