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# Probabilities

A comment that I just made in this topic Markets in Profile got me thinking about probabilities and I thought that it deserved its own thread.

Success at trading is all about have the probability of winning in your favor. That's a simple statement and it's how the casinos make money day in and day out.

One of the problems we face as traders is the calculation of the probability. How do we know if the series of trades that we are taking really does have a higher probability of success or not?

Well, for one thing we can back test our strategies. But that doesn't always give us the probability factor because of the many complexities of back testing.

Another is to do pure statistical testing of price movement after a signal. This is a type of back testing but without using money management.

In many ways I think that there is a lot of merit in having a very simple money management strategy of all-in and all-out and use probability of movement rather than trying to fool around getting the nuances of scaling in and scaling out down to a fine art.

There are two approaches to this all-in all-out strategy. You can find a signal that will "move" the market (1) more in one direction than the other 50% of the time or (2) the same amount in one direction a higher percentage of the time. You then go all in at entry and all out at target or stop. So long as the probabilities remain in your favor it is then a matter of repeating this as often as possible.

Examples in the E-mini S&P500:

(1) Your signal shows that the market will move at least 3 points in one direction without first moving 2 points in the other direction at least 50% of the time. Your win/loss ratio is 50% but you make on average 0.5 points for every trade you take.

(2) Your signal shows that the market will move 2 points in one direction 60% of the time and 2 points in the other direction 40% of the time. Your win/loss ratio is 60%. For every 10 trades you make 12 points and lose 8 points which is an average of 0.4 points for every trade that you take.

Success at trading is all about have the probability of winning in your favor. That's a simple statement and it's how the casinos make money day in and day out.

One of the problems we face as traders is the calculation of the probability. How do we know if the series of trades that we are taking really does have a higher probability of success or not?

Well, for one thing we can back test our strategies. But that doesn't always give us the probability factor because of the many complexities of back testing.

Another is to do pure statistical testing of price movement after a signal. This is a type of back testing but without using money management.

In many ways I think that there is a lot of merit in having a very simple money management strategy of all-in and all-out and use probability of movement rather than trying to fool around getting the nuances of scaling in and scaling out down to a fine art.

There are two approaches to this all-in all-out strategy. You can find a signal that will "move" the market (1) more in one direction than the other 50% of the time or (2) the same amount in one direction a higher percentage of the time. You then go all in at entry and all out at target or stop. So long as the probabilities remain in your favor it is then a matter of repeating this as often as possible.

Examples in the E-mini S&P500:

(1) Your signal shows that the market will move at least 3 points in one direction without first moving 2 points in the other direction at least 50% of the time. Your win/loss ratio is 50% but you make on average 0.5 points for every trade you take.

(2) Your signal shows that the market will move 2 points in one direction 60% of the time and 2 points in the other direction 40% of the time. Your win/loss ratio is 60%. For every 10 trades you make 12 points and lose 8 points which is an average of 0.4 points for every trade that you take.

Excellent input and thoughts Mike, thanks for your contribution to this important discussion topic.

I do agree with your assessment of the non-linear structure of the market, and any linear model (statistical or otherwise) will fail to provide much direct benefit. Tangentaly, this provides a direct rational for why most basic TA indicators found in retail charting packages fail, since they are all very simplistic linear derivations from the underlying complex non-linear time series.

In my use of the random coin-toss example, I chose this common and simple example to establish a standard or baseline against which one could easily compare their own individual long-term trading results. Part of my motivation in this choice was to indirectly challenge the trader's assumption of their trading ability and skill. It is my opinion, based on working with many traders at all skill and experience levels, almost universally traders overestimate their own trading acumen.

My second goal was to demonstrate the advantage gained by lowering the percentage of full losses taken, in this case using the break-even stop loss technique. My choice of 20 or 25 % hit rate on the b/e stop was arbitrary, but based also on many years of actual trading results. My personal experience has the b/e hit rate closer to 30% but I did not want to overly influence the results.

In terms of modeling and probability-

One thing that would need to be modeled is the streaky nature of results, trading systems tend to work really well or really poorly depending on when you apply them. This touches many of your points about the phases the market goes through. I think incorporating volatility into the model would make sense here. As a given trading system will fall into one of two basic categories: the method will work well in higher volatility trendy phases and under-perform in range bound or low volatility phases, or visa-versa. My personal trading method/system works well in increasing and high volatility and poorly in low volatility. The range (high-low) of the time frame I am operating in will govern my net $ profit. Saying this another way, my net results are always much higher when the daily range of the S&P 500 index is 20 points and much lower when the range is 5 points.

