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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.
Great idea for a discussion topic !

One of my essential trading credo's is: Make sure the math works in your favor.

This guides the trader to consider not only the entry, but to identify the risk (stop loss) and reward (profit target) before entering the trade. That's what I do every day and in every trade I take, before I act on the potential trade setup. Without exception. I have very specific guidelines I follow in defining risk and reward, if the risk:reward of the specific trade falls outside my guidelines, I will never take the trade. Why ? because the math is not in my favor enough to risk my working capital.

I agree 100% on the all-in / all-out strategy. Mathematically it is a superior strategy than scaling out. In real life however is very difficult to set your ego aside (self control), in this case the need to be right, which motivates a trader to scale-out. The scale-out trade is self-gratification in place of patience. In trading, patience and waiting for your reward is the where the hard work is found. There is an even more powerful strategy, adding to your winners as they develop. Now that level of trading is really hard work. The market will reward your self-control, patience and hard work.
Thanks for the comments pt_emini.

One of the problems that I have found with scaling (both into and out of positions) is the measurement of probability. Unless you have already analyzed it in the neccessarily complex mathematical manner that it requires it is unlikely that you know what your probability advantage/disadvantage in this case is.

You're right about the mental angle to scaling. If you've hit a series of losers then your mental condition will be one of requiring satisfaction and so you will want to see or guarantee some sort of profit and scaling out early provides you with the emotional quick-fix.
In a contract such as the E-mini S&P500 there is another angle to the measurement of probability which is the bid/ask disadvantage.

If the number of contracts bid and asked at each level above and below your entry price are evenly distributed then the market has to work through many more contracts in your direction than against your direction in order for you limit to be filled rather than your stop to be hit. What I am saying here is that if you enter a long position at 1400 even then the market has to lift (say) 5,000 contracts on the ask side to get to your target and only has to hit (say) 4,000 contracts on the bid side to get to your stop level. This assumes that your stop and target are the same size.

So with the all-in all-out strategy you need to measure the probability of going 1 tick more in your direction or one tick less in the direction of your stop.

Your probability equation will measure (from the signal) the chance of moving 9 ticks in your direction versus 8 ticks against your position and it is that probability that needs to be in the +60% area and not the 8 versus 8 ticks.
quote:
Originally posted by day trading

...After a series of losses, drop your trade size down to a pre-determined base level...

The problem with this is that it will destroy your edge, mathematically.

Say we were talking about the strategy where you are all in for 2 point target or stop and your edge gives you 60% winners. If you drop to 1 contact after 2 losses of 10 contracts each then you have only gained back 1/20th if the next trade is a winner and not 10/20ths as the strategy would have expected.

Cutting down the size might help you put the trade on or continue executing the strategy but you are not going to end up a winner at the end of the year doing that.
quote:
Originally posted by day trading



....

So with the all-in all-out strategy you need to measure the probability of going 1 tick more in your direction or one tick less in the direction of your stop.

Your probability equation will measure (from the signal) the chance of moving 9 ticks in your direction versus 8 ticks against your position and it is that probability that needs to be in the +60% area and not the 8 versus 8 ticks.




Correct, in live trading, market depth must be accounted for when using limit orders. In my strategy, I use limit orders to exit at the profit target. To ensure fills I give the exit up to 4 ticks of room off the theoretical ideal exit price level. For example, if my analysis identifies the ideal price target for a Long trade in the ES is 1406.50, then I will put my sell limits to exit in the range of 1405.50 to 1406.00. My profit:loss ratio will be retained to reflect the actual price levels identified (rather than theoretical or ideal). I consider this a form of slippage, a cost of trading.

Another valid approach is to use a market if touched order at the theoretical ideal exit price level. Obviously at least 1 tick or more of slippage will still be paid on each exit.

It is difficult to totally avoid slippage of one form or another when you need to ensure your orders are actually executed in real time.
quote:
Originally posted by day trading

...After a series of losses, drop your trade size down to a pre-determined base level...

The problem with this is that it will destroy your edge, mathematically.

