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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.
quote:

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.

This is more of an observation than a correction but I have seeing so many times (say) 3000 contracts at the bit/ask and when they are sold or bought you see more come in 100/200/5/20 and so on before it goes to the next price level and I learn to change my buy or sell position by one tick and get out because is more likely to revers and not hit my number. I never seeing this on equities if the shares are gone it moves to the next price. any one else observe this?

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.

I agree, you see that all the time in the ES. They clean out the bid of the 3,000 contracts sitting there and then before you say Jack Robinson there are another 500 contracts sitting on the bid waiting to be hit.
This is the sort of stuff that happens in live trading that causes slippage costs to influence your actual trading results.

In the ES it's the overabundance of liquidity that forces you to accept 1 or 2 ticks less than your ideal target to get a fill.

In the ER2 and YM it's the lack of liquidity that forces you out 2 or more ticks beyond your ideal target to find enough contracts to offset your order.

Liquidity in the NQ is actually just about right, similar to how the ES was trading in it's golden age a couple years ago.

Perhaps its the goldilocks scenario with these mini contracts, the porridge is too hot, too cold, just right.....

Point here is, in simulation it's just too easy to disregard slippage as a nuisance that messes up the results you expect to see. In live trading, slippage is a constant factor, and is very hard to escape. It is smart to build reasonable slippage expectations into your simulation scenarios from the start.
OK time for a new sim run....

Went back to square one with version 3 of the MC simulator.

Let's look again at that break-even threshold question. This will give us a baseline threshold of the minimum performance required by our trading system to break-even.

In this run, I ran 3 situations at the simulator for each risk:reward level.

Row 1 is the break-even level using no trailing stop to breakeven, thus each trade either gets the full win or takes the full loss.
Row 2 introduces the trailing stop at a frequency of 20%, that is the trailing stop is hit at b/e 1 out of every 5 trades. This has the effect of reducing the percentage of losing trades.
Row 3 increase the frequency of the b/e stop to 30%, or about 1 out of 3.
The idea here is to see how the trailing b/e stop influences the net results.

Constants:
commission fee = \$ 5 / RT
Slippage = 1
Frequency = 1
\$/Tick = \$12.50
commissions = \$ 5,000

```
R:R  win loss win%  b/e%  Loss%  win/loss   Gross     Net   slippage
1:1   8    8  55%    0%    45%     1.24    \$10,800    \$225   \$5,575
20%    25%     1.23     10,400  (-200)    5,600
30%    15%     1.24     10,800     225    5,575

2:1  16    8  38%    0%    45%     1.22     13,400     313    7,788
20%    43%     1.22     13,700     938    7,763
30%    32%     1.22     13,400     625    7,775

3:1  24    8  29%    0%    71%     1.20     14,000      63    8,938
20%    51%     1.25     17,000   3,775    8,825
30%    51%     1.23     16,000   2,175    9,875

4:1  36    8  23%    0%    77%     1.20     15,500     888    9,613
20%    57%     1.22     17,000   2,425    9,575
30%    47%     1.22     17,000   2,425    9,575
```

1. the win/loss ratio remains very stable, nearly constant
2. slippage cost jumps to a new higher level at each R:R level.
3. the trailing b/e stop has little to no effect on results at the lower R:R levels, 2:1 or less. A modest benefit begins to appear above the 2:1 level.
4. the break-even probability actually was a touch below the theoretical, likely due to using only 1 tick of slippage rather than the 2 that was used to produce the original break-even table.
OK with the break-even threshold question answered, lets look at a simulation from the pages of the random-walk theorists, I call this the coin toss scenario: out of 1000 coin tosses, the results should be evenly distributed, 500 should come up heads and 500 tails. So, we will set the win% equal to 50% for this simulation, that is, out of 1000 trades 500 will be winners and 500 will not.

In the table there are two rows for each R:R level, the first row uses no trailing stop to b/e, either the trade wins or it loses. The second row uses a trailing stop to b/e at the 20% frequency, that is 1 out of 5 trades, which will force the loss % to 30%. This will show us the general effect of the trailing b/e stop on the net result.

