# Positive expectancy and edge



## nizar (23 November 2007)

Hi,

What is the difference between a positive expectancy and an edge?

Iv always thought they were the same thing, but I suspect that my understanding may be flawed.

I'd appreciate some thoughts and discussion of this please.


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## tech/a (23 November 2007)

No I dont think so.

Its quantifiable.So by trading in a certain way you will have an expectancy of X.

But what is it an edge over?
Market average.
Everyone else.
Another of your methodologies.
Your other investments.


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## Nick Radge (23 November 2007)

I would suggest that expectancy is the mathematical outcome of a series of trades whereas an edge is the statistical probability of a specific setup being profitable. For example, buying a stock nearer its yearly low is statistically better than buying it near its yearly high from both a risk and reward perspective. Both have a positive expectancy but the yearly low strategy has an edge over the yearly high.


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## nizar (23 November 2007)

Nick Radge said:


> I would suggest that expectancy is the mathematical outcome of a series of trades whereas an edge is the statistical probability of a specific setup being profitable. For example, buying a stock nearer its yearly low is statistically better than buying it near its yearly high from both a risk and reward perspective. Both have a positive expectancy but the yearly low strategy has an edge over the yearly high.




Thanks for your response Nick.
You make the distinction quite clear in this post.


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## Temjin (23 November 2007)

I would say positive expentancy is more quantifiable like what Nick was explaining.

However, my belief on the definition of edge is quite broad and some may not be quantifiable. For example, a trader having the ability to code computer algoriums and utilise back testing effectively can mean he/she has an edge over another trader who have no understanding of such concept. 

A trader who is more discipline and have a higher degree of self control can be regarded as having an edge over other traders who are not in control. 

Having enough capital to practice effective money management strategies is also an edge by itself.

Diversification through multiple trading strategies in multiple markets is also an edge.

I have these beliefs because trading is a zero sum game, you are essentially competing with other traders of small of various "format" out there. Having an edge ultimately mean you can earn more money (from them) than losing (to them) in the long term.

Another example would be a private trader has an edge over insituational traders because they are not binded by strict rules and massive capital that is harder to trade/liquidate. 

I hope this is all clear. (again, my beliefs)


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## howardbandy (23 November 2007)

Greetings all --

Expectancy is the average amount or percentage won or lost on an average trade by a trading system.

The expectancy must be positive for a system to be profitable.

There is no trade size or money management technique that can transform a system that has a negative expectancy into a winning system.  But it is possible to transform a system that has a positive expectancy into a losing system by improper position sizing -- usually taking positions that are too large for the portfolio assets.

The average annual growth rate for a trading account depends on only two figures --  the expectancy of the system and its trading frequency.

Assume the expectancy is expressed as a percentage, call it e.  If the average trade gains 0.8%, e will have a value of 0.008.

Assume the trading frequency is expressed in trades per year, call it n.  If a system completes 12 trades per year, n = 12.

The final account equity at the end of a year, expressed as a multiplier (call it m) of the initial account equity can be expressed by this formula:

m = (1 + e) ^ n

where ^ is exponentiation.

For this example, m = 1.008 ^ 12 = 1.1003  = a ten percent gain per year.

For comparison, consider a 38 slot roulette wheel -- 18 red, 18 black, 2 green.  Bets on red or black pay even money.  Assume 38 individual bets are placed, each bet on either red or black.  $38 will have been bet and $36 will have been returned to you (on average).  The expectancy is -0.0526.  After 100 bets, the final value of every initial $1.00 is $0.0045.  That is, bet red or black 100 times and you are almost certain to lose all of your betting bank roll.

I have not heard a common definition of edge.

Thanks,
Howard


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## GreatPig (23 November 2007)

howardbandy said:


> For comparison, consider a 38 slot roulette wheel -- 18 red, 18 black, 2 green. Bets on red or black pay even money. Assume 38 individual bets are placed, each bet on either red or black. $38 will have been bet and $36 will have been returned to you (on average). The expectancy is -0.0526. After 100 bets, the final value of every initial $1.00 is $0.0045. That is, bet red or black 100 times and you are almost certain to lose all of your betting bank roll.



Another way of expressing this is saying the probability of a win is 18/38 = 0.4737, and as each win pays double, the average return per bet is 0.9474. If each bet returned exactly that amount, then 100 bets would return 0.9474^100 = 0.0045, or less than half a cent in the dollar.

And to think the average return on a poker machine is around 0.90 (used to be more like 0.85-0.87). $100 to $1 in 43 bets on average (at 0.85 return, the minimum set by the Liquor Administration Authority that licences poker machines, it only takes 28 bets on average). Modern machines have spin times down to only 2 or 3 seconds, so 43 bets could be less than 2 minutes! No wonder people can quickly blow their life savings.

GP


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## nizar (23 November 2007)

howardbandy said:


> I have not heard a common definition of edge.




I'd be keen to hear your definition, Howard.


