# System Expectancy

#### sidinuk

##### Established member
A lot of people want to compare their trading system with that of other people. To achieve this we need to calculate the expectancy of the system over the long term rather than just saying I made 100 pts last week and x made 50 pts therefore my system is better.

The best way to calculate expectancy is take a reasonable number of actual trades (at least 100) and calculate the following based on those results:

Average Win Size (AW) = The average of all trades which won (do not count the biggest win and do not count breakeven trades)

Average Loss Size (AL) = The average of all trades which lost (again do not count any breakeven trades)

Average Win Percentage (W%) = total winners/total number of trades excluding breakeven trades and the biggest winner

Average Loss Percentage (L%) = 100%-W%

Average number of trades per year (T) = number of trades in the sample size/number of weeks the sample covers * 52

Expectancy = ((AW*W% + AL*L%) / - AL ) * T

Attached is an Excel S/S with the formula in to help you.

Here are the figures for my trading system that I use on the E-mini S&P:

AW=10.79pts
AL=(5.14)pts
W%=51%
L%=49%
T=400

My expectancy is 232. So for each \$1 I risk on every trade I expect to make \$232 in a year.

Obviously the higher the expectancy the better, if it is negative then you will be losing money and should reevaluate your system.

I hope this helps people when they are designing their own systems and looking for comparisons.

Tim

#### Attachments

• expectancy.xls
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Hi Tim,

But you haven't enclosed the system rules for us to compare to

JonnyT

JonnyT,

All will be revealed in my book: 'How I made a million trading index futures'. I've only got about \$999,000 to go before I can start writing it!

I was hoping that others might let us know the expectancy of their own trading for comparison.

Tim

Disclaimer

This post is intended to be mildly humorous, no book actually exists. No free advertising or exaggerated hype intended.

Does Metastock calculates automatically these numbers?I think so...
i'll try to get an expectancy result for my system,although i think the best number to put here..
is ..how much money,in how much time , with how much capital

Greetings

You get almost 2 trades a day, and on average you make 10 points on your winners and lose 5 points on

I didnt think the S&P was that volatile?

Sidinuk,

I'm afraid your expectancy calculation doesn't seem right to me.

Expectancy is calculated on a PER TRADE basis as opposed to a PER YEAR basis, but aside from that, I still don't see where you get your \$232 dollars per year from. Let me explain the way I see it, and then maybe you can either agree with me or re-clarify your calculations.

The official calculation for expectancy is: (PW*AW) - (PL*AL)

...........where PW = Probability of a winning trade
AW = Average Win
PL = Probability of losing trade
AL = Average Loss

If we put your figures into this formula, then we get: (0.51*10.79) - (0.49*5.14) = 2.98pts per trade

Now here's where I don't get your figures. The average win and average loss that you have given are in points NOT dollars. Therefore, the annual expectancy of your system seems to be 2.98pts * 400 trades per year = 1193 pts over a 12 month period.

I don't see where your \$232 comes from. If you know what your AW and AL are in dollars (not points) then we could work out the true expectancy of your system.

Hope all this makes sense.

Thanks

Damian

@Sidinuk,

I prefer to analyse chances and possible account drawdowns of trading systems and concepts using monte carlo simulator software.

I've taken your input values (in your posting) and get the following mcs results (25.000 simulation runs with always 400 trades = 10.000.000 trades are simulated):

a) min.,average and max. profits and drawdowns (mcs1.gif attached)
b) distribution of simulation runs (mcs2.gif attached)

If your system results (and or the market conditions) remain constant and assuming 400 trades a year, you can estimate yearly profits between \$24.000 and \$92.000 (average \$59.000). The max. account drawdown or negative balance of your trading account was only -\$5.600...
...very good results.

But the conditions seldom remain constant, so it may be useful to test your system also with additional synthetic data (via data simulation, data scrambling procedures), which can also be build with mcs software.

Good luck,
zentrader (Volker Butzlaff, developer of Zen Monte Carlo Simulator v5.0)

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• mcs1.gif
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• mcs2.gif
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I suppose I should point out that sidinuk has posted only once since last December, and that was in July. So anyone wanting to attract his attention may want to send him an email . . .

