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# ES Fun Math Facts

I'm sure everyone is saying here goes Jim again with his math facts rambling. One of the things I like to do when I study a premise is to look at the various implications of what that premise are. For some reason, this is something I think very few people do. In doing this, I get a chance to examine the situation from a different angle, one that is usually lit with the harsh light of reality, given how I do the exam.

Let's look at something I hear all the time: "I only want to get three points per day (net) out of the ES, that's it. I see it move way more than that, and what I am asking for is very realistic." Sure sounds it. I see the ES move sometimes forty points in a day, and even a range day may have many swings of five or six points up and down. In this forum, you mention that you net three points a day and you better duck, because you're going to get blasted, and any 'good' vendor will tell you with an attitude like that, no wonder you're not a success, you're way too pessimistic.

Let's apply my implications approach and see what that shows us. (I'll assume slippage is factored into the net points, and commissions will at first be ignored, and then in 'part II' I'll show another startling math fact when we include them. Keep in mind this is a fictitious example for educational purposes only.) Here's how we do it (I'll show this for the ES, but also give the final numbers for the Russell, for those, like me, that prefer that vehicle). I simply calculate what rate of return this actually is, and see how realistic that sounds, since three points sounds incredibly realistic. Three points at \$50 per point on the ES is just \$150 per day, per contract (we'll just do one contract for now, since how many contracts has zero effect on the rate of return or the analysis).

Now, let's use the 'conservative' margin I have heard in here of \$2,000 per contract (I prefer \$10,000 per contract, as explained elsewhere, and most find that crazy). That means the daily rate of return is \$150/\$2000 = 7.5%. With an average 250 trading days per year, that's an 1875% return per year on the margin. For the Russell it's twice that, or 3750%. This is an uncompounded return, taking out all profits made every day. The compounded return is so astronomical I won't even show it here, in this mock example. Now, is that realistic, in my view? No, not even close. But the vendors are talking eight or ten points, and in here we hear twenty, thirty, and forty, but the implications of three points net is a rate of return on margin that is four times the available daytrader margin (and almost seven times what one place offers) is 1875% yearly return? 3750% on the Russell? Yep. So, three points net is very, very unrealistic to me.

Let's do this by reverse engineering, then. Let's look at Rogue Trader's example of where he feels 100% is realistic. This was discussed in this topic:
Traders, Forums & Unbelievable Claims. Let's say for the sake of argument one may think this may be a figure he or she might want to shoot for in his or her own 'Trading Plan'. What does this trader have to do to achieve that return? Now, grab your chair and hang on, because the answer is going to startle you, likely even if you are a long-term successful trader.

Let's crunch the numbers. 100% return in 250 trading days is 100%/250 = 0.4% per day. Now, with the margin at \$2,000, 0.4% of \$2,000 = are you ready (you sure?) \$8. Yep, if you net \$8 per contract in the ES per day you are making 100% return per year on your margin. That's 0.16 point net. In the Russell it is 0.08 points (less than a tenth of a point!!). Sorry, that's the facts. You have to net about 1/6 of an ES point per day to make 100% return on your money, without any compounding, taking out all profits every day. This isn't a Jim-ism, this is just arithmetic. It can't be denied or ignored, it is reality. This is one reason why I emphasize a 'small' edge in various areas of my methodology.

If I told you I had a way to net 0.16 ES points per day you'd probably laugh at me. I look at what the implications of that statement are, and then I evaluate the statement. This shows me just how small an edge really looks like. People think eight or ten point ES trades, and can't think 0.16 points net for the day. But if you get ten points, then lose nine, then get ten, then lose nine on four successive days, your net is 0.50 points per day. Yet people just talk about the ten pointers. Winning trade size and net points are two completely different things.

