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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.
Thanks pt! I put in the same figures that you use and ran it and get the same type of results.

Interesting that on the 1:1 the percent winners required jumps from 56 to 65 percent if you have 2 ticks of slippage. I tried that 1:1 again with no slippage and simulator turns a profit 95% of the time with a 55% win %.

It's an eye opener that even with a good bias that 1,000 trades is sometimes not enough to smooth out the equity curve to a profitable one.
Well that old 70% guideline does appear to have some validity after all

I do have a few observations to make based on this initial run.....

1. I am willing to concede the 1 tick of slippage on the exit at the profit target, but it will be hard to get around it on the stop loss. The assumption on the exit target fill is the market will trade through your limit order. To ensure this for simulation purposes, if long the bid will touch to your target price (meaning all the offers have been filled). We have all had the experience of watching trades go off at the offer price, but the order is not filled, or is partially filled. On the stop loss side, we must assume a stop/market order to ensure fill, thus the 1 tick of slippage since your exiting at the market. Based on my experience this is optimistic, but I am willing to live with it for the sake of discussion. Thus for each trade, 1 Tick of slippage + \$5 / RT. In the simulator we can accomplish this by adding 1 tick to the loss side and set the slippage control parameter to 0. For example, R:R = 1:1, gives us 8 tick profit and 9 tick loss.

2. Slippage and commissions are primarily fixed costs that are not going away, and we can't just wish them away either. This shows us, the method/system must first overcome this cost hurdle before showing a profit.

3. One thing this simulation does not account for is mistakes. One big mistake new traders make is to fight the market trend, and they usually do this in two ways. The first way is to not honor their initial stop loss, they use mental stops then adjust them on the fly. The second big mistake is to add to losers. In my experience the first mistake tends to lead to the second. Obviously this simulation clearly proves one thing, its hard to make money even if you make no mistakes. If you make the mistake of letting a small loss turn into a disaster, it will take forever to recover that loss... assuming you have any money left in your trading account to even try.

4. If you closely study the effect of the loss side, it is a powerful impeding force offsetting the profit side. The total \$ loss figure is much to high to be reasonable for an actual trading system. Fortunately, we can do something about the magnitude of this factor by introducing a trailing stop to break-even. We can then assume some number of losses and wins will become break-even stops. This introduces a third possible outcome: win, loss and break-even. Would it be possible to model this idea in the monte-carlo simulator ? Ideally, I would like to be able to control (set) the percentage of loss and break-even trades as well. For example, one scenario might be 50% wins, 20% loss and 30% break-even. The idea here is to dampen down the total \$ loss figure with the break-even stop, and adjusting down the % wins to account for more stops at break-even. Also, I would add the slippage at break-even as 1 tick to produce a true break-even, not break-even - 1 tick.
quote:
Originally posted by pt_emini

Well that old 70% guideline does appear to have some validity after all

This is true!
quote:
1. I am willing to concede the 1 tick of slippage on the exit at the profit target... For example, R:R = 1:1, gives us 8 tick profit and 9 tick loss.

I agree. Set the slippage to 0 and add 1 tick to the stops. I looked back at my trading records and see that slippage is not even that bad for me on the ES. But on something else like the YM this might be a problem.
quote:
3. One thing this simulation does not account for is mistakes.

Very true but if you are not using the slippage box for slippage you could relabel that "mistakes" and set it to a value which approximates the mistakes you make per X number of trades and their effect. So we can already take that into account - in a way.
quote:
4...This introduces a third possible outcome: win, loss and break-even. Would it be possible to model this idea in the monte-carlo simulator?...Also, I would add the slippage at break-even as 1 tick to produce a true break-even, not break-even - 1 tick.

Okay, I have created a new version of the simulator and will upload it below. Contrary to point 1. above I re-introduce slippage. Slippage is, however, only calculated for the losing and break-even trades and it is assumed that there is no slippage for the winning trades.

Also introduced break-even trades as a %. It should all be fairly obvious how to use this. Let me know how it works out...

This does however throw the mistakes instead of slippage out of the window. I suppose in the following version I could add a mistakes factor. How would you allow for mistakes? Would you assign a number of ticks per trades to get an average?

monte_carlo_v2.xls
Wow , thanks so much for your quick response DT !

I look forward to taking the new version out for a trial run

Yeah the occasional mistake is just a part of being mortal humans...stuff goes wrong once in a while: orders get lost in transit, posted to the wrong account number, or broken by the exchange, quote feeds fail, hard drives crash, broker servers reboot, planes fly into buildings...feel free to add to the list.....

Anyways, I think we can probably just leave the mistake factor out of the simulator for now and assume the stop loss order will take us out at a loss.
One has to have a specific software to test this?
Inventor: It's an excel spreadsheet. If you have modern version of Excel then you should be able to use it. Just download from the link above and open it. The press F9 to recalculate the simulation. Ask any questions here about anything that you don't understand.
edit - removed the simulation run results table, bug in the run messed up the results
pt_emini: My apologies. Both of the previous spreadsheets had a "bug" and they were only calculating correctly if the Win Ticks and Lose Ticks had the same value. I was looking at your result table and I said to myself "there is something very wrong about this" and so I went back over the formula in the spreadsheet and found the mistake. My apologies.

Please find attached version 3 which fixes this problem.