Say we were talking about the strategy where you are all in for 2 point target or stop and your edge gives you 60% winners. If you drop to 1 contact after 2 losses of 10 contracts each then you have only gained back 1/20th if the next trade is a winner and not 10/20ths as the strategy would have expected.

Cutting down the size might help you put the trade on or continue executing the strategy but you are not going to end up a winner at the end of the year doing that.
quote:
Originally posted by pt_emini

...To ensure fills I give the exit up to 4 ticks of room off the theoretical ideal exit price level...My profit:loss ratio will be retained to reflect the actual price levels identified (rather than theoretical or ideal). I consider this a form of slippage, a cost of trading.

When you say profit:loss ratio is that the same as the win/loss percent for this discussion? I would assume that profit:loss ratio is $value and win/loss is number of trades.

In my example the 2 are the same because I am all-in/all-out for the same number of points in either direction.

So I'm just trying to understand: Your measurement of "edge" (probability) is based on what the market actually does and not what the theoretical, ideal or actual result is?
pt_emini: Not sure what happened in the forums here. It appears that my reply with quote blatted out your original entry (with my reply) and I can't find your original entry to replace it. Sorry about that.
Not sure if you can remember exactly what you wrote and replace that post?
quote:
Originally posted by day trading

quote:
Originally posted by pt_emini

...To ensure fills I give the exit up to 4 ticks of room off the theoretical ideal exit price level...My profit:loss ratio will be retained to reflect the actual price levels identified (rather than theoretical or ideal). I consider this a form of slippage, a cost of trading.

When you say profit:loss ratio is that the same as the win/loss percent for this discussion? I would assume that profit:loss ratio is $value and win/loss is number of trades.

In my example the 2 are the same because I am all-in/all-out for the same number of points in either direction.

So I'm just trying to understand: Your measurement of "edge" (probability) is based on what the market actually does and not what the theoretical, ideal or actual result is?



Good idea, lets clarify our terminology....

profit:loss (P:L) ratio = profit potential : stop loss potential

this ratio is often called the reward:risk ratio (R:R), we can use R:R if it clarifies the discussion.

for example a 2:1 P:L ratio = 2 point profit potential : 1 point stop loss potential

win percentage = total number of wins divided by total number of trades

example: 5 wins out of 12 trades taken = 5/12 = 42 % win percentage

win/loss ratio = $ won / $ lost

example: the system produced a total of $ 5,000 in positive trade outcomes and a total of $3,500 of negative outcomes, thus the win/loss ratio = $5,000 / $3,500 = 1.43



Additional comments/clarification:
For me, the P:L ratio is something I use each day in evaluating each new trade setup for suitability. I have a specific minimum P:L ratio that I will consider risking money on. It is a practical guideline. I know from experience, as long as I stay within my P:L ratio, I will be profitable at the end of the week, month, year. Implied in this expectation of profitability is my long term win percentage.

To answer your last question, I allow market volatility and structure to define my profit and stop loss targets, then I apply my trading plan's P:L guideline to that structure to determine suitability to act on the opportunity.

For me, the win/loss ratio and win percentage are after the fact statistics, something I might look at the end of the month or end of the year. It is not something I think about in the daily flow of trading decisions.

One thing I do focus a lot of attention on in real-time is win streaks and loss streaks. That is, a series of consecutive wins or consecutive losses. This is where my position sizing guidelines are applied. In general, during a win streak I increase position size, and conversely during a loss streak I lighten up the size (risk exposure) very quickly. This is not a gradual process, its more like a binary wave form pattern.
quote:
Originally posted by day trading

quote:
Originally posted by day trading

...After a series of losses, drop your trade size down to a pre-determined base level...

The problem with this is that it will destroy your edge, mathematically.

Say we were talking about the strategy where you are all in for 2 point target or stop and your edge gives you 60% winners. If you drop to 1 contact after 2 losses of 10 contracts each then you have only gained back 1/20th if the next trade is a winner and not 10/20ths as the strategy would have expected.

Cutting down the size might help you put the trade on or continue executing the strategy but you are not going to end up a winner at the end of the year doing that.



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 ?

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.