## Win/ loss ratio and system expectancy

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rs

### Win/ loss ratio and system expectancy

Hi all,

Has anyone found that there is an inverse relationship between win/loss ratio and expectancy? I remember reading in William Eckhardt's interview in 'The new market wizards' that he says that win/loss ratio is the least important performance statistic and may even be inversely related to performance.

If this is the case, then does this mean that systems should be designed to only stick with the most perfect trends and discard the rest very quickly if they fail to perform almost immediately?

I appreciate any and all views.

Thanks

rs

Kiwi
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Just Some Thoughts.

From systems that I have looked at there does seem to be a reduction in expectancy (and profit factor) with higher win percentages. This is probably because the higher expectancy systems have been pattern based and take a profit at a target so there is a trade off to get the higher win ratio.

I've recently been using one system which has a 97.9% win percentage and an average winning trade 1/7th of the average losing trade. After years as a trend follower and discretionary trader looking for a winning trade that is three times the losing trade this took a bit of getting my head around.

Expectancy seems to be:
E = 0.97917*1/7 - 0.02833*1
= 0.119
but it trades 860 times per year so the annualised expectancy is
1.02 or just over 100% gain.

Perhaps this illustrates that these systems, if they are short term in nature can have a low expectancy but a high annual return. Because the expectancy is so close to 0 though I suspect that the other side of the equation is a high risk that failure will come from a slight degradation of the system. In a higher expectancy long term system I'd expect failure to come from a statistically bad run rather than slight degradation.

I'll post some monte carlo stats when I've got them.

John

Kiwi
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### Monte Carlo sim of high win percentage system

Amazing what trying to fit it into a monte carlo sim teaches you.

I use Alex Matulich's Excel model , Prosizer, available for next to nothing at http://www.unicorn.us.com/trading/. Alex even modified it for me once to try something unusual at no cost!

What I didnt say above was that a losing trade is "always" part of a sequence of around 18 trades. To build it into the monte carlo sim I had to use (for 50,000 capital) one -6300 trade and a series of differently sized winning trade series winning between \$900 and \$50.

Risking 12.6% of equity per trade gave the following results:
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### expectancy vs robustness

John,

I have got some thoughts too
Because you are calculating with expectancy, maybe you can clarify something for me. IMHO tells expectancy itself nothing about de robustness of a system......in your case of high probability of winning ( 97%!!! ) would there be any "room" for testing the robustness ( maximum slippage etc..) In other words, is there a relationship between expectancy and robustness? What are the changes in expactancy when changing the parameters of the system? Maybe it is interesting if you can examine the robustness of a system with this kind of expectancy and distribution of R-multiple's. I hope you understand my thoughts.....

I don't have the knowledge to examine these questions for myself at this moment. Maybe you?

Thanks,

Marc

Kiwi
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Marc,

I think that you are on the wrong track in being too concerned about trying to build a theoretical model of this. Robustness comes down to:
- what is the impact of slippage
- what will happen with a shock event
- what will cause the system to fall out of synch with the markets
- etc

and to me these things must be evaluated system by system. Its not just a function of expectancy or sharp ratio or any other parameter but of the way the system earns its money.

You really need to address these in terms of a system you are considering.

John

edward kim
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Hi John,

Doesn't robustness refer to a system's performance being indpendent of the variability of it's parameters? For example, if one of your parameters works with the value of "30" but doesn't work well for "29" and "31", then your system is not robust. On the other hand, if your system works well with any value from 20 to 30, 40, 50, and 60, then you can consider your system/parameter to be robust?

Edward

Kiwi
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Yes,

Thanks . Thats probably a more common interpretation than the effects I listed. Can we take it as being included under etc?

The funny thing is that I think that system failure may be less dependent on parameter robustness than on the second and third factors I listed. Perhaps the third often exposes poor choice of parameters and a lack of adaptiveness. Thats also funny because they may well be the factors that a monte carlo simulation can't take into account.

So to quote or missquote c.f. "what are we to do?"

John

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I tend to have a much broader definition of robustness.

I consider system robustness to be about how well a system is likely to hold up and deliver results that are similar to historical testing.

I've found that the most important aspect of building a robust system is testing using enough historical data and using the same set of parameters across a portfolio. Like many aspects of trading system development, there is a continuum where the risk is greater on one end but the potential rewards are higher to compensate, the other end has less risk and lower rewards. We each need to find something that we are happy with and willing to trade ourselves.

A parameter that doesn't affect the system results as it is changed may be robust but this doesn't mean that the system is.

In general, I also like to have some rationale for why I believe a system works. I want the source of the profit to be based on something that doesn't change. Systems that rely on human psychology and emotions tend to hold up very well because humans don't change very much, even when they really want to.

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### high expectancy is robust?

John,

As you probably know, in the book TYWTFF of Van Tharp, expectancy is a hot topic. One of the conclusions in his summary of this topic, Tharp says that a system ( at least 100 trades ) with an expectancy of >0.5 is a GOOD system. IMHO it could be a good system if I am convinced about the robustness of it. This is what I assume. A scientific approach is to research my assumption. That is what I would do. Questions like: Is a high expectancy system robust? Is there any correlation between these? It will be difficult to measure because robustness can not be calculated in a simple way like expectancy.

But I totally agree with you ( and Edward and c.f. ) about the procedures to test (or convince yourself about) the robustness of a system.

