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I can understand the reason for your raw response.

have you done any testing?? why do you state it has an expectancy of 0?
I am getting 6.3 consistantly. now this isnt a smooth curve but i think with the MM being used, there is something here.

an idea I have tested in this 98 trade sample size is mapping the 20 period moving average of the expectancy and basically waiting for a dip to start the "real" trading as this will create a higher probability for a reversion back to the mean average of 6.3. for example I theoretically "paper" traded until the expectancy was below -25 and started "real" trading again until the expectancy went "oversold".

so as I know that a $6.3 expectancy is not worth trading if the standard deviation is too wild trade to trade. but there could be something else to pull from it

every trade has a 50/50 chance of being a winner or loser. if that is the case, then this strategy of expectancy mean reversion should create the edge that will push it into consistant profitability in the long run.

my goal is to get a 1000 sample size and really get a good idea of how the expectancy deviates

if anything it is a good exercise for risk management and mechanical trading for your mental game

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I am sorry, I can see a lot of confusion. Let us have a look at the strategy again. You enter a position at random, then you set a profit target of 5 ticks another profit target at 10 ticks and a stop loss at 5 ticks. I assume that half the position is exited at a profit of 5 ticks and the other half at 10 ticks.

The interesting thing here is that the strategy is asymmetric, the stop is closer to the entry price than the average profit target. In case that there is a positive autocorrelation between consecutive price moves, this might have a positive impact, in case that the auto-correlation is negative, the impact would be negative.

First Step: Neglecting Order Types, Slippage, Commissions and Auto-Correlation

For the first half of the position, with both a stop and a profit target of 5 ticks, there is a 50% win rate and the ratio of the average winning to the average losing trade is 1.

If we assume that the first 5 tick movement does not favor a subsequent five tick move, a simple tree diagramm allows us to calculate the winning probability for the second half of the position

Even without using the formula for a geometrical series, you can see that the winning percentage of this game is 33.3%, which means that there is one winning for two losing trades. The ratio for the average winning to the average losing trade is 2 (the winning trade gains 10 ticks, whereas the losing trade loses 5 ticks).

This confirms that the expectancy for both the first and the second half of the position is Zero.

This calculation ignores autocorrelation, which would allow us to benefit from a progressive betting strategy and it ignores order types. It also neglects slippage and commission.

What about order types?

The most interesting aspect of the little experiment is not the expectancy but the cost of entering and exiting a position. Let us make a standard assumption

-> we enter the position with a market order
-> the profit target is a limit order
-> the stop loss is a stop market order

Now assume that we enter a long position. If this is done via a market order, the best ask is crossed with
with our order, and we pay the ask, which is we denote p. The strategy will now set targets at p+5 and p+10 and a stop loss at p-5. Let us now have a look at the first half of our position.

The current best bid is at p-1. The stop price is attained when bid and ask move down 4 ticks and price trades at the bid for the first time. The limit order for taking profits is attained, when the bid and ask move up 5 ticks and the price trades at the ask until it has worked through the order book and our profit order gets time priority.

This is no way a symmetrical constellation. For profit taking the bid/ask needs to move up 5 ticks and trade at the ask for some time until our order is filled. The loss is triggered when the bid/ask has moved down 4 ticks and a first trade has occurred at the bid. I cannot calculate the win rate here, because it depends on the order book, which is not known, but one thing is sure

-> for scalpers the expectancy shows a strong dependence on the order types
-> the win rate of this game is far below 50% and the expectancy becomes negative

This is a strategy that seeks liquidity and it therefore has a negative expectancy.

Slippage and Commissions

The strategy is already negative before slippage and commissions. No point to continue calculations, slippage and commissions will make things worse.

And what about Auto-Correlation ?

The strategy enters the market 30 times, with a pause of 30 seconds between an exit and the consecutive entry. Assuming that there is a strongly trending market ( = positive autocorrelation) during the test period, the strategy may be profitable. If the market is not trending the opposite would hold true.

In general there is no reason to assume that financial time series show any positive auto-correlation within any timeframe over a longer period. As a rule of thumb, autocorrelation is insignificant, except for high frequency trading approaches, where it becomes negative.

This is a fascinating subject, but I do not want to discuss it within this thread, as it would take as away too far from the original question. For those who are interested, there is a lot of literature available in the internet.

Conclusion

The zero expectancy quickly becomes negative, as the strategy uses liquidity seeking orders to enter and exit (stop). Adding slippage and commisions make things worse. Supposing a slightly negative auto-correlation within this setup, there will be three different reason why the expectancy will be negative under real market conditions.

Who is going to show the opposite?

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@Fat Tails:
I neither use nor endorse this strategy.
I also would never use such a strategy to trade real $$.

If you watched the FuturesTrader71 webinar you will see that FT71 suggested using a coin toss trading strategy to show the difference in trading with and without firm stops and targets on a simple entry/exit.

I asked in that thread if anyone had created such a strategy and was told it had not been done so I created it to see the results. There were many posts in the thread about the positive and negative aspects of a coin toss.

The simplest way to solve the issues raised that that thread was to create the strategy to see the pit falls.
(Big Mike suggested I start a separate thread with the indicator attached.)

The CoinToss strategy is flexible in that the stop, targets, sample size and time between trades can be adjusted.

The ability to change the settings does not make the strategy any more or less profitable but simply gives it flexibility.
As I said in an earlier post, this should only be used in Simulation Mode.

Because there is no 'Edge' I doubt that any positive or negative results can be considered reliable or reproducible.

