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Positive Expectancy

  • #1
  • First Post: May 16, 2009 9:09am May 16, 2009 9:09am
I've been studying the Forex Market for over 5 years and have recently run into a concept I was completely unaware of. That of positive expectancy. Does anyone here use this concept when designing their trading strategies?

For those that don't know, it is a mathematical formula used to determine whether your trading system will win over the long term. It uses the probability factor and average wins/losses to determine this number. This is what large casinos use to determine their profitability when hosting games of chance. While the concept to me seems fairly obvious, the determination of position sizing and risk management seems to me to be counter intuitive.

Also from what I've read thus far this theory has one abiding flaw. It assumes a constant probability score, and win/loss ratio. Which we all know will change from month to month, year to year.

So I would truly apreciate a few minutes of your time in responding. Specifically, I am wondering if you used this concept when you designed your system, and if so how do you manage your risk, and/or position sizing based on the concept of positive expectancy.

Anyone?
  • #2
  • May 16, 2009 10:09am May 16, 2009 10:09am
You already have that when you print out a DetailedStatement with MT4.
Look for Expected Payoff that's nothing more.

You can only determin this after the fact not in advance. It uses past results do determin the probability of winning.
  • #3
  • Edited 10:53am May 16, 2009 10:52am | Edited 10:53am
Quoting Tjpld
You already have that when you print out a DetailedStatement with MT4.
Look for Expected Payoff that's nothing more.

You can only determin this after the fact not in advance. It uses past results do determin the probability of winning.
Tjpld,

Thank you for your response. I have seen those results but they vary grossly from doing the actual math (as per my spread sheet). I have recorded the trades...Also the data skews if you "split" your trades by taking profit on a portion of the trade, thus producing a falsely higher win ratio, as the Strategy tester counts each split as if it was new trade, but in reality it is the same entry.

What I am interested to find out are opinions and insights regarding the use of this concept in position sizing and risk management, its use of Kelly % and finally how to address a dynamic market where the presumed constants really arent constant.

Can you spread any light on these ideas?
  • #4
  • May 16, 2009 12:05pm May 16, 2009 12:05pm
Risk assessment will vary upon your trading style. Are you a 'swing', position' or intraday (scaling) trader?

Apparently, you are scaling out of trades. In order to provide appropriate commentary, you need to provide a few more specifics on how you are trading. This will provide insight as to what others feel is proper position sizing for you.

Also, there are No constants with regards to trading. A win/loss ratio is irrelevant when trading in a 'probability theory' mindset and positive expectancy is foremost above all else as, without such, ANY trading plan will fail in the long run.

So, if possible, give us a better look at how you are trading if possible.
  • #5
  • May 16, 2009 12:51pm May 16, 2009 12:51pm
Quoting Edgetrader
Risk assessment will vary upon your trading style. Are you a 'swing', position' or intraday (scaling) trader?...
Edgetrader,

Thank you for your input. While I really don't like to "classify" my trading style, I would suppose most would consider it a "swing" style of trading. I trade using a 4 hour chart, and hold trades anywhere from 12 hours-7 days depending when my exit signal comes along.

My general method of trading includes taking 1/2 the position off the table at a dynamically determined target point based on the Average True Range the instrument is currently showing. (meaning if the average true range is 71 pips, I don't hold out for 300).

After the first target is hit, I close 1/2 the position and raise the stop to break even and let the remainin portion run until the exit signal or limit out. I generally set the limit really high 900+ pips, and every once in awhile I get a nice surprise.

Initial stops are placed 10 pips beyond the swing low or swing high and are trailed along a "hanging stop" after the first target. This again is based on the average true range and a multiplier of 2.5.

Overall the system wins about 55-58% of the time, and the average win is slightly higher than the average loss. Again these numbers are variable with market conditions, and as they are used as a constant in the expectancy equation, AND the Kelly % I'm really unclear what if any advantage these formulas provide.

Finally, the data I have going back from 4-1-2006 to present shows a positive expectancy "magic number" of 25. Which I take to mean that the system makes 25 pips for each trade-win or lose. But this number can change drastically if the market conditions change, and assuming the same system rules, I don't see how the expectancy "at this moment" says anything about the future viability or non viability of the system.
  • #6
  • May 16, 2009 1:49pm May 16, 2009 1:49pm
Quoting gspajon
I've been studying the Forex Market for over 5 years and have recently run into a concept I was completely unaware of. That of positive expectancy. Does anyone here use this concept when designing their trading strategies?