Modeling volatility correctly will once again bring us back to the non-linearity issue, as volatility expansion and contraction as an integral part of the overall system is also dynamic and not linear.

On an intra-day basis one could divide the session into three segments: morning, lunch, and afternoon. Volume and volatility patterns fit this model well most days. A simple model might use this pattern: In the morning volatility is high then declines into lunch, in the afternoon volatility is relatively low and increasing. Using your example, the probability model built around the test or break-away from a well advertised pivot point would have three different volatility factors applied based on when the event occurs during the trading session. Perhaps this model would be constructed of three separate test periods producing three separate probability curves.

Another issue along these same lines is the temporary chaotic effect the release of economic reports has on volume and volatility. Although the event can be anticipated in advance, it has the potential to significantly influence the actual results a trading system experiences and the probability curve the system produces (i.e. long tails, 6 sigma outliers ect...).

Something your observations indirectly touch on is the concept of entropy (measure of randomness), and how that influences the probability curve. In a purely random system, i.e. the coin-toss monte-carlo simulation, it's entropy is well know, in this case the uncertainty of an individual outcome is very high. You stated, in viewing the market, momentum will tend to predicate (influence) the probability curve. I stated this another way, trading system results tend to be streaky, win streaks and loss streaks. Assuming this is true, then the entropy of this system is being influenced and the uncertainty of an outcome is lower than the purely random case. One could use historic market data to determine the 1-sigma range of entropy, then fit this expectation of randomness into the larger simulation model.

I do agree with your assessment of the non-linear structure of the market, and any linear model (statistical or otherwise) will fail to provide much direct benefit. Tangentaly, this provides a direct rational for why most basic TA indicators found in retail charting packages fail, since they are all very simplistic linear derivations from the underlying complex non-linear time series.

In my use of the random coin-toss example, I chose this common and simple example to establish a standard or baseline against which one could easily compare their own individual long-term trading results. Part of my motivation in this choice was to indirectly challenge the trader's assumption of their trading ability and skill. It is my opinion, based on working with many traders at all skill and experience levels, almost universally traders overestimate their own trading acumen.

My second goal was to demonstrate the advantage gained by lowering the percentage of full losses taken, in this case using the break-even stop loss technique. My choice of 20 or 25 % hit rate on the b/e stop was arbitrary, but based also on many years of actual trading results. My personal experience has the b/e hit rate closer to 30% but I did not want to overly influence the results.

In terms of modeling and probability-

One thing that would need to be modeled is the streaky nature of results, trading systems tend to work really well or really poorly depending on when you apply them. This touches many of your points about the phases the market goes through. I think incorporating volatility into the model would make sense here. As a given trading system will fall into one of two basic categories: the method will work well in higher volatility trendy phases and under-perform in range bound or low volatility phases, or visa-versa. My personal trading method/system works well in increasing and high volatility and poorly in low volatility. The range (high-low) of the time frame I am operating in will govern my net $ profit. Saying this another way, my net results are always much higher when the daily range of the S&P 500 index is 20 points and much lower when the range is 5 points.

Modeling volatility correctly will once again bring us back to the non-linearity issue, as volatility expansion and contraction as an integral part of the overall system is also dynamic and not linear.

On an intra-day basis one could divide the session into three segments: morning, lunch, and afternoon. Volume and volatility patterns fit this model well most days. A simple model might use this pattern: In the morning volatility is high then declines into lunch, in the afternoon volatility is relatively low and increasing. Using your example, the probability model built around the test or break-away from a well advertised pivot point would have three different volatility factors applied based on when the event occurs during the trading session. Perhaps this model would be constructed of three separate test periods producing three separate probability curves.

Another issue along these same lines is the temporary chaotic effect the release of economic reports has on volume and volatility. Although the event can be anticipated in advance, it has the potential to significantly influence the actual results a trading system experiences and the probability curve the system produces (i.e. long tails, 6 sigma outliers ect...).

Something your observations indirectly touch on is the concept of entropy (measure of randomness), and how that influences the probability curve. In a purely random system, i.e. the coin-toss monte-carlo simulation, it's entropy is well know, in this case the uncertainty of an individual outcome is very high. You stated, in viewing the market, momentum will tend to predicate (influence) the probability curve. I stated this another way, trading system results tend to be streaky, win streaks and loss streaks. Assuming this is true, then the entropy of this system is being influenced and the uncertainty of an outcome is lower than the purely random case. One could use historic market data to determine the 1-sigma range of entropy, then fit this expectation of randomness into the larger simulation model.

