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Proof of Profitability

  • #1
  • First Post: Edited Mar 19, 2015 11:55am Mar 14, 2015 2:20pm | Edited Mar 19, 2015 11:55am
Questions about stop loss. I was reading a little in ff and hit up on that topic again. Let me come up with an interesting fact about it.

Here is the experiment: You are trading with a take profit of 20 pips. You want to know the probability of being stopped out when your stop loss is 1 pip. Believing Laplace it is

P (SL) = SL / (TP + SL) = 95 %

Spoon-fed: Stop loss in pips divided by the sum of take profit in pips and stop loss in pips equals the ratio of hitting the stop. If your stop loss is 1 pip and your take profit is 20 pips than it is likely about 95% that you are being stopped out.

Now lets calculate the ratio for every combination of stop loss and take profit from 1/20, 2/20, , 20/20 and plot it on a chart.

Attached Image (click to enlarge)
Click to Enlarge Name: chance to hit sl.JPG Size: 73 KB

The chance of being stopped out is decreasing with a growing stop loss. The bigger the stop loss the better it is? I dunno for sure as I blow up more than one account using no stop loss at all ...

Step two of the experiment: It will show a really good reason not only to trade with a stop loss but to trade with a stop loss as small as possible. Assuming you have a strategy that is only somewhat slightly profitable. You should have, otherwise I see no reason at all of taking part at this game. In case you have, the relationship between the drawdown of your account and the size of your stop loss is as follows:

The smaller your stop loss is the smaller is your drawdown as well. Although a small stop loss means to be stopped out quite more frequently.

I try to proof that relationship with a neutral approach. That means I am not relying on my own or someone elses trading experience but on an experimental estimation.

I wrote an algorithm that is carrying out 1000 trades by chance. It is doing that until it has a result that is at least a bit profitable. In the next step the drawdown of those 1000 trades is calculated. The procedure is done for every combination of stop loss and take profit from 1/20, 2/20, ... , 20/20 and the draw down is plot on a chart:

Attached Image (click to enlarge)
Click to Enlarge Name: drawdown.JPG Size: 72 KB

That is probably the reason why you have heard so often to cut your losses short.

Some details about the estimation:

The initial account balance is 1000 USD. The volume is 0.1 lot. For every combination of stop loss and take profit the calculation is done 100 times. The values plotted are the averages of each 100 calculations.
  • #2
  • Mar 19, 2015 12:05pm Mar 19, 2015 12:05pm
I actually wanted to make a live test between to EAs. One trading with a stop loss of 5 pips and one trading with a stop loss of 2 pips to check out the difference between the draw down. The first one is attached as a trade explorer. Can someone tell me if I can set up a second trade explorer on FF?
O.k. done

MicroBOT 5 trades with a stop loss of 5 pips and starts to trail at a profit of 5 pips.
MicroBOT 2 trades with a stop loss of 2 pips and starts to trail at a profit of 2 pips.

Entry setup is the same for both. They are on different brokers so the quote is not exactly the same. But I hope it will work like expacted.
  • #3
  • Mar 21, 2015 3:02pm Mar 21, 2015 3:02pm
Ive chosen the name of this thread for a specific reason. Although I did not hit the topic directly in my first post. Let me do that now. I trade forex for about five or six years. I learned to code mql4 before I started to trade as I wanted to run my strategy in a backtest before going live with it. As a beginner I had no idea what kind of strategy would fit my needs. And I had not enough skill to code it properly. As I could not wait longer I started to dig through all that fancy threads on FF until I found a strategy that looked good in my eyes. I followed it for a while. Sometimes I won, sometimes I lost. I tried other strategies. In the end I lost more than I won. Money - my wealth of experience was growing consistently. A break and reflection led me back to my initial thoughts. Proof of profitability must be step one. Going live is step two.
What does proof of profitability mean? I define it to analyze a strategy in a quantitative manner. What does it not mean? To cherry-pick a hand full of charts where a setup does work in hindsight.
I attached two trade explorers on this thread. This is the result of combination between two pieces. An elementary trading strategy trained in a sophisticated way. The strategy is explained in one sentence: Put a zig zag on your chart, buy the highs and sell the lows. Fascinating simple, isnt it? Question is how to find the right setup for entry and exit using the zig zag. That is the more tricky part to solve. You need quantitative strategy analyses if you want to succeed.
I had a lot of effort shaping the right instruments. I use MT4 optimization cycles. Raw data is exported into csv, vba algorithms are working it up.
Here are the results of testing it for a time period from 2013/1/15 to 2013/12/31 (0.1 lots):
Attached Image (click to enlarge)
Click to Enlarge Name: evaluation.JPG Size: 163 KB
  • #4
  • Mar 21, 2015 5:12pm Mar 21, 2015 5:12pm
Quote
The smaller your stop loss is the smaller is your drawdown as well. Although a small stop loss means to be stopped out quite more frequently.