For those that don't know, it is a mathematical formula used to determine whether your trading system will win over the long term. It uses the probability factor and average wins/losses to determine this number. This is what large casinos use to determine their profitability when hosting games of chance. While the concept to...
Sounds like you understand it anyway. It's like a moving average,changing all the time. Your expectancy might be positive over the last 10,000 bars but will be different over the next 10,000 . If you know HOW to trade, don't worry about it.
  • #7
  • May 16, 2009 2:41pm May 16, 2009 2:41pm
Quoting gspajon
I've been studying the Forex Market for over 5 years and have recently run into a concept I was completely unaware of. That of positive expectancy..........
IMO statistical expectancy (aka EV, profit factor, PF or 'edge') provides an effective, objective way of evaluating a trading system. Provided that you have a large enough sample size of results (wins, losses), it doesn't matter that the probability of each trade can't be calculated. The statistical measure is being applied to the results across the entire sample size.

Statisticians use experimental results to create their hypotheses. As an example, it can be shown statistically that instances of lung cancer are higher among smokers than non-smokers. Obviously smoking is not a casino game, like craps or roulette, where the odds can be precisely calculated. But if I take a large enough sample of smokers, and tabulate the results, then I can gain a statistical measure, within an appropriate confidence level, that X% of people who smoked at least Y cigarettes per day for more than Z years developed some form of lung cancer. Smoking is perhaps not a great analogy to trading, LOL, but hopefully you get the idea.

The larger the sample size, the smaller the margin of error. There's a table here illustrating this point. What it's saying is that if I test my system over 100 trades, and obtain a profit factor of (say) 1.5 there's a 10% margin of error, i.e. I can say with 95% confidence that the profit factor lies between 1.35 (i.e. 1.5 – 10% x 1.5) and 1.65 (i.e. 1.5 + 10% x 1.5). Whereas if I re-test over 2,000 trades, and the PF is still 1.5, then I can now say with 95% confidence that it lies between 1.47 (i.e. 1.5 – 2% x 1.5) and 1.53 (i.e. 1.5 + 2% x 1.5).

You mention that the results will fluctuate from month to month. Remember, with EV we are talking long term 'average'. Given a large enough sample size (number of months), there are also ways of measuring the expected statistical monthly fluctuation.

As you point out, EV = (# wins / # losses) x (average net win size / average net loss size)
Of course, since
# wins x average net win size = $ won, and
# losses x average net loss size = $ lost,
then EV can be restated as simply = $ won / $ lost.

A positive expectancy system (EV > 1) will (mathematically) deliver profit over time; a negative expectancy system (EV < 1) will eventually cause ruin. Everything else being equal, a system with a higher profit factor should deliver greater return for the same level of risk, over the long term.

EV is ultimately determined solely by the accuracy of your entries and exits, and operates independently of money management ('MM'). I attempted to discuss this in more detail here.

The Kelly formula
% of account to risk = win% – (1 – win%) / (average net win size / average net loss size)
gives the bet (position) size that will deliver the optimal result. However, see the 'Reasons to bet less than Kelly' section in the Wiki article. My understanding is that Kelly maximizes return without giving ruin the special consideration that it warrants, especially in the context of trading.

All types of market analysis make the assumption that what's happened in the past is more likely, than not, to repeat itself similarly in the future. Even though (as the disclaimer aptly tells us) past performance offers no guarantee of future results, we must assume that a system that has tested positively thus far will continue to perform going forward. Otherwise it's stating the obvious to say that one is trading on the basis of a completely fortuitous outcome, and that as a negative sum game (taking costs into account), every trader must eventually lose. Expectancy uses these past results to provide an objective mathematical basis on which to measure the potential of a system.
  • #8
  • May 16, 2009 9:27pm May 16, 2009 9:27pm
Quoting hanover

As you point out, EV = (# wins / # losses) x (average net win size / average net loss size)
Of course, since
# wins x average net win size = $ won, and
# losses x average net loss size = $ lost,
then EV can be restated as simply = $ won / $ lost.

