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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.
quote:
Originally posted by pt_emini

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.




Doing this over random prices results in getting stopped out twice as many times as hitting your profit target. Therefore, your true reward:risk is not 2:1, it's 1:1.

I'm glad you brought this up. You cannot set your own reward:risk by simply specifying your profit target as a multiple of your stop loss. This does not give you the "real" reward to risk ratio.

The real reward to risk ratio is the result of the trading method laid on top of the behavior of the asset prices. Is the method sufficiently "in sync" with the asset prices to produce a positive reward:risk?

Your "real" reward:risk "to date" is your P/L. If you have a postive P/L, then you so far have a positive reward:risk. Does this mean you will continue to have one for all time?

Consider the coin toss example. At some stages in the game, you will be up. During these stages, you have a positive P/L. You may therefore believe you should always have a positive P/L. But we know for a fact (and it's easy to show with a computer simulation), that if you continue to play, your P/L is guaranteed to disappear.

I am not a math whiz, like some of the other posters on this forum, but I do understand a little about logic. This debate is like the one that discusses the number of angels that can dance on the head of a pin. It can be entertaining but of little practical value.
I do have to agree, if mmartinez is talking about, a wholly mechanical trading method relying on some combination of squiggly lines based on a single instrument, that this will always end in, given enough trades, a negative p&l. That is not to say, that a discretionary method relying on experience, correlated markets, disciplined order placement and money management skills- cannot or will not end in a profitable outcome.
Look, I'm completely sick of all this, and I'm not going to continue. I had planned to lock this thread down, only because it has my name on it, and I didn't want to see it get threadjacked and all perverted from the original concept. I will leave it open for now and let some of the other long-term readers tell me if they want it left open for them to post in. I don't really care. I am unsubscribing to any and all threads mmartinez posts in, and I won't be reading anything he posts once I finish here and find out whether to lock this or not. It is wasting my time. I don't care if he thinks he is helping others or not. If he is, great. That's for the forum owner to decide. I will leave with the advice to others that we are not generating a community to help traders by using our time continuing this topic.

A few quick points that will come to no use, but I'll post them anyway. Since mmartinez is not an actual trader, he is saying things and mixing terms that makes that clear. First off, reward/risk and expected value are two completely different things. What you are calling your P&L is essentially the results of the expected value. With your math background if you had any experience trading you'd know this. I can set my reward/risk at 2 to 1 as PT suggested with a bracket order, and it will be 2 to 1 period. It will fill me or stop me out, there can be no other outcomes. Now, over time I can get a feel for the winning percentage, and see what that is. The breakeven point is 33% winners, without accounting for commissions. Anything over 33% makes the expected value positive, and hence it's net positive outcome i.e. profitable. Since you say this can't be done, we are back to the same old thing.

Don Miller is 'lucky', and will give it all back, since he can't win over time, as you said. Speaking of Don Miller, you said you talked to him. I'm not sure how well you listened. As I said, I didn't think he traded over 100 lots. You said he traded several thousand contracts per trade. His trade size range is 15 to 100. So, back to what I said before. Say an average of maybe a 40 lot, 6.25 million RT's, you've got say over 150,000 trades. But you said he was trading maybe 5-6 years. I recall seeing his video course in 2002 with live trading. He was no beginner then, and that was like 7 years ago. So the number of trades is probably quite a bit higher. I think we have statistical significance in his results. I doubt he's 'the luckiest guy in the world'.

This lack of understanding of actual trading just makes me realize there is no point to keep engaging a computer programmer in trading discussions. You can't backtest my methodology. I made that clear. You said you surely can. I have over 32,000 screen-hours experience. I use that in subtle reading of the price action to make tick by tick decisions within the framework of my methodology. Things I see change the course of each and every possible trade. How can that be accounted for? There isn't an AI program, neural net, or genetic algorithm that could come even close to replicating that (note that I didn't say they couldn't out trade me, I said replicate what I do, since we are debating backtesting my discretionary methodology, exactly as I apply it). There is no way, and I mean no way my trading could be backtested. To say otherwise is just ridiculous.

