Assessing the Profitability of All Possible Trading Strategies

Additional order types are really useless and confusing. SL/TP/{buy,sell}{stop,limit} are no more than net exposure variation. Look at your graph (1) thinking exposure instead of orders. In the case n=1 your sell limit is simply cancelling the exposure of the buy order. Your are now net flat. The profit is locked and it is pointless to wait for the SL or TP to be reached: the PnL won't change. You only pay an additional spread to close a position!

If the price comes back to the original price you open a buy. If the SL is hit you lose the previous gain and you're BE. The BE doesn't come from the smart way of arranging the orders. The next coin flip just loses the previous gain.

After either scenario n=0 or n=1 happended, either the price comes back and you play again from the original level or you can start the process again from another price level. But since you assume a RW, the starting level is irrelevant and the previous PnL have no influence on the future.

Now it is trivial to see that the system either wins 1 or loses 1 with 50% chance each and is therefore BE long term before spread. From this fact it is pointless to try to mix it with any other system, including the (2).

Now by thinking in term of exposure, I leave you as an exercice to discover that the second system is actually the very same as the (1). And, therefore, has the same 0 expectancy.

Hi,

You can solve-ish the martingale problem, convert the exponential martingale to an linear martingale.

With exponential martingale you have X^n+1 you can differentiate this (incorrect) to (n+1)*X. If you trade your first idea you have profit when n=0 and when n>1 then you break-even. Ofcourse you will lose spread etc. Because this is still some sort of a martingale you run out equity but way slower then the normal exponential martingale. Because you differentiate it incorrect it only works till n=3.

To be continued....

Quoting Jysticim

Disliked

Hi, You can solve-ish the martingale problem, convert the exponential martingale to an linear martingale. With exponential martingale you have X^n+1 you can differentiate this (incorrect) to (n+1)*X.

Ignored

I have a few questions.

Where did you get the equation x^(n+1) and how does it relate to the exponential growth of the martingale hedge matrix?

Also, how does differentiation (a concept of calculus), relate to the notion of a linear martingale?

I think we can all understand the benefit of linear martingale— so, how exactly do you think this would be possible?

As a thought experiment I will ask the following: assuming it was possible, would you risk trading with a linear martingale?

I am inclined toward the answer “yes”.

Thanks.

y= x^(n+1)
y = size of the trade
x = size of the first trade, x>1 otherwise the function does not work how we want it to work. x<1 | y= x*2^(n+1)
n= the waves

First trade; 0,01 lot is 0.01*2^(0+1)=0.02
Second trade; 0,01*2^(1+1)=0.04
Third trade; 0,01*2^(2+1)=0.08
etc, just normal martingale

Just forget the differentiation part (It wasn't even proper math), I was just searching for a way to get an exponential function into a linear function.
My idea is to use y=(n+1)*x this obivously won't work after x>3 because for this to work the growth in the numbers need to be exponential 1-2 is increase of 100% 2-3 is increase of 50% and 3-4 is an increase of 25%. This function only works when exponential increase in numbers is higher then 50%. Conclusion we are still using a exponential martingale.

So what now? As I said before this hedging strategy is totally based on martingale, maybe I am missing something?

And ofcourse if you have a working linear martingale forumula you are done. But I think this is not possible to create, my math level is not that high to oversee this. Maybe rewriting it with somesort of logarithm?

-Jysticim

Quoting PipMeUp

Disliked

Additional order types are really useless and confusing. SL/TP/{buy,sell}{stop,limit} are no more than net exposure variation. Look at your graph (1) thinking exposure instead of orders. In the case n=1 your sell limit is simply cancelling the exposure of the buy order. Your are now net flat. The profit is locked and it is pointless to wait for the SL or TP to be reached: the PnL won't change. You only pay an additional spread to close a position!

Ignored

Yes.
I understand your critique. The trading setups, as they have been presented in my example, are useless for the reasons you have presented.