A positive expectancy system (EV > 1) will (mathematically) deliver profit over time; a negative expectancy system (EV < 1) will eventually cause ruin.
There are actually a couple of definitions of expectancy including the one David gave above. That one's a bit confusing though because the values are always positive, meaning that you have to remember that "positive" expectancy by that definition is actually greater than 1, not greater than zero.

The one I prefer is the win rate multiplied by the average win size minus the loss rate multiplied by the average loss size:

(#wins/#trades)(win size) - (#losses/#trades)(loss size)

or equivalently

(win rate)(win size) - (1-win rate)(loss size)

This has the semantic advantage that all positive values are actual positive expectancies while negative values lead to ruin. It has the added system design advantage of providing the expectancy PER TRADE, allowing the designer to take trade frequency into account in a clearer way.

Now, just as Hanover's equation above simplified to $won/$lost, the definition I use here simplifies to (total gain or loss)/#trades. However, there are very good reasons to use the expanded version, which I've discussed more fully in this post.

You also asked about keeping track of expectancy over time as the variables change. I do this for my intraday trading method using win rate and what I call "required win rate" which is simply the breakeven win rate required given my average win and loss size. "Required win rate" is just:

(average loss size)/(average loss size + average gain size).

You can also think of it as a measure of how likely a trader is to let profits run vs. letting losses run. A low value like 20% means that a trader tends to have losses that are only 1/4 as large as the gains, so this trader cuts losses short and lets profits run. A larger value like 70% would mean that this trader tends to use wide stops, but grabs profits at a point only 3/7 the distance to the stop on average. Scalpers might have high values like this.

Anyway, the Required win rate tells you what your actual win rate would have to be to break even. A RWR of 40% means the ratio of losses to wins is 4/6, so to break even you'd have to have a win rate of 40%:

(40%)($6) - (60%)($4) = 0

So I plot both on the same chart, and I update the chart for every trade I do. This allows me to see how my average performance is affected by each trade. As long as the Win Rate line stays above the Required Win Rate line, then my expectancy is positive. Here's the chart:

Attached Image


That teal line at the bottom is the difference between the WR and RWR, and I refer to that as my current "edge" even though I don't think that's the actual mathematical definition.
  • #9
  • May 17, 2009 10:00am May 17, 2009 10:00am
Quoting capitalist88
There are actually a couple of definitions of expectancy including the one David gave above.
I agree, both are valid, and merely express the same concept in a different way, i.e. as a difference as opposed to a ratio.

I prefer the ratio, as it gives me a dollar return figure for each dollar risked.
  • #10
  • May 17, 2009 10:47am May 17, 2009 10:47am
Gentlemen,

I found your responses intelligent and helpful. Thank you very much. So in keeping with what you've said, I went ahead and programmed my system into an EA. And to prove a point to myself, I ran the EA back over a period of time to 2004 to see the results, and found something very interesting.

While currently the system shows a very strong positive expectancy, as measured by the end number. If you start further back in time and run the test up to present, that positive number declines. Finally if you start back far enough, the number drops to a negative number, meaning a negative expectancy...

Why is this? While it appeared in all pairs I tested, it was especially rapid in the EUR/USD.

While at first glance I am tempted to say the system needs more work, I also have to ask myself if that isn't "curve fitting" to make the system fit the historical data.

So all this brings up at its core the very validity of the concept of "positive expectancy". The formula requires two constants percent of wins/losses (read probability of success) and average win/loss ($ gained or lost). Then this formula projects a positive or negative outcome based on these two very important numbers. But what if market conditions change?

Is it more valid to say my system has a 54% win rate over the past 5 years or an 80% win rate over the past month? I think neither and both are valid. It only means the market conditions are favorable to the system over the perod of time that is being measured...but cannot project that profitability into the future.

Why? Becuase the math formula at its core uses these constants in a finite way, as with games of chance where the odds are also finite. But trading, and particularly trading in the FOREX market has an infinite possibility of combinations and therefore odds. The positive expectancy formula assumes the probability of wining is constant, and that the average win/loss is increasingly accurate the larger the sample core. I don't think those assumtions are valid.

The example I like the best is the example of the coin toss. Where the odds are 50/50 win or loss...again a finite probability. However, take note of the next condition...Wins MUST be greater than losses....You must win more for each toss of the coin than you lose, or the expectancy quickly becomes negative.