As far as the coin flip strategy you want to run so bad in the other thread, knock yourself out. It has zero to do with real trading. In fact, you can't show it 'fails' with infinite capital and infinite time, because it doesn't. It runs forever. If you have finite capital it always busts out. Wow. Cool. It takes a lot of math genius to know that one. Big deal. Zero to do with trading. So, go to your thread, prove how much you know over there. Here's another 'it takes a lot of math smarts to figure this one out' factoid. If a trading plan is net negative outcome and you run a simulation it grinds to zero, and if it is a net positive outcome the equity curve rises (assuming a reasonable initial equity amount to cover the drawdowns). So, why run any simulations? You won't run any with a net positive outcome because you say none exists in the real world. So, the point is to simply demonstrate what happens when you trade a net negative outcome trading plan? Hmmm, thanks for telling us that, but I think we already knew what would happen with that.

So, all us discretionary traders who can't backtest, we should just quit because we know it can't be done, net positive outcome is impossible. And for those system traders, let mmartinez just backtest this for you on his super-advanced backtesting engine (wait, just use your super-advanced Trade Station), and you'll see you are a fool for trading. No matter what, the outcome is the same. Trading is a waste. We should just fold this forum, it is doing everyone a disservice. The bottom line for me is, I'm planning on trading for the rest of my life. By using correct position sizing, even if I lost every trade I made until I hit my average life expectancy I'd be able to do it. And that's my plan. It's fun, I like it. Let's call it my hobby. If others like to hear aspects of what I am working on, and want to discuss that with me, I'm willing. I make no claims, I never have. If it's luck like mmartinez says, fine. Then I'll stop looking at my trading like professional poker (let me guess, all those guys who wins millions, the same guys over and over, that's all luck, too?) and more like going to Vegas. Doesn't matter, I'll still be here tomorrow, and the next day, and the next day, in my deluded world of being lucky if I'm winning.

Since I know mmartinez has answers for all this, and those answers will be fraught with things I'd like to counter, if I don't stop reading his posts this will go on forever, which is what he wants. I want to focus on my trading, not on this endless debate. So I am unsubscribing from all threads. I won't see any answers. I'll leave it to everyone else not to be swayed by 'fuzzy math' and outright misstatements. And think long and hard about our forum, and where we want to spend our energy. I think this is the best forum out there. Will it still be the best years from now if this debate is still going on?
It takes an experienced, skilled carpenter to build a barn ... but only a jackass to kick it down. The following is a rhetorical question: Why does someone who does not trade and, in fact, states categorically that it cannot be done profitably, post on the mypivots trading site so prolifically?

Personally I find most information related to threads/posts regarding "impossible to trade profitably" useless and counterproductive to the mypivots environment/community.
quote:
Originally posted by mmartinez

quote:
Originally posted by pt_emini

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.




Doing this over random prices results in getting stopped out twice as many times as hitting your profit target. Therefore, your true reward:risk is not 2:1, it's 1:1.

I'm glad you brought this up. You cannot set your own reward:risk by simply specifying your profit target as a multiple of your stop loss. This does not give you the "real" reward to risk ratio.

The real reward to risk ratio is the result of the trading method laid on top of the behavior of the asset prices. Is the method sufficiently "in sync" with the asset prices to produce a positive reward:risk?

Your "real" reward:risk "to date" is your P/L. If you have a postive P/L, then you so far have a positive reward:risk. Does this mean you will continue to have one for all time?

Consider the coin toss example. At some stages in the game, you will be up. During these stages, you have a positive P/L. You may therefore believe you should always have a positive P/L. But we know for a fact (and it's easy to show with a computer simulation), that if you continue to play, your P/L is guaranteed to disappear.