However, those examples were only intended to give some background and allow me to transition into the following topic:

Consider the trading systems I have included in the attached images. They have the following properties:

1. The system does not use martingale. We are only concerned with n values up to 3. This is because the profit outcome will oscillate between a break-even and a loss (here, we must accept a loss). We don’t open any new trades after n=2 so we fix the system.

2. The presence of a buffer zone. For instance, in example 3, when n=0, the system has profit X, when n=1 and when n=2, the system will break-even. The system is only in loss under scenario n=3 (profit –X). The profit to loss ratio is 1:1 however there is a buffer zone for two directional changes—this means if one order is executed and the market then changes direction entirely (to n=1) you do not necessarily suffer a loss— and you can do this without applying martingale.

I do not think these two properties can exist without including all 4 order types and modifying the TP/SL lines (the buffer zone is the primary benefit). I understand this may seem messy or inefficient but there are potential benefits to doing this.

It is important to acknowledge that these systems have problems related to probability; since there is a difference in the TP/SL for the orders, the probabilities associated with each scenario are not the same.

Note: This part is rather confusing and difficult to convey (I have also omitted much of the detail). I acknowledge that this explanation is not very clear-- but hopefully you will understand the gist and I can clarify in future posts.

Shall we understand that B+C means open both a long and a short at the same time and same price?
Do you realize that opening X1 lots long and X2 lots short is the same as opening a single order of size |X1-X2| plus paying additional spread?
If X1>X2 it is an expensive long entry
If X2>X1 it is an expensive short entry
If X1=X2 it is a useless spread give away to the broker.

For any order of size X:
buy stop -> add X to the exposure
sell stop -> add -X to the exposure
buy limit -> add X to the exposure
sell limit -> add -X to the exposure
TP of long -> add -X to the exposure
SL of long -> add -X to the exposure
TP of short -> add X to the exposure
SL of short -> add X to the exposure

There is only one single action a trader can perform: adding X to his exposure at time t.
Other point: without loss of generality you can always set X1=1 for all the scenarios.

Hi,

As PipMeUp already said Buy and Sell orders at the same time won't make any differences. Please don't break your head on that because many did that. Only thing that you can change is the exposure or TP and SL. To find anything that is worth while we have to look at TP and SL. Some months ago I discovered a way to trade with less "risk" see the picture below.

Quoting PipMeUp

Disliked

Shall we understand that B+C means open both a long and a short at the same time and same price? Do you realize that opening X1 lots long and X2 lots short is the same as opening a single order of size |X1-X2| plus paying additional spread?...

Ignored

Ok. You are correct.

After a bit of reassessment, I realize I was wrong when I said: “I do not think these two properties can exist without including all 4 order types and modifying the TP/SL lines.”

The attached image contains a more efficient version of what I was trying to do in example 3 (you should also be able to simplify examples 1 and 2). It does not use confusing limit orders and has the same properties as example 3. How can we improve this setup?

Additional things should be considered. You can use a trailing stop in scenario n=0 if there is profit before the TP is hit-- you only need to apply the hedge if the market direction changes immediately after the execution of the first order. [Remember: if this directional change is sufficient to close the system at n=1 (or again at n=2), the buffer will minimize the loss as much as possible.] However, if you use a trailing stop during n=0, the profit/loss is no longer a fixed ratio. Also, as I have said, the probabilities associated with each n value are not the same.

Do you think including a partial close will increase the number of possible configurations or is this just another useless operation? Do you know of any other operation(s) that would increase the number of configurations we can work with?

n=1 profit not -1?
n=3 profit not -2?
n=4 profit not -1?

You can use a calculator to solve the matrix-- the answers make sense.

[n=0] 1(1) = 1

[n=1] -2(1) + 1(2) = 0

[n=2] 1(1) - 2(2) +1(3) = 0

[n=3] -2(1) + 1(2) - 2(3) +1(2) = -4

[n=4] 1(1) - 2(2) +1(3) - 2(2) = - 4

The beginning is just like martingale but the system is fixed at n=3.