Db

Thanks dbphoenix,

but I think the discussion concerning system expectancy is interesting for every (system) trader, not only for sidinuk...

bye,

Thanks dbphoenix,

but I think the discussion concerning system expectancy is interesting for every (system) trader, not only for sidinuk...

bye,

I suspect so. But sometimes people get upset if they don't get a response from the person they've addressed.

Db

I found the following information on correctly analysing system expectancy in the TradeStation strategy chat forum, posted by ghkramer. It really is very good info:

#### Attachments

• 20061128092750ExpectancyEq1.gif
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• 20061128092816ExpectancyEq2.gif
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• 20061128095512ExpectancyEq5.gif
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• 20061128092850ExpectancyEq3.gif
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Last edited:
A lot of people want to compare their trading system with that of other people. To achieve this we need to calculate the expectancy of the system over the long term rather than just saying I made 100 pts last week and x made 50 pts therefore my system is better.

The best way to calculate expectancy is take a reasonable number of actual trades (at least 100) and calculate the following based on those results:

Average Win Size (AW) = The average of all trades which won (do not count the biggest win and do not count breakeven trades)

Average Loss Size (AL) = The average of all trades which lost (again do not count any breakeven trades)

Average Win Percentage (W%) = total winners/total number of trades excluding breakeven trades and the biggest winner

Average Loss Percentage (L%) = 100%-W%

Average number of trades per year (T) = number of trades in the sample size/number of weeks the sample covers * 52

Expectancy = ((AW*W% + AL*L%) / - AL ) * T

Attached is an Excel S/S with the formula in to help you.

Here are the figures for my trading system that I use on the E-mini S&P:

AW=10.79pts
AL=(5.14)pts
W%=51%
L%=49%
T=400

My expectancy is 232. So for each \$1 I risk on every trade I expect to make \$232 in a year.

Obviously the higher the expectancy the better, if it is negative then you will be losing money and should reevaluate your system.

I hope this helps people when they are designing their own systems and looking for comparisons.

Tim

I think this is your true expectancy.

10.79 points is 10.79* 50= \$539.5 for the average win
5.19 * 50= \$259.5

((.51*539.5)-(49*259.5)) = \$147.99

Therefore you will make an average of \$147.99 per trade.. sure you prob already know this now.

1+ (147.99/ 259.5)= 1.57.. so you'll be making about \$ 0.57 for each \$1.00 you risk.

Looks a nice system...

This calculation is obvioulsy assuming theat u are risking 5.19 points per trade!!

Cheers Charlie

Why expectancy?

Why would anyone apply expectancy to actual trades that have occurred? Expectancy is applied to projected or anticipated outcomes. If you have actual trades (100) with actual profits and actual losses, then the outcomes are already known and the expectancy application is simply useless.

Let's assume that a Stock Trader with \$300,000 executed x number of trades and made a profit of \$75,000 in one year. His roic or return on investment capital is 75/300 or 25%.

Now a Commodity Spread Trader with \$100,000 executed y number of trades and made a profit of \$150,000 for the year. Her roic is 150/100 or 150%.

Why make a simple problem complex? It does not matter how much of the investment capital you are trading with at any one time. The stock trader can use only \$100,000 of the \$300,000 while the Commodity Spread Trader might use only \$15,000 of his \$150,000 at any one time. The bottom line is that they are both tying up \$300,000 and \$100,000 respectively that could have been invested elsewhere.

The main point is that once you have the actual outcomes or results, your roic should be the basis for comparison and not expectancy which is a probabilistic methodology for anticipating the direction of the market through weighting.

Why would anyone apply expectancy to actual trades that have occurred? Expectancy is applied to projected or anticipated outcomes. If you have actual trades (100) with actual profits and actual losses, then the outcomes are already known and the expectancy application is simply useless.

Let's assume that a Stock Trader with \$300,000 executed x number of trades and made a profit of \$75,000 in one year. His roic or return on investment capital is 75/300 or 25%.

Now a Commodity Spread Trader with \$100,000 executed y number of trades and made a profit of \$150,000 for the year. Her roic is 150/100 or 150%.