I try to proof that relationship with a neutral approach. That means I am not relying on my own or someone elses trading experience but on an experimental estimation.
​

I can't understand this part. Drawdown isn't determined by the stop loss size. It depends of your risk only. As a loosing trader you can have a minor drawdown than a successful trader.
  • #5
  • Edited 3:59am Mar 22, 2015 2:39am | Edited 3:59am
Quoting Unabletrader
{quote}​ I can't understand this part. Drawdown isn't determined by the stop loss size. It depends of your risk only. As a loosing trader you can have a minor drawdown than a successful trader.

The relation between stop loss and drawdown is estimated for a winning trader, not a losing one.
(Look above: It is doing that until it has a result that is at least a bit profitable.)
If your trading strategy is successful then your drawdown will be smaller if you use a smaller stop loss. Of course your strategy still has to be profitable when you are minimizing your stop loss.
My experience until today is that a big draw down means a big chance that your account will be blown. Because of the bigger risk you take. If you limit your risk then your stop loss is limited by the position size you trade and the balance of your account. Trading 0.01 lot EURUSD means 10 Cent per pip. If you do not want to risk more than 5 % per trade then you cannot have a stop loss bigger than 5 pips (if your account balance is only 10 USD or you are trading 0.01 lot per 10 USD balance). The successful trader who is not being stopped out because of a big stop loss is taking a big risk because of that relationship. One day a big risk will lead into a big loss. At that day the drawdown will be big, too.

Btw Unabletrader: Thanks for first answer and taking part on that thread
  • #6
  • Mar 22, 2015 7:41am Mar 22, 2015 7:41am
You can be right mathematically but markets don't go one direction or another straightforward. Even casino principles won't work here.

All I want to say that there must be another element in your equation. Something like volatility. I don't know. I mean 5 pips is too near to be hit independently from yr analysis. The market can easily touch it and go forward or backward. Not speaking about spread widening and etc etc etc
  • #7
  • Mar 22, 2015 7:59am Mar 22, 2015 7:59am
Quoting B-Naire2B
You can be right mathematically but markets don't go one direction or another straightforward. Even casino principles won't work here. All I want to say that there must be another element in your equation. Something like volatility. I don't know. I mean 5 pips is too near to be hit independently from yr analysis. The market can easily touch it and go forward or backward. Not speaking about spread widening and etc etc etc
That missing equation is win rate. It doesn't matter how often the stop gets of the profits rendered on the win can offet it and then some. I win about 40% of the time. I always have my profit targets twice that of my stop losses. As I result, I only need to be right 33% of the time to be profitable.

Every trading plan needs to mathematically make sense or it's not a complete plan.
  • #8
  • Mar 22, 2015 8:03am Mar 22, 2015 8:03am
This thread is very interesting !

But, i 'm not a stoploss user ferving, only maybe for ultimate protection

I think, more your system is rigid more you lose great opportunity.
  • #9
  • Mar 22, 2015 8:09am Mar 22, 2015 8:09am
Quoting ForexSamsam
This thread is very interesting ! But, i 'm not a stoploss user ferving, only maybe for ultimate protection I think, more your system is rigid more you lose great opportunity.
Perhaps that might be true, but some trading plans work well going after the fast nickle over the slow dime.

Hitting huge wins are fun, but if you can get twenty 100 pips wins for every 1500 pip win, I'd prefer the former as opposed to the latter.
  • #10
  • Edited 2:23pm Mar 22, 2015 9:04am | Edited 2:23pm
Quoting B-Naire2B
You can be right mathematically but markets don't go one direction or another straightforward. Even casino principles won't work here. All I want to say that there must be another element in your equation. Something like volatility. I don't know. I mean 5 pips is too near to be hit independently from yr analysis. The market can easily touch it and go forward or backward. Not speaking about spread widening and etc etc etc