I have attached some variations of example 3 (I believe they are correct interpretations).
They are not necessarily profitable-- just something to consider.

The profit/loss is not a fixed ratio; this would depend on the scenario and TP/SL (min of 1:1 and max of 1:4).
The second one is more risky for larger values of n.

A trailing SL has no effect until it is hit. It can be seen as a regular SL. Partially closing is the same (up to the spread) as closing and re-opening with a smaller lot. Or it is the same (again up to the spread) as adding an opposite position ("hedge") with a smaller lot size. Just another modulation of the net exposure over the time.

Whatever the matrix you might imagine the net exposure of the system is constant between two orders (buy limit, SL, TP, ...). The net exposure is a piece wise constant function. This picture shows three scenarios:
A.1 I'm flat I open 1 lot long.
A.2 I feel the timing was wrong I open another lot to average down.
A.3 I was wrong I go 4 lots short to recoup the loss
B is the regular martingale
C is a stop-and-reverse martingale.


Let's call segment the slice of time between two orders. Over a segment the exposure is constant. Which segment comes next depends on the previous segments. The next segment depends on the market. For example, in your schema, segment C-D can only exist if n=3. The segment B-C will not start if n=1...

The money made or lost at the end of the segment is linearly proportional to the net exposure which is just a scaling factor. Each segment happens with some probability. The first segment appear with probability one. The others happen with the probability that the path to them is reached. The total money made or lost at the end of any series of n segments is the sum of the money made for each of them. With X_i the net exposure during the segment i, p_i the probability that segment i happens and E_i the P/L of the segment i we can write the P/L as:


P_i is a probability and we aren't interested in the segments which can never happen: 0<p_i<=1. X_i.p_i is a constant. The P/L realized at the end of the n segments is a weighted sum of the pips realized over each segment.

Since you assume a pure RW the expectancy of the outcome of each segment is zero. The total P/L is a sum of zero times a constant. Whatever the arragement of the evolution of the exposure over the time, as long as you assume a pure RW, you can't find any system with a expectancy different from 0 before spread.

Any matrix will generate an edgless system against a RW.

I dropped here following an FF tweet.

One of my renewed robots does what you're suggesting in a less risky way.
In the system used by the robot the Black Lines in your chart represent the "Inner Trap", while the Red Lines represent the "Outer Trap".

Trader can control the risk by :

1. Trap Sizes, the Bigger the safer
2. Outer to Inner trap distance, the Bigger the safer
3. Profit Target, the Smaller the safer
4. Lot Size Percentage, the Smaller the safer

If I may, here is the link to the system description, and here is the link to the robot.

I hope you don't mind, otherwise I can delete the post.

Quoting PipMeUp

Disliked

A trailing SL has no effect until it is hit. It can be seen as a regular SL. Partially closing is the same (up to the spread) as closing and re-opening with a smaller lot. Or it is the same (again up to the spread) as adding an opposite position ("hedge") with a smaller lot size. Just another modulation of the net exposure over the time. Whatever the matrix you might imagine the net exposure of the system is constant between two orders (buy limit, SL, TP, ...). The net exposure is a piece wise constant function....

Ignored

I agree with your post.

First, I should have mentioned-- the examples I presented are only viable if we assume the probability associated with a profitable outcome is higher than that of a losing outcome(s). This assumption is not a nuanced version of the gambler's fallacy-- it is potentially useful during periods of high volatility. However, if we make this assumption, we are no longer operating under conditions of a pure random walk. Because of this, I am inclined to reject the assumption.

Intuitively, the systems don’t really seem to work but you have presented a concrete argument to support this intuition (I was looking for a proof of impossibility).

Unfortunately, your critique has strengthened my conviction that the entirety of trading is, fundamentally, an exercise in futility. So why bother? If the assumptions of technical analysis are flawed, and if you can’t arrive at any net profit under conditions of a pure random walk— what is the point?

But maybe I am missing something— considering the vast universe of possibilities.