THIS is where I think the untold secret is. Whether, you win more on each trade...or have a larger percentage of wins than losses, it doesn't seem to matter. The bottom line is that you must somehow find a way to win more than you lose...Always.

Whether it is a win rate of 30% and win to loss ratio of 4:1 or a win rate of 70% and a win to loss ratio of 1:1.

Finally, be ready to adapt to market conditions as they change....like the mouse in the maze...if you bump into a wall, turn around and go the other way, don't keep banging your head against the wall.
  • #11
  • May 17, 2009 11:53am May 17, 2009 11:53am
Indeed, market conditions do change. In fact, they change with each trade you put on as there are a different amount of buyers as sellers in the market on a second by second basis.

So, as for myself, I rely heavily on both a probability aspect to my trades, and an adjoining decent PE, and have found that it is in my best interest to trade only higher volatility times (London/U.S. session overlap and subsequent three hour period).

Further, I am solely dependant upon the PE formula's mentioned earlier by some fine posters as my sole means of taking trades based on my signal development analysis which was derived from backtesting and 'forward' testing some 2500 trades during my chosen time to trade.

As an admitted semi-scalper, I trade with a 'ZERO' TP/SL level per trade. The zero TP/SL is based upon my own method which allows me the potential of capturing the maximum pips available on a positive trade dependant upon what my charts are showing at a particular time, while closely monitoring and exiting losing trades quickly.

IMHO, the more targeted a time period combined with the well established volatility associated with said period, provide even more credence to the positive expectancy formulas set forth previously.

You are indeed correct in your statement that winners must exceed losers from a win/loss perspective. As my own PE runs at approx. a 5:1 ratio, and my win/loss ratio is approx. 57 to 62%, that combination has been beneficial over a sustained period of time.

Sure, the percentages and ratio's fluctuate pretty much daily. However, as none of us has a crystal ball in which to see into the future, all traders are forced to do a bit of 'curve fitting' when developing their methodologies if for nothing more than to derive a positive mental perception of their plan.

With regards to MM, which arguably is my second most important aspect, I choose to simplify the complicated and just trade in a 2% of available trading capital range wagered on each trade.

This allows my to withstand the largest known drawdown to account based upon my testing and trading efforts to date, and still be able to come back to the table for some more rewards or punishment as the market deems appropriate to bestow opon my each day.

All in all, each trader, regardless of their style, simply trades that with which they are most comfortable with.

Once again, a PE that is positive, a decent win/loss percentage, and the ability to have the intestinal fortitude to trade each setup provided regardless of outcome have been relatively good to me personally.

It seems the single issue many traders encounter is faith in the system they develop. When the ingredients for placing a positive trade are all present, it is only the trader themself that invites further problems by over analizing that with is symplistic in its design.

Sorry, just felt like rambling on a bit here. No more blah blah.
  • #12
  • Edited 12:03pm May 17, 2009 12:01pm | Edited 12:03pm
I failed to mention one more area of consideration that needs addressed when looking to develop a system with a postive expectancy.

The style of charts also will lead to widely varied results. That is, bar chart v. candlestick, v. Renko etc.

IMHO, Renko charts have a good ability to filter noise better than most others. As a TS platform trader, it is simply my own preference and does not intend to impune any other type of chart used by any other trader. Just works better for me is all.

Thx!
  • #13
  • Edited 9:27pm Aug 11, 2009 8:31pm | Edited 9:27pm
Stated on May 17th:

Quoting Edgetrader
A win/loss ratio is irrelevant when trading in a 'probability theory' mindset and positive expectancy is foremost above all else as, without such, ANY trading plan will fail in the long run.
Thread started on July 10th:

Quoting Edgetrader
Note: Trading this methodology is not going to give you a 1:1 R/R. Scalping is built on probability theory as mentioned. Further, PA will tend to repeat small intricate movements repeatedly. This is simply historical fact. As such, a scalping plan is based upon a decent win/loss percentage and very good MM. Just playing the odds and trying to stack them in your favor now and then.
It seems this lying, cowardly sack of sh*t doesn't know whether he's coming or going. Well, what can you expect from an ignorant scammer.
  • #14
  • Aug 11, 2009 8:41pm Aug 11, 2009 8:41pm
My signature tells you what you need to know about expectancy. When you learn how to make it work for you, then you will be a successful trader.
  • #15
  • Aug 11, 2009 9:36pm Aug 11, 2009 9:36pm
Hi guys,

I notice that people write about positive expectancy all the time and once they understand the formula they think that it's just about running your profits and cutting your losses. That's very misleading because your win rate is coupled to your profit vs. loss ratio.