Why make a simple problem complex? It does not matter how much of the investment capital you are trading with at any one time. The stock trader can use only \$100,000 of the \$300,000 while the Commodity Spread Trader might use only \$15,000 of his \$150,000 at any one time. The bottom line is that they are both tying up \$300,000 and \$100,000 respectively that could have been invested elsewhere.

The main point is that once you have the actual outcomes or results, your roic should be the basis for comparison and not expectancy which is a probabilistic methodology for anticipating the direction of the market through weighting.

I would hardly call the expectancy calculation a complex one. I'm confused with your statement of saying that expectancy is a probabilistic way of trying to anticaipate the direction of the market, i have never seen it used in this manner. If one wanted to try and do the more 'complex' method of Monte Carlo Simulation this could be used to help anticiapte the 'probability' of where inflation and interest rates might go in the future (Central banks uses this). This would still be caculated from past data, its all we have to use. We're better off with past data than no data at all otherwise what are we trying to calculate.. our own wishful thinking, our hope, dreams, fears... what?

Oohh and expectancy is useful as a form of benchmarking, it is another way of measuring how likely a system might be profitable in the future, just like how people use Profit Factor as a important guage of a system.

I would hardly call the expectancy calculation a complex one. I'm confused with your statement of saying that expectancy is a probabilistic way of trying to anticaipate the direction of the market, i have never seen it used in this manner. If one wanted to try and do the more 'complex' method of Monte Carlo Simulation this could be used to help anticiapte the 'probability' of where inflation and interest rates might go in the future (Central banks uses this). This would still be caculated from past data, its all we have to use. We're better off with past data than no data at all otherwise what are we trying to calculate.. our own wishful thinking, our hope, dreams, fears... what?

Oohh and expectancy is useful as a form of benchmarking, it is another way of measuring how likely a system might be profitable in the future, just like how people use Profit Factor as a important guage of a system.

The original premise of using expectancy to compare two different trading systems with completed trades and known results of profits and losses is wrong and here it is again:

"A lot of people want to compare their trading system with that of other people. To achieve this we need to calculate the expectancy of the system over the long term rather than just saying I made 100 pts last week and x made 50 pts therefore my system is better.

The best way to calculate expectancy is take a reasonable number of actual trades (at least 100) and calculate the following based on those results:"

If for example, both of us have traded for one year and we have our profits and losses statements for the year, we can only compare our trading system and methodology using roic or return on our investment capital, not Expectancy or Expected Value.

You, SCFX can use Expectancy or Expected Value Calculation to project the performance of your trading system (only) into the future. There are too many variables and unknowns for you to compare my Expectancy to your Expectancy .....from emotional trading to human errors to broker fraud to you name it.

Expectancy or Expected Value Calculation in itself is not complex but the assumptions you make in calculating it for your own trades create the complexity. Wrong assumptions create wrong Expectation of market direction and profitability (Expectancy) with resultant losses.

I hope my explanation is more explicit this time around.

If traders are wanting to compare systems, then expectancy is only half the story. You also have to take into consideration the opportunity factor.

For example, system A might have an expectancy of \$1.46 per trade and system B might have an expectancy of \$0.57 per trade. On the face of it, system A looks the better system, until you learn that system A averages 100 trades a year whilst system B averages 1000 trades a year, meaning that system B is actually nearly 4 times as profitable as system A over a 12 month period.

Thanks

Damian

Sure, but then just use a % value over a period of time and you get an easily comparable expectancy measure.

I posted something similar of ET not so long ago and I think the idea of knowing the expectancy of any trading system (whether it's some complex formula or a simple visual backtest - doesn't matter it's what works for you) is vital to trading psychology.

For example, I have a few strategies and for each one I have the trade entry expectancy fully documented in my trading plan so that I know the probability of loss after pulling the trigger. I know entries are like only 5% of the trade, and the other 95% is made up of trade management and psychology, but if you know the chance of success against loss before you pull the trigger, then it helps deal with losses psychologically and it removes some of the emotion out of trading (well it does for me anyway). My evaluation of entry expectancy also takes into account drawdowns which I find helps out in trade management (i.e. know what drawdown is likely or to be expected over a set period of time) which in turn lends itself to knowing when a trade has gone wrong and what level a suitable stop loss should be.

I probably haven't explained myself very well but just my two cents worth.

Mikey

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