Now, some are likely saying 'Great example Jim, but commissions play a big role, and you can't ignore them', and others may be saying 'Nah, you catch a ten pointer on the Russell and make \$1,000, what does \$5 in commissions matter...'. Well, strap yourself in for a trading reality that most never explore, and it is a monster. Let's add commissions to our play example, and see what the implications of that are. If we use a \$5 round turn commission, that would be the same as 0.10 points in the ES, and 0.05 points in the Russell, and let's assume three trades per day for this example. So, our figures would become 0.46 points net per day for the ES, and 0.23 points on the Russell. My first impression, commissions don't really change the overall observation that much. To make 100% per year I have to net 0.46 ES points, less than half a point, or 0.23 points in the Russell, less than a quarter point. But don't you see the other implication?

If I am able to net that amount, let's say 0.46 points, I keep 0.16 points, or just under 35% of what I earned. And at 0.46 points, my actual return is 287.5%, but I keep the 100%. In other words, over 65% of my return 'disappeared'. Where did it go? My broker took it with his tiny little nominal \$5 round turn commission. I am able to achieve a 287.5% return for the year (in this example), but my broker grabs me in a dark alley with his goon squad and takes about 2/3 of my money? Yep, welcome to reality. And that's with a 287.5% return. And I thought taxes were harsh. Anybody realize this? And if you trade more than the three trades per day, the numbers get worse. I just thought I'd pass on some critical thinking for newbies and experienced traders alike. Maybe now, too, when you hear someone say they net twenty points a day, you can realize that 0.16 points per day is 100% return per year, or with three trades per day and commissions factored in, 0.46 points. And that's a mathematical fact that nothing in the world can change.

This material is from a copyrighted 2008 Kane Trading website article, all rights reserved.
Thanks for the info, Rogue. I think you are making a great contribution here, and I applaud your willingness to put it all out there, and I hope others come forward and tell you so also. No smoke and mirrors, here are the numbers.

Now, let's look at this, as it is fascinating. First, I'll state how I am reading what you said, so my calculations are clear, and you can correct me if I am wrong. And 'for the record', this is an example, I have not seen or verified Rogue's results, and I have no idea who he is, this is just a mathematical example showing the implications of a given set of numbers, that's it.

You traded 417 times, at an average of 1.6 contracts per trade. That's about 667 contracts for the year. Let's assume a \$5 round trip commission (I know, many pay low 4's or less for the YM), which would be about \$3335 for that. Let's add that to the \$36,000 you made, meaning you actually made \$39,335 and you kept \$36,000. Now, for 667 contracts you made \$39,335 / 667 = \$58.97 per contract per trade, on average, which is just under 12 ticks per contract per trade (before subtracting commissions).

Now, you traded about 417/250 = 1.668 trades per day, so you made 1.668 * \$58.97 = \$98.36 per day per contract, just under 20 ticks (\$5 per tick). Let's just confirm this in another way (I wanted all the calculations to be available, though). \$39,335 / 250 trading days = \$157.34 per day (wait, I thought it was \$98.36?). This is per day, not per contract. You said you averaged 1.6 contracts per day, so \$157.34 / 1.6 = \$98.34 per contract. Great, it checks. Keep in mind these are all estimated calculations based on the numbers provided.

Now on to the implications of this (other than I think these are fantastic results). I wanted to do an ES example (anyone else who is willing to provide their numbers?), so I will scale this to the ES for comparison purposes. The YM is trading at say 12755 right now and the ES 1396.25, so the ES is about 1396.25 / 12755 = .1095 of the YM. So, the net points per day per contract was 19.672 YM, and that is 19.672 * .1096 = 2.156 ES points. You are doing the equivalent, give or take, as an approximate, of just over 2 ES points per day per contract on average, and you made \$36,000 for the year after commissions, or \$22,500 per contract (1.6 average contracts per trade). But what was that as a rate of return?

The YM intraday margin at most places is \$1,400 when the ES is \$1,800, so to make this roughly equivalent to the ES using \$2,000, you'd be using 1,400 / 1,800 * 2,000 = \$1,556. So, your rate of return would be \$22,500 / \$1,556 = 1,446% using just above exchange margin. Using the margin most in here say they use, you have an incredible rate of return. Not only that, but you did this incredible rate of return with a net of only about 2 ES points per day per contract. A 2 ES point per day average per contract and you made 1,446% return, uncompounded!