The only way you can get a positive expectancy is by having a genuine edge. When you design your system, rather than concentrating on entries/exits/profit size/loss size, etc. try focusing on whether your method actually makes sense. Fine you've discovered a pattern, but does it describe something about the way the market works? If so, you may have struck upon an edge that will give you a positive expectancy. If not, you may be just seeing patterns in randomness and any success you've achieved through backtesting is just luck in the past and has no bearing on the future. Any further profits you get do not reflect a positive expectancy but rather temporary gains due to just taking on risk (i.e. gambling).

If you're interested, I wrote an article on this at the link below, and I also talk about positive-expectancy strategies on my blog as often as I have time to update it.

http://ezinearticles.com/?Maximize-E...tem&id=2675712

All the best for your trading,

Kris Matthews
  • #16
  • Aug 11, 2009 10:07pm Aug 11, 2009 10:07pm
Quoting kristdm
Hi guys,

I notice that people write about positive expectancy all the time and once they understand the formula they think that it's just about running your profits and cutting your losses. That's very misleading because your win rate is coupled to your profit vs. loss ratio.

The only way you can get a positive expectancy is by having a genuine edge. When you design your system, rather than concentrating on entries/exits/profit size/loss size, etc. try focusing on whether your method actually makes sense. Fine you've discovered a pattern,...
Some of your posts are great, and so is that article... Id vouche for you but im confused about why you are marketing your product/service here. Can you not trade profitably using what you undoubtably know? You seem like a clever guy, what gives?
Living the adventure in my head.
  • #17
  • Aug 11, 2009 10:57pm Aug 11, 2009 10:57pm
Quoting gspajon
THIS is where I think the untold secret is. Whether, you win more on each trade...or have a larger percentage of wins than losses, it doesn't seem to matter. The bottom line is that you must somehow find a way to win more than you lose...Always.
Positive expectancy = 1.20

Win rate is irrelevant. You need to make more than you lose. A system with a positive expectancy means, for example, every $100 you lose you will win $120.
Don't wish it were easier, wish you were better. ~ Jim Rohn
  • #18
  • Edited 11:15pm Aug 12, 2009 11:13pm | Edited 11:15pm
Hi Leon,

I'm glad you like some of my posts. I haven't sold anything yet. That may change since I've had a lot of requests to condense my strategy into a product or a book, and I've been trying to when I have time, but right now I'm trying to contribute as much value as I can and also learn from people in the process. A lot of people have helped me along the way and I owe it to them to give back. I've been promoting a blog by writing articles online but as you notice it's not littered with adverts and spam. As for my trading, I don't make 2,000% per year and don't have some fancy system. That said, I make a comfortable return that beats the market any year because I adapt to the market. If you look at my system on my articles and posts it's really just common sense and I don't see how it wouldn't be profitable in the future in addition to the present, for those who have patience. I don't hoard my system from others because it's based on human behavior and not a mechanical formula- the opportunities will always be there because human beings aren't about to change any time soon. I hope that clarifies things and thanks for asking an honest question.

Kris M.

Quoting Leonlorenzo
Some of your posts are great, and so is that article... Id vouche for you but im confused about why you are marketing your product/service here. Can you not trade profitably using what you undoubtably know? You seem like a clever guy, what gives?
  • #19
  • Aug 17, 2009 6:41pm Aug 17, 2009 6:41pm
Quoting Leonlorenzo
Some of your posts are great, and so is that article... Id vouche for you but im confused about why you are marketing your product/service here. Can you not trade profitably using what you undoubtably know? You seem like a clever guy, what gives?
What difference does that make?
  • #20
  • Last Post: Aug 23, 2009 11:35pm Aug 23, 2009 11:35pm
Quoting gbppip
What difference does that make?
Shouldn't you be rat hunting?
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