The Myth of Averaging | Forex Factory

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The Myth of Averaging

  • #1
  • First Post: Edited Jun 22, 2023 1:55pm Jun 17, 2023 6:55am | Edited Jun 22, 2023 1:55pm
Introduction

Mathematicians will tell you that a strategy without an edge can not be made profitable with "smart" money management. Grid, averaging down, Martingale, etc. will all fail in the long run when an unfortunate series of loosing trades drains your account. In this thread I would like to do some silly experiments with averaging down to verify that idea.

Simple Expert Advisor

I created a simple expert advisor for Metatrader 5 to do some tests. You can download the EA below, if you want to play along. Basically:

Each day we make a random buy or sell with a fixed SL/TP


More specifically:

  1. Each day at a fixed hour, we make 1 trade.
  2. The trade will either be a buy or a sell; chosen at random each day.
  3. For simplicity, we don't open a new trade if the trade of the previous day has not closed yet.
  4. Each trade has a fixed stop loss and a fixed take profit.

Here you see the inputs of the expert advisor:

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For now, please ignore the settings for level 2, 3 and 4. We will come to that later.

  1. EntryHour specifies at what time the EA will make an entry each day.
  2. RandomSeed determines the random buy/sell sequence.
  3. L1_StopLossPoints and L1_TakeProfitPoints specify the stop loss and take profit distance.

For non-programmers the RandomSeed input probably needs some more explanation. Your computer does not have the hardware to generate truly random numbers. Instead, computers generate pseudo-random numbers using a calculation that gives numbers that jump all over the place effectively looking "random". Given a certain starting value (the RandomSeed) this calculation will always generate the same pseudo-random buy/sell sequence. With another seed you will get a completely different buy/sell sequence. For example:

RandomSeed=1: buy, buy, sell, buy, sell, sell, buy, sell, ...

RandomSeed=2: sell, buy, buy, sell, sell, buy, sell, buy, ...

RandomSeed=3: sell, sell, buy, sell, buy, sell, sell, sell, ...

... etc.


This is useful if we want to replay an earlier backtest. If the EA would give different results each time it is run, it makes it impossible to examine settings we found earlier during an optimization.
Attached File(s)
File Type: ex5 yzAveragingDown-1.1.ex5   79 KB | 330 downloads | Uploaded Jun 22, 2023 1:29pm


- - -
Below is another EA that actually implements averaging UP (instead of averaging down). This is a different strategy than described above. See post #43 for more details.
Attached File(s)
File Type: ex5 yzAveragingUp-1.0.ex5   78 KB | 294 downloads | Uploaded Jun 22, 2023 1:31pm


(Note: we are going to run MILLIONS of backtests, so we need the EA to be fast. The EA will ignore all ticks and only enter/exit the market at the open tick of a new M1 bar. We are not relying on the "1 minute OHLC" setting of the MT5 strategy tester, but coded this in the EA itself. Also, trades are not given a SL/TP, but are checked at the open of each M1 bar and closed by the EA itself using a market order. This ensures the EA will show the same behavior in demo/live trading as it did during backtesting.)
  • #2
  • Jun 17, 2023 7:22am Jun 17, 2023 7:22am
Level 1 - SL/TP

Let's get started! For testing an averaging/grid strategy it makes sense to choose a symbol that is fairly ranging in nature. For example AUDCAD is often used with grids.

Since this EA is going to make a trade every day, it makes sense to ensure the trade will not remain open for more than a day on average. Also, if the trade is only open a few minutes the trading costs are relatively high for the profit we are going to make. So let's aim at trades being open a few hours on average.