If you try to find regularities with a statistically approach you need to reduce the framework until you can put it into a model. So it will be hardly possible to transfer it one to one on a market because markets simply do not behave like that. I am with you at that point.
But it has some usable value. Otherwise you need to adapt your framework. The heatmap on the bottom left from the four posted above shows drawdown in relation to stop loss and trailing stop loss. Those results are not mathematically calculated. They are from a backtest with tickdata. The drawdown is growing with growing stop loss.
  • #11
  • Edited Mar 23, 2015 6:29am Mar 22, 2015 9:11am | Edited Mar 23, 2015 6:29am
Quoting mastergunner
{quote} That missing equation is win rate. It doesn't matter how often the stop gets of the profits rendered on the win can offet it and then some. I win about 40% of the time. I always have my profit targets twice that of my stop losses. As I result, I only need to be right 33% of the time to be profitable. Every trading plan needs to mathematically make sense or it's not a complete plan.
I would not say there is something missing . It is just focussing on the relation between drawdown and stop loss for a strategy that is at least a bit profitable. What about drawdown and stop loss for a strategy that has a win loss ratio of 2 is another question. An interesting one
  • #12
  • Mar 23, 2015 6:35am Mar 23, 2015 6:35am
Quoting ForexSamsam
This thread is very interesting ! But, i 'm not a stoploss user ferving, only maybe for ultimate protection I think, more your system is rigid more you lose great opportunity.
What do you think about the statement that using no stop loss means not limiting risk. What basically means to risk the whole account with each trade.
  • #13
  • Edited Mar 28, 2015 6:19am Mar 27, 2015 1:12pm | Edited Mar 28, 2015 6:19am
To analyze a strategy means to screen it in an extensive way. After that the results must be visualized in a way that allows forming an opinion at the first view. To make a backtest or an optimization with Meta Trader is easy. But it is not that easy to visualize them. The more data you gain the more difficult it becomes.
One way is using heatmaps. I have attached four of them in post #3. Let me explain the heatmap correlation. I found the idea and how to use it at MQL5 (Mathematics in Trading: How to Estimate Trade Results). Here I will explain it in my own words. Lets have a look at two accounts. At the end of the trading period both of them have a value of 250 $. We cannot prefer one of them as they are the same in monetary aspects. The next step is a look at the balance curves.

Balance 1 looks like this (blue line is the balance curve):
Attached Image

It looks like a steady growth, doesnt it? The winning trades are bigger than the loosing ones, the balance is rising. If we expect a similar behavior in the future, then the balance will go on growing.

Balance 2 looks like this (blue line is the balance curve):
Attached Image


Not that promising. Each profit is followed by a loss as big as the profit. With the next trade the gain of 250 $ will be probably gone again.

The black line on the charts is the linear regression line of the balance curve. For those do not know it: It is a line drawn in the way that it has the smallest deviation from each point of the balance curve.
Now the correlation between the balance curve and the linear regression line is calculated. A higher correlation means that the balance curve is more similar to its linear regression line. That means the balance curve is developing more smoothly without big wavering above or (and much worse) below the linear regression line. That is what we want: A steady and smooth growing balance curve.

The heatmap correlation (top right of the four) shows the correlation of 100 different backtests from the same strategy. The backtests are made with every combination of stop loss 1 10 pips with trailing stop loss 1- 10 pips. The heatmaps gives a clear overview what adjustments are leading to the best results. And it shows that the results proceed evenly. That indicates that results are not made by randomness. If you got one good value and every other around it is bad, than the good one is probably a lucky shot.
Now put the Heatmap profit (top left of the four) beside it and start to compare both. Look for adjustments of stop loss and trailing stop loss where you have both: High profits and high correlation.
Now bring the other two heatmaps drawdown and winner% into the game. Look where the drawdown is small and what win rate can be expected.
That means to screen a strategy over a broad spectrum with quantitative analytics.
I could never do that by putting 100 balance curves beside each other and trying to get them into my brain, could you?
  • #14
  • Edited 2:46am Mar 28, 2015 12:26am | Edited 2:46am
Quoting JT4xPro
Questions about stop loss. I was reading a little in ff and hit up on that topic again. Let me come up with an interesting fact about it. Here is the experiment: You are trading with a take profit of 20 pips. You want to know the probability of being stopped out when your stop loss is 1 pip. Believing Laplace it is P (SL) = SL / (TP + SL) = 95 % Spoon-fed: Stop loss in pips divided by the sum of take profit in pips and stop loss in pips equals the ratio of hitting the stop. If your stop loss is 1 pip and your take profit is 20 pips than it is likely...
Great thread and in this post (that quoted above), in my opinion you have nailed a very important aspect of risk management. This is exactly what I am finding with the trend following approach I use. The game significantly changes then when you then apply this consideration to a technique with a demonstrated statistical edge.

Thank god for the analysts out there.

We are so used to optimisation with EA testing....sometimes we just need to slow it down and try to understand that those damned statistics are actually telling us...as opposed to a simple blind application of the optimal settings.