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## howardbandy (24 November 2007)

nizar said:


> I'd be keen to hear your definition, Howard.




I don't know.  

If someone asked me a question about the "edge" a trading system had, I would probably ask if he or she meant expectancy.  If they were not familiar with the term expectancy, that might be what they meant.  If they were familiar with expectancy, I would ask for their definition of edge and go from there.

Thanks,
Howard


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## theasxgorilla (24 November 2007)

I'll wade in with a thought or two.

To me 'edge' is found in the way you arrange the components and parameters of the system to help bunch and favourably shift the distribution of results observed during Monte Carlo analysis.  As tech/a is suggesting...it's relative to something ie. what it was before you made the change.

Expectancy might be all that is needed to measure a single run through a set of data and declare it positive (likely to be profitable given sufficient opportunity), but it won't tell you whether there exists 'negative expectancy' paths through such data, or the probability of trading along such a path. 

ASX.G


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## tech/a (24 November 2007)

I personally think each are distinctly separate.

For an edge to appear we must have a fixed starting point.
If a system has a positive expectancy of 2 then that point is Zero.

So the edge over zero is 2.
If its against 2 systems one with 2 and the other 4 then its an edge of 2 one over the other and 2 and 4 respectively over zero.

Well as I see it.


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## wealthlab (25 November 2007)

Hi Guys
	An interesting thread with some worthwhile points of view. So what is the difference between an edge and expectancy, this is what the dictionary offers us

Edge
•  noun:   a slight competitive advantage (Example: "He had an edge on the competition")

Expectancy
•  noun:   something expected (as on the basis of a norm) (Example: "An indicator of expectancy in development")

Quantify
•  verb:   express as a number or measure or quantity (Example: "Can you quantify your results?")

I recently read Curtis Faith's book “The way of the Turtle” Curtis was one of the original turtles and he offers these explanations in his book (excellent book BTW)

“The term edge is borrowed from gambling theory and refers to the statistical advantage held by the casino” 

“An edge in trading is an exploitable statistical advantage based on market behaviour that is likely to recur in the future”

“Expectation was one way of quantifying that edge”

I think Curtis has summed it up fairly well. It was interesting reading his book that the chapter on expectancy didn’t offer a way of calculating it (as other books do and is usually misleading as well) but rather Curtis offered a entire chapter on how to calculate your “edge” and he calls this the “e-ratio”. I noticed that the ASX gorilla has posted on this thread and he has done some work with the e-ratio if he would care to comment on his findings

Cheers max


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## theasxgorilla (25 November 2007)

wealthlab said:


> I think Curtis has summed it up fairly well. It was interesting reading his book that the chapter on expectancy didn’t offer a way of calculating it (as other books do and is usually misleading as well) but rather Curtis offered a entire chapter on how to calculate your “edge” and he calls this the “e-ratio”. I noticed that the ASX gorilla has posted on this thread and he has done some work with the e-ratio if he would care to comment on his findings.




Agreed, he understands what he is writing about very well and sums it up best.

I've applied the e-ratio as he calculates it to compare entry methods against one another and components of entry like setup conditions, as the chart below shows.  I don't remember exactly what I was testing here but clearly the index filter seemed to degrade the entry edge.  As you can also see the lines are quite erratic, so I think it's important *not* to look beyond the obvious.  Sometimes the results from this measure aren't very useful at all.  I believe he suggests this himself in the book.


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## wealthlab (25 November 2007)

Hi ASX.G
	Thanks for that yes I see what you mean. It’s also interesting how the edge can change over different time frames, as Curtis put it

“It is possible for an entry to have an edge that is significant for the short-term but not the medium-term or long-term”

And this is what my own testing has shown, although I have been calculating the Expectancy though the iterations between 1 and 100 because I haven’t worked out how to calculate the e-ratio in wealth-lab as you have done in Amibroker

Cheers max


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## tech/a (25 November 2007)

> “It is possible for an entry to have an edge that is significant for the short-term but not the medium-term or long-term”




An important point.
You see this with entry.
Entries and their importance pale as a profitable trade matures.
IE how important is an entry 12 mths after you've entered a trade.

So is the edge governed by timeframe?
Or is the edge simply static over a period to an end?
Do you need an end to measure or define an edge?
Is it dynamic?
When can an edge be defined?


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## nizar (25 November 2007)

wealthlab said:


> “It is possible for an entry to have an edge that is significant for the short-term but not the medium-term or long-term”




Yes I agree as well.

Some of ASX.G's testing has shown that the edge is actually against you (negative) in the very short term ie. a few days after entry. And this is possibly why short term mean reversion systems work so well.


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## wealthlab (25 November 2007)

> Originally Posted by Nizar
> 
> Yes I agree as well.
> 
> Some of ASX.G's testing has shown that the edge is actually against you (negative) in the very short term ie. a few days after entry. And this is possibly why short term mean reversion systems work so well.