For simplicity, let's stick with a R:R of 1:1 and try 50/50 for the stop loss and take profit setting (that is 5 pips):
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I run a backtest in MT5 on AUDCAD from 2012 to 2021(*):
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If we look at the backtest results, we can see the average position holding time is 32 minutes:
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That is a bit short. Instead, let's try 100 points (i.e. 10 pips):
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Now positions are open for 1 hour 49 minutes on average:
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That is a bit better, but let go for 200 points (20 pips). That gives 5.5 hours on average:
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Good. We will stick with 200 points for now. Looking at the other backtest results, we see no surprises:
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The EA made roughly the same amount of buys and sells. Only 50% of these were profitable as can be expected from an EA that trades randomly. Without trading costs that would be break-even, but of course we pay a little bit in commission and spread with each trade resulting in the equity going south:
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(*) I never use the last few years in my backtests until I have done all my optimizations and am ready to go live. Only then will I use these last years as a last sanity check or Out-of-Sample test.
  • #3
  • Edited 1:09pm Jun 17, 2023 7:38am | Edited 1:09pm
Level 1 - EntryHour

Now that we chosen a SL/TP to work with, we can search for the best time of day to enter the market. We let the MT5 strategy tester do an optimization run trying out 1 to 23. Note that we skip 0 because at midnight the spread is typically huge.
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If we plot the balance at the end of each backtest in a graph, we see there is no clear winner:
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EntryHour=9 is slightly better than the rest, so let's choose that one although it apparently doesn't matter much.

Level 1 - Distribution of possible profits

One single backtest does not say a lot. When we run a strategy on new future data, we will encounter different market conditions or might get an unlucky sequence of buy/sell trades that cause a lot of drawdown. To find out, we are going to run another 1000 backtests, each with the exact same settings but with different random buy/sell sequences. That says nothing about future market conditions, but says a lot whether or not our finding was just a lucky shot.

Although we are not really "optimizing" any setting, we can trick the optimizer to run 1000 backtests for us with the same settings but different RandomSeed values. This causes each backtest to have a different random buy/sell sequence:
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After drinking several cups of coffee, we finally get our results:
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When we plot the results of these tests in a histogram, we see a normal distribution centered around a mean of -6300:
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No surprises so far. What happens if we make a scale-in when the stop loss is hit (or a "recovery" trade as some call it)?
  • #4
  • Jun 17, 2023 11:05am Jun 17, 2023 11:05am
Hey hey! Very interesting ideas!

Try to add random lot sizes too, and also try to simulate not 1 asset, but 20 (at once).
And decrease the leverage to less than 1x.
It will be profitable.
Observer effect
  • #5
  • Edited 1:16pm Jun 17, 2023 11:25am | Edited 1:16pm
Level 2 - SL/TP

Now we are adding a second level. Once the first trade hit the stop loss, we now leave open the first trade and add a second trade in the same direction as the first trade. For both trades we now set new stop loss and take profit levels relative to the entry price of the second trade.

We use the MT5 backtester to optimize the best SL/TP level. This second trade must compensate for a first trade that is already 200 points in drawdown by the time we open the second trade, so we should search relatively large SL/TP levels. Let's try levels between 200 and 2000 points:
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This finds the following settings:
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The best settings found have huge levels of 1800 or 2000 points, or have relatively few trades. The setting highlighted in the screenshot seems like a good compromise. We choose L2_TakeProfitPoints=1000 and L2_StopLossPoints=1200 for our next experiments.

Level 2 - Distribution of possible profits

Like we did for Level 1, we like to see if we just got lucky or whether the strategy is actually any good. The best way to find out is to try many times, each time with different random buy/sell choices. We trick the optimizer in running 1000 backtests with the settings below:
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After running these backtests overnight, we get the following results the next morning:
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When we plot these results in a histogram, we get the following distribution:
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The mean improved from -6300 to about -3500! Still not profitable on average, but we now have a long-tail with backtests that gave a positive profit!
  • #6
  • Jun 17, 2023 11:40am Jun 17, 2023 11:40am
Interesting read, will keep following. The level 2 shows a long tail that gave positive profit, however, given that it looks to be a normal distribution that could be the case on the negative side as well. It just isn't shown because the account balance is 10k. Can you try decreasing the risk or upping the account balance as I suspect you would also see that long tail on the negative side if it was possible.
  • #7
  • Edited 3:09pm Jun 17, 2023 12:30pm | Edited 3:09pm
By adding a second recovery trade if the market goes against us, we improved the mean outcome of our strategy by almost 3000! The best case strategies give a nice profit, but admittedly the worst case also became worse. However, the mean is the most likely outcome, and that one improved!