Constants:
commission fee = \$ 5 / RT
Slippage = 1
Frequency = 1
\$/Tick = \$12.50
commissions = \$ 5,000
win% = 50% -> # wins = 500

```
R:R  win loss win%  b/e%  Loss%  win/loss   Gross     Net    slippage
1:1   8    8  50%    0%    50%     1.00         0  (-11,250)   \$6,250
20%    30%     1.00         0  (-11,250)   \$6,250

2:1   16    8  50%   0%    50%     2.00    \$50,000    38,750   \$6,250
20%    30%     2.00    \$50,000    38,750   \$6,250

3:1   24    8  50%   0%    50%     3.00    100,000    88,750   \$6,250
20%    30%     3.00    100,000    88,750   \$6,250

4:1   32    8  50%   0%    50%     4.00    150,000   138,750   \$6,250
20%    30%     4.00    150,000   138,750   \$6,250

```

1. The trailing stop to b/e has no effect on the results.
2. The win/loss ratio, gross and net are all reduced to a simple multiples of the R:R ratio.
3. The commission cost is reduced to a constant.
4. This demonstrates the extremely powerful influence the R:R ratio has on the entire table and results.

This coin-toss simulation really brings into question the validity of the very common practice of taking a quick partial profit at 1 point (on the initial move into profitability). Taking an initial partial profit at anything much less that 2:1 is really going to degrade the long term overall performance of the system. I think this is because every stop loss that is hit takes the full sized stop. Look again at the net on the first row of that sim results table...

```
R:R  win loss win%  b/e%  Loss%  win/loss    Gross     Net      slippage
1:1   8    8  50%    0%    50%     1.00          0  (-11,250)     \$6,250
```
You're going to hate me for this. I was looking at your results and couldn't understand why the profit was not increasing when some of the losing trades were replaced by break-even trades. After looking at the spreadsheet I discovered that there was another bug that I introduced when adding the break-even parameter. I didn't adjust the losses down appropriately. I've made the change and produced this.

However, I don't think that using the simulator for a comparison of different break-even levels and other comparisons is a good idea though. What I will do (when I have a bit of time) is to make another spreadsheet that allows us to compare things like that.

The simulator is best at showing you how a probability scenario can change and give you realistic expectations. If you press the F9 button then you will see the results change as new trades are "randomly" generated with the bias parameters that you set-up. For example, if you set a 75% win percent and 0% break-even then the simulator will generate a series of trades with random win/loss profiles with a bias towards the 75%. Sometimes you will see that exactly 75% of the trades are winners, sometimes it will be less like 69% and sometimes it will be more like 83%.

This demonstrates that any trading strategy will produce ups and downs when taken over a series of trades. In this case the simulator is set to 1,000 trades which is a fairly high number and could be about a years worth of trades but sometimes 5 years.

If after running the simulator several times with your strategies numbers in it (i.e. probabilities) and you don't see a losing series then it is unlikely that in real life you will see a losing series. This assumes that the initial figures for the probabilities are accurate. If however, you frequently see losing series then there is a good chance that you will have "bad spells" when it seems that nothing is going right. This "bad series" is in fact something that you have already seen in the simulator and something that should be expected with this strategy.

My deepest apologies pt!
I'm really sorry I messed up with the simulator again.

monte_carlo_v4.xls
As always guy you are one of the most gracious people I know in this business. As we have seen all to well in the Advisory Services threads, you integrity is a welcome respite from the more typical <insert appropriate descriptive noun here> in the industry.

Think of it this way, If I were not using the worksheet in my usual atypical fashion, we would not be flushing out these little nuances
If you think this is bad, you should see how I use oscillators in my trading....
I must admit, that last set of run's had me questioning what I thought I knew about the validity and value of using a break-even stop. This is a deeply held (sacred) belief that I have lived by for a good many years in my career. Thankfully, with version 4, that golden light is once again shining in my little corner of the trading world...

One enhancement you might consider incorporating into this worksheet is changing the color of the net profit/loss cell to red or yellow when it is a loss, that way when you press F-9 a bunch of times, you will have this visual clue flashing on and off as a pretty simple indication of the ability of the particular scenario to stay profitable... ie the stability/profitability issue you had mentioned.

Anyways, here is scenario 1 from above (the random coin-toss scenario), updated using version 4.