Thanks for the comments Mike and pt_emini. The main reason behind creating this monte carlo simulation is to demonstrate (1) how an edge will not always work out (except in the very long term) and (2) how critical slippage and commissions are when evaluating what edge you need for trading successfully.

In respect to point 1, if you have a marginal system then you must expect longer and more frequent losing streaks and this is easily demonstrated with the simulator.

I agree with all your comments and each trade has a unique probability of success. What I am looking at here is a simple money management strategy of all-in and all-out which makes this demonstration easy to create combined with an average probability taken over the entire population of trades that you execute.

Even though you do not know the average probability before you trade you can look back over your last 1,000 trades (say) and calculate this and assuming that your style and method of selecting trades does not trade then the average probability should be fairly representative and close to what you should expect for the future.

In respect to point 1, if you have a marginal system then you must expect longer and more frequent losing streaks and this is easily demonstrated with the simulator.

I agree with all your comments and each trade has a unique probability of success. What I am looking at here is a simple money management strategy of all-in and all-out which makes this demonstration easy to create combined with an average probability taken over the entire population of trades that you execute.

Even though you do not know the average probability before you trade you can look back over your last 1,000 trades (say) and calculate this and assuming that your style and method of selecting trades does not trade then the average probability should be fairly representative and close to what you should expect for the future.

So would you use your actual trading results to establish the expected future probability of success ?

This assumes your using the same system going forward, and just modifying the money management strategy.

This assumes your using the same system going forward, and just modifying the money management strategy.

Yes you would and it does make that assumption. The problem with that assumption as you probably already know is that trading is a continual learning process and your skills improve each day so the probabilities for your older results are less representative than the most recent results. You almost have to use an weighted moving average of your results to do this calculation to give the more recent results a higher weighting.

quote:Originally posted by day trading

quote:Originally posted by pt_emini

True, a 60% win probability using a 1:1 risk:reward ratio will lose money over the long term (when commissions and slippage are accounted for).

So while we are considering this point, what is the win probability required to break even with a 1:1 risk:reward ratio using a R/T commission of say $5, 1 tick of slippage on exit, and 1 tick of slippage on stop loss ?

It's actually not as high as one would think. If you assume that you make 8 ticks on the winners and lose 10 ticks on the losers then you need to win 56% of the time to come out ahead. In my opinion, the extra 2 ticks on the losers covers slippage and commissions in the ES. So you have a R:R of 1:1 but in reality you lose an extra 2 ticks when you lose.

If your targets are larger then obviously your commission and slippage per amount gained/lost will drop and so a quick calculation shows me that targets of 20 ticks (5 points) with stops at 5 points (but stops+slippage+commission at 5.5 points) you will need a win ratio of 53% to come out just ahead of break-even.

Those win % requirements are a lot lower than I think a lot of people expect. It is more in line with casino odds requirements which we know work.

On the roulette wheel there are 38 slots. Numbers 1 through 36 and 0 and 00. If you play red/black or odds/evens your chances of winning are 18 in 38 or 47.4% and your chance of losing is 52.6% to put it in perspective.

You also failed to mention that the casino doesn't pay out winners at true odds. In the roulette example, the casino's edge is 1/19 or 5.26% on all bets for double zero wheels.

quote:Originally posted by ahk

You also failed to mention that the casino doesn't pay out winners at true odds. In the roulette example, the casino's edge is 1/19 or 5.26% on all bets for double zero wheels.

I don't understand what you're trying to say here? Is it something specific about double zero wheels that I have missed or misunderstood?

Im making a point that the odds are worse than you reported with a roulette wheel because the casino takes their edge. And yes, a single zero wheel has a house edge of 2.63 against the player on every outcome.

The odds of hitting any number are not as important as the payout on those odds.

The odds of hitting any number are not as important as the payout on those odds.

The odds of hitting red/black or odd/even are 47.4% and the payout is 1:1. The odds of hitting any single number on a double zero table are 1 in 38 and the payout is 36:1. Is that what you are talking about?

The odds of hitting any number on a double zero wheel are 1/38 and the payout is 35 to 1. The odds of hitting any number on a single zero wheel are 1/37 and the payout is 35 to 1. Hence, the house edge is smaller on the double zero wheel (but still huge to my way of thinking).

quote:Originally posted by ahk

The odds of hitting any number on a double zero wheel are 1/38 and the payout is 35 to 1. The odds of hitting any number on a single zero wheel are 1/37 and the payout is 35 to 1. Hence, the house edge is smaller on thedoublezero wheel (but still huge to my way of thinking).

OOPS. Should be single, not double.

One would be better off taking that all or none shot with the don't pass line in craps or banker in baccarat where the house is not as strong.

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