Can we improve even further by adding a third level? Let's try...

Level 3 - SL/TP

When price hits the stop loss of the second trade, we keep it open (same as the first trade that is also still open) and add yet another trade in the same direction, and give all three open trades new stop loss and take profit levels relative to the entry price of the third trade: L3_StopLossPoints and L3_TakeProfitPoints.

Again, we use the MT5 optimizer to search for good levels:
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This gives:
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Of the best settings, the third (highlighted) has a fair amount of trades and not too wide SL/TP levels. Let's choose L3_TakeProfitPoints=600 and L3_StopLossPoints=600

L3 - Distribution of possible profits

Like before, we use the MT5 Optimizer to run 1000 backtests with different random buy/sell choices to see what possible outcomes we can expect when using these settings:
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This gives the following histogram of possible profits:
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The mean has moved again and is now nearly at break-even!! To my surprise, the long-tails have shrunk and the distribution is less wide than before?! At first I though this was a problem with the tool I use to make a histogram, but looking at the worst and best backtest results, we can see the distribution is actually less wide:
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Any mathematicians here on FF who can explain this?
  • #8
  • Jun 17, 2023 12:39pm Jun 17, 2023 12:39pm
Quoting ryuryu
Try to add random lot sizes too
In this thread I will focus on "averaging down", but you are right that it might be interesting to do a similar thread on Martingale!

Quoting ryuryu
try to simulate not 1 asset, but 20 (at once)
Diversifying over multiple symbols will certainly yield a smoother equity curve as the peaks and valleys of the individual symbols average each other out. For the educational purpose of this thread, running 20 assets in parallel will complicate things too much. I would like to show the effects of averaging down in a simple understandable way.

Thank you for your suggestions!
  • #9
  • Edited 2:00pm Jun 17, 2023 1:34pm | Edited 2:00pm
Quoting Scotteyy
The level 2 shows a long tail that gave positive profit, however, given that it looks to be a normal distribution that could be the case on the negative side as well. It just isn't shown because the account balance is 10k.
Good observation! When I sort the profits in the backtest results in ascending order in a spreadsheet, I can see only 11 of them hit the -10k:
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so we have 1.1% chance of completely ruining our 10k account.

Quoting Scotteyy
Can you try decreasing the risk or upping the account balance as I suspect you would also see that long tail on the negative side if it was possible.
The lot size is already at minimum at 0.01, but we could try a larger account balance. Why don't you give it a try and let us know what you find? The EA can be downloaded from post #1 and the settings are in the screenshots.

Nonetheless, how realistic is this for doing real-life trading? Nobody in his right mind is going to run a random strategy on a 100k account. However, some might consider gambling with a smaller account in the hopes they get lucky?

Edit: look what happened at level 3! Somehow the distribution became less wide and this is no longer a problem!
  • #10
  • Edited 2:20pm Jun 17, 2023 2:09pm | Edited 2:20pm
Level 3 - Equity Curves

Let's look a bit closer to what we got so far at level 3. The worst backtest was -1020, the mean of the distribution is at about -200, and the best backtest gave +861 profit. Their equity curves look like this:
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The distribution profile in post #7 looks fairly symmetric with a peak at -200. However, if we sort all backtest results in ascending order we see that the median value is actually -119:
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This indicates the distribution is slightly skewed, although we can not easily see this from the histogram from post #7.
  • #11
  • Jun 17, 2023 2:47pm Jun 17, 2023 2:47pm
This is an Interesting Idea

I can tell you one thing from my own setup and research. Currently I use 2 setup plan. One is private I am currently using.