If we compared that to my ES example at 100%, a 100% return would be 100% / 1446% * 2.156 ES points (should there be a margin adjustment?) = 0.149 ES points. Based on my non-commission example, that's pretty close to the 0.16 points I came up with. One thing becomes clear, as the rate of return based on exchange margin jumps up, commissions do become less and less of a factor, in this case being around 8%, most of that because of the higher rate of return, and some of it because the trading volume is less than my example of three trades per day. The point here is that Rogue's return is, scaled, coming from just about the daily net rate that I calculated before.

If this was deleveraged to the same amount I prefer for the mini's (about 7 to 1), the margin would be about \$9,111 per contract, or \$18,222 for 2 contracts, and you had \$20,000, so you are right in line with what I would prefer. Let's look at your return using that margin: \$22,500 / \$9,111 = 247%. This is more of an approach that I would be comfortable with (as far as margin), but it requires a very high rate of return (1,446% in this case) to accomplish, calculated on near minimum 'standard' daytrading margin.

All in all I think a few things came from this. First, the net per trade is much, much smaller than many people think, or generally mention. Rogue made about 1446% per year on a bit more than 'exchange' margin doing about 2 ES (equivalent) points net per contract per day, and if you look at it with almost six times that margin to deleverage, he made about 247% on those 2 ES points per contract. Next, as the rate of return jumps way up, commissions do become a lot less significant, but down around 100% on exchange margin they are almost overwhelming.

I hope this was instructive. This is a lot more calculation that I think almost everybody does, even on a one time basis. Keep in mind, too, I may have made an arithmetic error, so take it all with a grain of salt, and check the figures for yourself. And yes, I love doing calculations.
Kane,

I love you, man!

I am either too lazy, bored or stupid to do the math on my trading, so help me out. I started with a \$10K account about a year ago and have not compounded the profit/loss. I haven't calculated how many trades I did in 12 months, but I can tell you I averaged approximately \$410 per day in net profit inclusive of commission.

What is my annualized rate of return and do you think I can market myself as a trading prodigy to raise \$10 million+ in a so-called "hedge fund" whereby I charge my investors a 2% fee on assets under management and a 20% cut of the profits?
I think that must be a rhetorical question, because you don't need me for that calculation, Ruvan, you made about \$410 a day for about 250 trading days, or about \$100K. \$100K/\$10K is 1,000% return. Nice job. It looks like the average successful trader in here, many of whom don't even think they are extraordinary, is making over 1,000%. I guess I am dead wrong in my assessment of what is reasonable? Might have to redo my articles on realistic expectations?

As far as hedge funds, it's funny, because I have seen people that make 50% a year consistently get wooed like they were first round draft picks, with more money than I can comprehend thrown right at them, and people making 1,000% or more, they won't touch them with a stick. You even mention hundreds of percent and they say thanks, but no thanks. Very curious, to say the least.

What is also interesting here is that if someone with these numbers (I won't say Ruvan, because I suspect he trades less, and a different numbers of contracts) traded three times per day using the favored margin I here about in here of \$2,000, meaning they traded 5 contracts, they would be averaging about .547 points per trade per contact (.547 points @ \$50/point = \$27.35 per contract per trade, times 3 trades times 5 contracts is \$27.35 * 3 * 5 = \$410). Hmmm, is that first article starting to make sense? This trader made 1,000% return and averaged just over a half of an ES point per trade per contract. Not 20, or 30, or 40. That's not to say runs of that size weren't caught, but the net was about a half of a point. And if the trader did this with one trade a day, it was still made on barely a point and a half. And this was for a 1,000% return. Amazing, huh? But I've never seen it mentioned in one single place before.
Just for fun I would like to have a go at this problem from a slightly different approach just to examine it with a different set of metrics. In so doing, the exercise might give some added dimension or at least food for thought and further discussion.