If we go back to the real-time trading results that I posted covering 5 weeks of trading (basically the month of April + the last week of March). In order to produce those results I used a very specific and well defined trading plan. We see the method produced an average win/loss ratio at about 2 with a loss % less than 40%. (For readers: the avg win/loss ratio is the "real reward:risk" ratio mmartinez mentioned). What that means is, during that 5 week period of time, the trades were stopped out a lot less than 50% of the time, while consistently using a reward:risk ratio higher than 2. Your assumption that using a reward:risk ratio of 2:1 will double the probability of a loss is a false assumption.

Also, I agree with Jim, it will help everyone if we take care not to mix words and definitions. Expectancy is not the same as reward:risk, they are two entirely different things. Mixing up terms may confuse readers trying to follow the concepts being discussed.
Yes, PT, I agree with your numbers. I only mentioned doing 70% in the simulation just to show what effect it had. 70% would line up better with a 1 to 1 Reward/Risk ratio, perhaps like Kool's style of trading. My style is trend trading, so I'm selecting 3 to 5 to 1 R/R and looking at 30% to 50% winning percentage. I should have added the 1 to 1 R/R, but I didn't want to keep adding simulations. As I said in one of my books, and I think somewhere on the website, as you go up the winning percentage scale, you start to drop in the R/R, and vice versa. Together these two give us the 'expected value' (I use this term because it is the one used in probability theory), and that stays relatively constant as we slide up and down the scale. There doesn't appear to be any advantages anywhere on the curve, it more becomes an issue of what best suits the trader's personality. There may be an advantage, though, in terms of potential drawdowns, higher on the curve (towards the scalping end).
quote:
Originally posted by MonkeyMeat

...The following is a rhetorical question: Why does someone who does not trade and, in fact, states categorically that it cannot be done profitably, post on the mypivots trading site so prolifically?...
Monkey, I don't want to keep this thread going, and I don't want to post anything that needs any kind of reply, so I'll be very cautious here. And my comment isn't directed to mmartinnez here at all. I was just pondering your comment here, and something hit me. If I wanted to find a system that really did work, one that could be backtested and run over and over and shown to be robust, and on top if it, I didn't want to pay a fortune for a proprietary system, here's what I'd do. I'd go to reputable forums where I knew a lot of traders hung out, ones that really devoted their lives to trading. I'd then antagonize them by saying none of them could possibly make money. I'd challenge them to prove me wrong. You show me one system that I can backtest through a significant number of iterations, and if it proves to hold up, I'll admit it can be done. Many try, but they fail. I antagonize more, saying see, I told you it can't be done. Finally, after many, many claims, one is handed to me that actually 'tests out', and I've got my moneymaker. Then I disappear without so much as a thank you. See ya later, chumps, Merry Christmas to me. Just a possible reason why I might do such a thing...
quote:
Originally posted by jimkane

Yes, PT, I agree with your numbers. I only mentioned doing 70% in the simulation just to show what effect it had. 70% would line up better with a 1 to 1 Reward/Risk ratio, perhaps like Kool's style of trading. My style is trend trading, so I'm selecting 3 to 5 to 1 R/R and looking at 30% to 50% winning percentage. I should have added the 1 to 1 R/R, but I didn't want to keep adding simulations. As I said in one of my books, and I think somewhere on the website, as you go up the winning percentage scale, you start to drop in the R/R, and vice versa. Together these two give us the 'expected value' (I use this term because it is the one used in probability theory), and that stays relatively constant as we slide up and down the scale. There doesn't appear to be any advantages anywhere on the curve, it more becomes an issue of what best suits the trader's personality. There may be an advantage, though, in terms of potential drawdowns, higher on the curve (towards the scalping end).



Thanks Jim, I was fixated on the 2:1 thing and transferred that onto the higher 70% win%, which I feel is pushing the envelope in terms of being realistic for new traders. Anyone doing 70% consistently at 2:1 gets my vote as an accomplished trader. Also, I agree completely with your sliding scale concept.

I realize mmartinez will never run the basic simulation, but perhaps the discussion and ideas presented here will benefit other readers. What I have found surprising is many traders I meet have never thought about anything we are discussing in this thread. They tend to look at the P/L and maybe the win%, and never get beyond that level.
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 :-)