Subscribed :-)
  • #15
  • Edited 4:34am Mar 29, 2015 4:22am | Edited 4:34am
Quoting Copernicus
{quote} Great thread and in this post (that quoted above), in my opinion you have nailed a very important aspect of risk management. This is exactly what I am finding with the trend following approach I use. The game significantly changes then when you then apply this consideration to a technique with a demonstrated statistical edge. Thank god for the analysts out there. We are so used to optimisation with EA testing....sometimes we just need to slow it down and try to understand that those damned statistics are actually telling us...as opposed...
Glad to hear that someone sees it the same way. The two trade explorers attached above are on different brokers. So it is a little bit hard to compare them (especially gainsy seems to be really some kind of bucket shop with a huge lack of liquidity. Sometimes a SL is hit, the price moves 5 pips further and then the position is closed when the price pulls back at the initial stop loss...). I have the EA running at OctaFX (where the trade execution works much better) with 2 pips stop loss (as attached as trade axplorer) and with 5 pips stop loss. Here are the last 35 trades with the same entries:

Attached Image (click to enlarge)
Click to Enlarge Name: comparison 1.JPG Size: 163 KB


Top graphs are the balance curves. Smaller stop loss leads to a bigger balance in the end.
Bottom graphs are the drawdowns. Smaller stop loss leads to a smaller drawdown.
Have a look at the table: The maximum drawdown is 0.28 Euro compared to 0.98 Euro.

And now there comes the really fancy stuff: If the drawdown is minimized by the factor 3.5 - why not trade a position size that is 3.5 time bigger? That would mean to have a 3.5 time bigger gain with the same drawdown.
Lets multiply the column "profit" of the "2 pips stop loss" with the factor 3.5. The profits are bigger and the losses as well:

Attached Image (click to enlarge)
Click to Enlarge Name: comparison 2.JPG Size: 164 KB


The blue line is skyrocketing. The maximum drawdown of 2 pips stop loss is still not bigger than the one of 5 pips stop loss.

That is the second reason why not only to trade with a stop loss but to trade with a stop loss as small as possible! With a small drawdown there are to options available. Trade on with a small risk or use the opportunity to raise your risk because you have left some space. With a bigger risk it is possible to aim at a bigger gain.
  • #16
  • Edited 5:18am Mar 29, 2015 4:58am | Edited 5:18am
JT4xPro, this is great stuff. :-)

I would love to see you mimic the results above using a stop loss amount as a % of trade capital. It will produce the same result as above but if performed as a % of trade capital will be scalable. From there you could look for an optimal relationship and then see what happens to the result with varying levels of profit target also expressed as a % of trade capital.

Regards

C
  • #17
  • Mar 29, 2015 5:19am Mar 29, 2015 5:19am
Quoting Copernicus
In your algorithm, are you assuming a positive expectancy, and if so, what is this assumption? Regards C
The last post shows results from my trading accounts (just to make sure that this is not mixed up as I want to compare the theoretical estimation in the first post with live ruslts).

The assumption is that for the average drawdown a simulated trading series has to be at least a profit bigger than 0. That can be any positive value. At least zero and with no maximum.
  • #18
  • Edited 5:57am Mar 29, 2015 5:36am | Edited 5:57am
Quoting JT4xPro
{quote} The last post shows results from my trading accounts (just to make sure that this is not mixed up as I want to compare the theoretical estimation in the first post with live ruslts). The assumption is that for the average drawdown a simulated trading series has to be at least a profit bigger than 0. That can be any positive value. At least zero and with no maximum.
Thanks J :-)

PS If I was using an EA with my approach I would love to join you in this testing exercise. Unfortunately that's not the case. I will watch with interest and participate where possible. In a far less rigorous way I have come to a similar conclusion in that with my approach a trade risk % of <=0.5% is achieving a max drawdown with about 700 trades under the belt of 4.0%. Given this result, a doubling of the trade risk % is going to double the profit performance and correspondingly double the max drawdown to 8.00%.

Interestingly the old 2% trade risk rule you frequently hear about in trading circles is way to ambitious if you ask me and simply not necessary to generate good returns, provided of course you have positive expectancy.

Using the technique you propose, it's a great way to ensure you are scaling into increased risk in a considered and measured manner.
  • #19
  • Mar 29, 2015 5:15pm Mar 29, 2015 5:15pm
JT4xPro, I think looking at the stoploss vs profit has some flaws - even though it is largely correct. I can show the flaw by giving a simple counter example.

support you have a strategy (for now lets just assume it is just one signal and our position sizing etc is equal) that predicts the move of 50 pips very accurately when you look at 1 hours fwd but in next 5 mins, the price goes against it by say 10 pips in many cases. Now the relationship of stoploss size vs TP size vs prob(hitting stop loss) is not very linear here. if you stop loss is less than 10 pips, then prob(SL) is very high but if SL is > 10 pips, it gets low. So for this signal, the analysis you have will not be correct at all.

So my point is you cant make a general argument like this. The SL and TP sizes etc are very much dependent on the signal itself.
Think : Trade : Live Life
  • #20
  • Mar 30, 2015 4:07am Mar 30, 2015 4:07am
The flaw #1 is in the first post. When you write P(TP)=SL/(TP+SL) --I fixed the typo-- you're assuming a random walk with no edge. Therefore, per definition,
you can't have any strategy even slighly profitable. From there, there is no point in optimizing the SL and TP: the expectancy is always 0 before spread and commission.
No greed. No fear. Just maths.
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