Forum Mgmnt,

You made a nice point about robustness i.e. the psychological part of all participants of the markets. Can you tell me/us more about your view of this topic. I think it is very interesting!

Marc

Chuck B
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Re Expectancy: I can think of many systems/data combinations that look great over 100 trades and which fall apart over 1000 trades. Sample size when dealing with market data, aka pathological price distributions, is one of the biggest challenges facing system design. Similarly it's probably one of the main reasons many "good" discretionary traders disappear...once enough trades get under their belt, the poor expectation of their overall method including costs and slippage plays out....sigh...

MCT
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Hi kiwi,

Was your Monte Carlo analysis based on a single issue?

If so, have you had a chance to rerun a Monte carlo simulation utilizing position sizing at the portfolio level [to account for serial correlation] with a list of trades that were optimized for expectancy using the ProSizer software?

MT
Last edited by MCT on Wed Sep 17, 2003 7:53 pm, edited 1 time in total.

rs
Forum Mgmnt,

Regarding the original question I posed at the start of the thread. You said in the Turtle Rules that the whipsaw method of entry was more profitable than the standard method yet it generated more losses which were correspondingly smaller.

This in effect backs up the premise that win/loss ratio and expectancy are inversely related. Would you say that was a fair assumption to make?

rs

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I'm not sure I'd make the claim that they are inversely related, however, I think it is easier to find a high expectation system that has a low win/loss ratio than one with a high/win loss ratio.

There certainly are some high win/loss ratio systems that have good expectation, they just tend to be more obscure. They also tend to be based on principles that have a shorter lifespan. An extreme example of this is an arbitrage opportunity.

Kiwi
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Zeno, The analysis was based on running the system on a single instrument. Sorry but I am not planning more complex MC analysis because the issue of robustness for this system hasn't anything to do with the sequence of trades as revealed in a MC simulation; its about what you do when certain market conditions occur. I really only put it up to illustrate a point that I hope to make in the next posting.

Chuck, You make an excellent point.

I agree and hence am timid, paranoid and perfectionist about testing things in as many different conditions as I can download or simulate - but brave and decisive in trading when I wear my ActionMan hat . I tested this system over 13 years daily data and multiple market conditions (around 6,500 trades) as it works on both daily and intraday data. The main thing that it hasn't been tested on is a low volatility multiyear late bear however my projections say that this will simply reduce profitability (theoretically to zero but not negative).

Personally I think that the best protection from a pathological condition is diversification - multiple systems as well as multiple markets - along with strategic withdrawal if failure is detected.

John

Kiwi
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RS,

You put up two questions. The first was whether "win/loss ratio and expectancy are inversely related". The second was "does this mean that systems should be designed to only stick with the most perfect trends and discard the rest very quickly if they fail to perform almost immediately?"

I think that the answer to the first is No. It appears that way but this is similar to the old problem of confusing "cause" with "correlation". The reason that it appears to be yes is that it is generally easier to find low win loss systems with high expectancy (most of them are the obvious long term trend followers) than high win loss systems with high expectancy.

{added 0823: Another reason is that people frequently increase win/loss ration to make a system more comfortable to trade and to achieve that often reduce the expectancy. An example is that when I trade breakouts on 3minute bars I take 50% of my position off when I have a 4pt profit and move the stop up to 1 off breakeven - this reduces the long term profit but gives me over 70% profitable trades and makes it easy to take the next trade that comes along. What I have done is reduced the theoretical expectancy - but at the same time I may have increased the real world expectancy because I do not become shell shocked (and perhaps unable to pull the trigger) because of a series of losing trades.

What Eckhardt said was "win/loss ratio is the least important performance statistic and may even be inversely related to performance."

The answer to the second depends two factors. The first is on whether or not the expectancy is the key factor in determining the value of a trading system. In the NMW article, Eckhardt said:
"The desire to maximize the number of winning trades (or minimize the number of losing trades) works against the trader."

He didn't say that you need high expectancy for a good system.

Van Tharp in TYWTFF, who most people take as a proponent of long term high expectancy systems also reviewed a low expectancy* high frequency system and made the point that you need to multiply expectancy times the number of trades per annum to give return (and thus your standard of living).

A system with a low expectancy but a large number of trades can provide both a good return and smoother equity curves than a high expectancy low frequency system (like a weekly traded trend follower).

The second is whether you need to "stick with the most perfect trends and discard the rest very quickly." I'd suggest the answer to this is no. In my experience you will increase your expectancy if you give a trend some time/range to prove itself. If you discard it too quickly you may find that the frequent small whipsaws reduce the expectancy and the win loss ratio.

So I would suggest that the answer to the second question is also No, but despite that I would not discourage the choice of high expectancy systems for your trading (just stops that are too tight ).

John

*My apologies if the assertion that it was a low expectancy system is incorrect as I lent my copy of his book to someone several years ago. I also apologise for this confusing posting.
Last edited by Kiwi on Fri Aug 22, 2003 6:47 pm, edited 1 time in total.

Toni
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### Re: Win/ loss ratio and system expectancy

%Win*AverageWin=%Loss*AverageLoss

Just a picture

MCT
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Toni,

Im sure William Eckhardt and other long-term trader would agree with you. But it is not necessarily so. There are a few discretionairy traders where the above doesn't apply.