Thanks for your input on the subject.

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Knowing it's not about Clouds or Wind. . .
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@DavidHP: I agree, the strategy has no edge, the only theoretically possible edge would have been that the profit target is further away than the stop, if there was auto-correlation. But this effect is really too small to be considered.

The idea to study exits with random entries is not new. There is a whole section in this book

which was published in 2,000. See Part III, The Study of Exits (approx. 70 pages) .

I like the coin toss model, because it allows to discuss some specifics that would be otherwise lost, that is why I responded. Thanks again for bringing up the subject.

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@DavidHP, thanks for sharing this and furthering this discussion. I think any discussion along these lines is a hundred times better than all the magical indicator charts being posted

Mike

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Umm, interesting stuff. There may be a layer of 'reality' that may also have an impact. The frequency and distribution of runs of winning and losing trades. Random in and of themselves but likely to be experienced in a large enough sample?

If you could get pretty close to 50:50 results after slippage, commissions etc, then in principle could such runs be a source of profit? Say cutting risk to 90% of the previous trade size after a losing trade and increasing to 120% after a winner. No doubt the volatility of the equity towards of the sample would be gut-wrenching - but we're just talking here so we no doubt we've all the emotional capital to handle it!

I've very quickly run such a test in Excel using the RAND function and it comes in with a hearty profit on 5 batches of 200 trades. No time to do a more thorough test with varying win %, or risk allocation. And I'm dubious of the results, looks too much like a free lunch and I haven't tried to break it yet. Perhaps just got lucky on the parameters, or the RNG in Excel isn't that random afterall?

But the logic seems sound? File attached if you're interested.

Last edited by mokodo; May 16th, 2012 at 09:18 AM.

This is the old question of progressive betting systems. Progressive betting implies that the outcome of the current bet somehow depends on the outcome of the previous bets.

If you have a card game, such as Black Jack, this is indeed the case. The cards which are available on the stack depend on those that have already been played. In his famous book "Beat the Dealer", Edward Thorpe has described how the edge of the casino may disappear depending on the cards already played.

However, if you draw random numbers, no progressive betting strategy is possible, as each new bet does not depend on any prior bet. Some people think that if you toss a coin, the odds are increased to obtain heads, after you have had 10 tails in a row. This is not the case but a fallacy, which is known as the Gambler's Fallacy. For a larger number of toin cosses. you may expect that the percentage of heads converges to 50%. Some people think that if you have ad 10 tails in a row, convergence now implies a larger number of heads. Again this is not the case. The convergence is achieved exclusivley by diluting the impact of the prior bets, not by actively offsetting them.

If you want to study runs of bets or trades, this makes only sense, if you have a hint that the correlation of two consecutive bets is non-zero. There has been a lot of scientific work on the correlation of returns for consecutive periods. The correlation has been shown to be close to zero. Only if you delve into the realm of high frequency trading, there is a slightly negative correlation, which cannot be exploited by retail traders.

Monte Carlo simulations are based on the assumption that all bets are non-correlated, thus allowing to change the order in which the trades have occured, to obtain a better estimation for the drawdown.

I do get that there is no connection in outcomes between a trade and the subsequent trade. And precisely because there isn't we can get runs of winners and losers within a sample that comes in flat.

I guess my point (and I admit perhaps a naive point) is that if you will get runs of losers and runs of winners, why not tweak the odds in your favour by assuming you are on a winnng or losing run based on the last trade. If you lost last time, bet smaller, if you won last time bet bigger. If the difference in bet size is asymmetric, i.e you bet proportionally more for winners than the reduction for losers you may amplify any benefit.

I'm not making any reference to Monte Carlo engines with this, it's not about the drawdown but about whether runs of wins can be exploited for profit and the negative impact of runs of losers restricted.

If you have time please take a quick look at the spreadsheet. I'd like to get deeper into this.

Good exercise as I see it. Of course, my eyesight is a bit blurry. However, thought I'd mention that I evaluated a trading analysis system that allowed a study of exactly what you're talking about. For the life of me I can't remember the name of the system. Maybe someone else can provide that answer...Anyway, at the time, I had a system that back tested well but had a draw down that was unacceptable. So, I did a study of the exact thing you mention using this software and found that it did nothing to solve the draw down issue and in fact the draw down was worse and so were all the other statistics. I know this in only one example but I also created other systems just for the purpose of studying strings of wins/losses and none were improved by this type of management. I would like to think that some systems would lend themselves to this type of management but certainly none that I have.

In my judgement, you are a victim to the Gambler's Fallacy.

A priori, that is prior to betting, there is no such thing as a winning or losing run. You will only notoce them with hindsight. If you lost last time, this has no impact on the outcome of the current bet. So why should you bet smaller? If you won last time, this has no impact on the outcome of the current bet. So why should you bet bigger?

You can not tweak the odds, if you play dice. You cannot tweak the odds for any series of bets, which are stochastically independent, or - just using different words - you cannot tweak the odds for any series of non-correlated bets.

I repeat it again: Studying a series of runs of a series of non-correlated bets is a futile exercise.

I had a look at the spreadsheet. If you can produce consistent profits with your random generator simulation, you have in fact shown that your random generator produces bets with a positive auto-correlation and is a bad random generator.

In fact none of the commercially available random generators produces real random numbers. All of them use algorithms, which produce more or less correlated results. The generator that you have used is not suited for testing your ideas.

Last edited by Fat Tails; May 16th, 2012 at 02:50 PM.

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