My goal is to figure out the position size Jim's hypothetical trader would need in order to generate the stated goal of \$40,000 per year of profit.

We need to introduce some assumptions into this example. Let's assume for the sake of discussion our trader is able to achieve a conservative 50% win rate. Next, let's assume the trader's plan calls for a conservative reward:risk ratio of 3:2, now what this specifically means in the ES (for this example) is the trader will risk 2 ES points to gain 3 ES points of profit (risking \$100 per contract to gain \$150). Combined with the 50% win rate, the trader's plan has established a positive expectancy to gain (on average) a gross profit of \$50 per contract out of every two trades. Jim mentioned a commission rate of \$5 per Round Turn, when applied in this example reduces the gross profit to a net profit of \$40 per contract every two trades, or simply \$20 profit per contract per trade (on average).

Also, we will need to make an assumption about the frequency of trades per day, let's assume our hypothetical trader averages 4 trades per day and trades 250 days per year, giving us 1,000 trades per year.

Based on this information and assuming the trader just trades 1 contract per trade, generating on average \$20 per contract of net profit per trade (and \$80 per day), the trader will generate \$20,000 per year. Thus, the trader will need to trade 2 contracts per trade in order to achieve the goal of \$40,000 per year of net profit.

Applying a "middle of the road" margin rate of \$5,000 per contract, the trader will need to start with \$10,000 to trade the two contracts. As in Jim's examples, the trader stays fixed at a consistent trade size, in this case 2 contracts per trade start to finish (no compounding by increasing trade size).

For the sake of completeness, I am also assuming the trader does not scale into or out of trades, using instead a simple all-in / all-out strategy. Also the trader does not use trailing stops or break-even stops, thus it is assumed each trade ends with a full win or full loss.
Nice example, pt. Based on that info the rate of return on the \$10,000 margin for 2 contracts is \$40,000 / \$10,000 = 400%. The really interesting thing is that this 400% return is achieved, in this case, on an average profit, after commissions, of \$20 per trade per contract, or 0.4 ES points. You guys are really helping me out with my original point, which was how small the net ES points have to be to make what I consider outrageuously great returns. And in this example of 4 trades per day, the overall objective is achieved on 1.6 ES points net per day total, per contract. And sorry to beat a dead horse, but not 20, not 30, and not 40 points net, but just 1.6 points net in total. And hence to my way of thinking, that's what a solid edge looks like. Now, since I'm hogging this thread, anyone else want to get into the discussion?
quote:
Originally posted by jimkane

...The really interesting thing is that this 400% return is achieved, in this case, on an average profit, after commissions, of \$20 per trade per contract, or 0.4 ES points.

It's amazing that an average profit of just two ticks in the ES combined with a 50% win rate can produce that annual rate of return... these math facts really fly in the face of the vendor's pushing the idea that you need a 90% win rate to be successful trading...
Or that you need 20 or 30 or 40 points a day (or the 8 to 10 many vendors say). Hence my reason for creating this topic. I'm really surprised how little response this topic has garnered now that what I showed is clear by examples from our very own members.
Hi Jim,
Well I have just joined after watching you guys for a while.
I just want to say thank you very much for this particular posting(s) and to the other fellas data and consequent math calcs/logic. For me a light bulb went on.
To a degree I understood knowing your trade setup up risk/return and its win/loss % ....now I can add this bigger account picture to my thinking.
For me it has had a two fold effect. 1. It takes the pressure off having to try and make 50 pts or more (say on the YM) each day 2. Puts in perspective the Edge concept and what it really means ie you dont need much of an edge to get ahead in this gane.

I dont have the hard data of my own account to add further to the discussion. Perhaps in 6 months I will.
Thanks again
All The Best
John
John,

What you got from this is just what I was trying to show. Reality is tough enough for me, I don't want to deal with fantasyland, too.
Jim, Thanks for starting this great topic. Incredible value and sense in here and thanks to everyone for some excellent comments and figures.
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