Ditto Nizar and ASX.G that’s exactly what I have found as well with my testing. The chart below compares the Expectancy for the first 20 days (bars) of 2 entries. The blue line is a short-term high volatility entry and the pink line is a long-term trend following entry, which is an excellent entry for that purpose as it just keeps rising after the 20 days but as you can see it has a negative expectancy for the first 12 days whereas the short-term volatility play has a positive expectancy from day one and rises to around the 4/5 day level and then falls away thereafter.


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## theasxgorilla (25 November 2007)

Three key things with entry IMO:

1. Get your trailing stop up to 0 before price falls to your 1R initial stop.  This way your win/loss ratio is satisfactory and you avoid the worst kind of exit ie. initial stop.

2. Increase the probability that your trade will be profitable during your desired timeframe (short, medium, long, whatever).  This allows you to match an appropriate exit to the entry.

3. Increase the degree to which your trade is profitable ie. more price movement relative to time.


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## emerger (29 November 2007)

Nizar,,,
           i don't recon these guys have any idea at all,,,

expectancy is hope 
edge is luck :

 Emerger


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## bingk6 (29 November 2007)

theasxgorilla said:


> Three key things with entry IMO:
> 
> 1. Get your trailing stop up to 0 before price falls to your 1R initial stop.  This way your win/loss ratio is satisfactory and you avoid the worst kind of exit ie. initial stop.
> 
> ...





ASX,

Does 1) mean that you get your trailing SL to breakeven as soon as possible ?? and could you explain 3) a little more ?

Thanks

Bingk6


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## emerger (29 November 2007)

if your risk is 100 bucks 
        when at 150 in profit move your stop loss to breakeven

and then expect (hope) for it to run on and not hit your breakeven stop out

get lots of stop outs this way and stuff up your entire plan ,,and often not re enter when price does run on cause you did your head in on yet another stop out,,,

 i think it's all crud and designed to fail and not only that but the cfd provider's know where your stop is  and will flick you all out ,,,,you can guarentee that you'll get the worst slippage possible,,

 leaking boats eventually sink,,,
death by a thousand cuts

better of learning how to fade into a position on a stock where there are no warrents/options/shorts and steer clear of the big pricks


emerger


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## stevo (29 November 2007)

Expectancy is a measure of performance. 

Edge is performance above  average, or above what random trading might give us. 

If a system gives the market average or a long period of time (> 5 years), or can't beat average random trading then it doesn't have an edge. An edge puts a strategy above the crowd. 

But what a trader benchmarks themselves against is up to them. 

If you are happy with the returns over the long term and can soundly beat bank interest, or other opportunities that the money could be used for is this not enough?

I just had a long lunch sponsored by a Bank, plied with wine and food, so if anything I say above doesn't make sense it wouldn't surprise me!

stevo


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## theasxgorilla (30 November 2007)

stevo said:


> I just had a long lunch sponsored by a Bank, plied with wine and food, so if anything I say above doesn't make sense it wouldn't surprise me!




On the contrary Stevo...it ought to be making more sense than ever


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## theasxgorilla (30 November 2007)

bingk6 said:


> ASX,
> 
> Does 1) mean that you get your trailing SL to breakeven as soon as possible ?? and could you explain 3) a little more ?
> 
> ...





Re: 1), not exactly, not manually or by way of a trigger at least.  

Lets say you trade an x-day breakout entry and use some kind of trailing stop, again for the purposes of this example lets say its a moving average.  You also use a fixed initial stop of 10%.  This initial stop represents a 1R loss, the worst outcome for any trade, catastrophies notwithstanding.  Even if price does not move up, over time the MA trailing stop will close the distance to breakeven and get inside your initial stop preventing a 1R worst case scenario loss.  Shortening the number of periods in an MA will make it converge faster, but if you make it too tight you risk of not giving the trade sufficient room to find it's way.

The other way to speed up this convergence is for price to move higher after entry, thereby dragging the trailing stop toward breakeven (and hopefully beyond!).  How can you encourage this?  Great question isn't it??? Encourage probably isn't the right word, but maybe you can add a trend or momentum filter or some other tweak which helps you capture real breakouts which keep moving and avoid false ones that stall and collapse.

Re: 3) nothing fancy here, this is the ambition with most trading.  Here's a question on this topic though...if a stock has increased 1000% in the last 12 months and your long only LTTF system gives you a buy signal, do you trade it?  Or do you second guess or even reprogram the system?  I know what the right answer is from a trading discipline standpoint.  Altough how many stocks that have increased in price 10-fold over 12 months did something spectacular during their next phase of business?  I don't know the answer, just asking.


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## wealthlab (2 December 2007)

> Quote by Nick Radge 23/11/07..... buying a stock nearer its yearly low is statistically better than buying it near its yearly high from both a risk and reward perspective. Both have a positive expectancy but the yearly low strategy has an edge over the yearly high.




Hi Nick, I was wondering if you would care to offer any “Statistical” evidence to back such a statement, or is the statement more one of a personal opinion ?


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