Constants:
commission fee = \$ 5 / RT
Slippage = 1
Frequency = 1
\$/Tick = \$12.50
commissions = \$ 5,000
win% = 50% -> # wins = 500

```
R:R  win loss win%  b/e%  Loss%  win/loss   Gross     Net    slippage
1:1   8    8  50%    0%    50%     1.00         0  (-11,250)   \$6,250
20%    30%     1.66     19,800    8,550    \$6,250

2:1   16    8  50%   0%    50%     2.00    \$50,000    38,750   \$6,250
20%    30%     3.32    \$69,900    58,650   \$6,250

3:1   24    8  50%   0%    50%     3.00    100,000    88,750   \$6,250
20%    30%     5.05    120,300   109,050   \$6,250

4:1   32    8  50%   0%    50%     4.00    150,000   138,750   \$6,250
20%    30%     6.60    169,700   158,450   \$6,250

```

Break-even stops still work !!!!

What I found most compelling in this run is the effect the b/e trailing stop has on the win/loss ratio. If you look at the 1:1 test using the 20% b/e trailing stop, it managed to pull the win/loss ratio almost all the way up to the 2:1 test (b/e=0%). At 2:1, the b/e stop actually outperformed the 3:1 test (b/e=0%)... what a remarkable and powerful demonstration of this simple tool.... I always suspected minimizing losses was a good idea
Thanks for the kind words pt_emini.

That 2:1 with b/e stop outperforming the 3:1 is very insightful!
Just a couple of quick observations here, after looking over what the first pursuits amounted to. I hope not to sound like a wet towel, but this is what strikes me about this kind of analysis...

The analysis is attempting to make a linear or static assessment against a data set that has many dynamic influences within it. It's a little like trying to force the market to fit within the model, rather than building a model that works from the influences within the market.

Some areas to consider in that light might be...

Momentum will tend to predicate the non-linear nature of probabilities as a direct relevance to the data. In other words, probabilities are always improved relative to momentum fueling a given direction or rate of change, as compared to the affects on testing in a sideways market that's gone pretty much flat.

Volume surges and market price incline or decline are heaviest at or near celebration points like S/R pivots. Probabilities will always tend to me more favorable in the areas closest to those price levels initially and then taper off dramatically in a more parabolic manner as consolidations form and break on the way to the next major celebration.

Any given move tested will be a derivation relative to the prior major move immediately preceding it, who's limits will tend to want to remain contained within the greatest major move within that day's context, so momentum will be affected also by having attained or escaped the break beyond that adjacent prior move and the daily context.

Another extremely elusive influence is bull/bear pressure and how momentum is affected by the relationships of the long term market trend, intermediate term and then short term being intraday.

Certain times of day also show significant influence on momentum like pre-market, open, mid-morning and early/late afternoon.

I realize the coin toss theory is to centralize such variables in order to test the basis of a theory, but in order to see a true reflection of "probability" in this kind of data set, it may make more sense to model the tests against a declared "Relative" picture, rather than simply running a linear set of tests.

By isolating and providing a relative score as to the degree of effect those or other major considerations prove to hold, a much more reliable picture of true probability can be formed.

Means to accomplish that may tend to be more calculus based for one and nearly form what would be a rudimentary form of AI or very basic neural structure, but capturing simply the more dramatic affects and making some relatively mild assumptions, may paint a much more dynamic result in the scores that could highlight a more realistic picture.

For example, locating the greatest probability of initial pull back following the immediate departure from pivot, could dramatically reduce the stop distance, (i.e. identification of the lowest risk entry point with tightest possible stop to succeed not being slapped out). This however could only be accurately determined in a "relative" model as a flat model will essentially induce skew or kurtosis in the theoretical distribution, compared to the real market distribution.

Again, these are just impressions that would concern me that while the linear method may well "appear" to be giving you some sound guidance, following it in actual trading may have a completely different result not only leading to potential loss, but also leaving one scratching their head as to why the theoretical didn't pan out in the real world application of it.

I continue to look for ways to paint the relational picture with a simple model, as I think probability modeling holds a lot of promise, but rarely seems to pan out with solid results in typical linear approaches. I feel the difference of linear testing against non-linear influences may be one of the big reasons it so often doesn't seem to pan out.

Food for thought anyhow.
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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