Other is under Test

I have noticed that if you use on all currency pairs under belt there is no need to increase lot size and is profitable. Test is underway already and I will post a Trade Explorer
once some history is gathered

Alright See You For Now

I will be watching this as in my opinion only maths can score in any business no matter trading or other
HBS - Hussain Bin Salman
  • #12
  • Edited 3:56pm Jun 17, 2023 2:51pm | Edited 3:56pm
Level 4 - SL/TP

By now you can guess what is coming next...
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From the optimization results:
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we choose the highlighted entry which has relatively much trades and a nice tight stop loss. Note that all settings above had a positive profit in the backtest! Coincidence or are we on to something?

Let's find out by running 1000 random backtests using these settings:
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This gives the following distribution of possible outcomes:
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The mean in the histogram is around about -80, the median is -3.37, the average 6.99. This suggests the histogram is skewed and not fully symmetric.

Again we improved the mean, but not enough. If we would trade this system live we have a bigger chance of loosing money than to make money. We could add yet another level, but let's try something else. Let's think about what we have been doing so far and if we can find better settings...
  • #13
  • Jun 17, 2023 3:43pm Jun 17, 2023 3:43pm
Statistical Optimization Approach

Looking at the optimization results above, it is remarkable how wide the range of SL and TP parameters varies in the top results. This suggests the results vary wildly due to the random nature of the strategy. In post #10 you clearly see how the same settings can give completely different equity curves due to random chance.

At each of the levels we have merely searched for SL/TP settings using a single fixed RandomSeed=1 value. Some of these SL/TP settings were lucky, others were unlucky. The best settings found by each optimization are therefore not necessarily the best but just by lucky chance. We probably have chosen sub-optimal settings.

To properly select the best SL/TP setting, we should run 1000 backtests for each SL/TP setting and calculate the median profit for each setting, not the maximum profit of the lucky outliers. Considering running 1000 backtests on my old machine takes about 2.5 hours, running 3 x 100 x 1000 backtests for all levels would take one full month of running backtests day-and-night...
  • #14
  • Jun 17, 2023 3:53pm Jun 17, 2023 3:53pm
Quoting yoriz
{quote} In this thread I will focus on "averaging down", but you are right that it might be interesting to do a similar thread on Martingale! {quote} Diversifying over multiple symbols will certainly yield a smoother equity curve as the peaks and valleys of the individual symbols average each other out. For the educational purpose of this thread, running 20 assets in parallel will complicate things too much. I would like to show the effects of averaging down in a simple understandable way. Thank you for your suggestions!
1. You can't simulate 20 assets at once in you "strategy tester" not because of your thread name, but because you can't.
2. Start with 0.01x leverage and even with 0.005x and YES you can average up or down. But: min lot size is 0.01 and it is 100$.

P.S. with all the respect you are trying to show the "effect" from the wrong side. "Effect" here is the min lot size.
Observer effect
  • #15
  • Jun 17, 2023 4:03pm Jun 17, 2023 4:03pm
Quoting ryuryu
1. You can't simulate 20 assets at once in you "strategy tester" not because of your thread name, but because you can't.
I am not sure what you mean by "because you can't". In MetaTrader 5 you can run one single backtest using multiple symbols at once. So you could create an EA that trades 20 symbols simultaneously in the strategy tester. But like I said, this only makes things complex for this thread.

Quoting ryuryu
2. Start with 0.01x leverage and even with 0.005x and YES you can average up or down. But: min lot size is 0.01 and it is 100$.
Leverage and lot size just magnify the profit/loss and give more/less drawdown. For now we can ignore that because we are focussing on create a good strategy. Later when we are about to trade the strategy we need to think about leverage and lot size. Usually I use a Monte Carlo simulation to determine what lot size I should trade. But that is for later...

Quoting ryuryu
P.S. with all the respect you are trying to show the "effect" from the wrong side. "Effect" here is the min lot size.
Can you elaborate what you mean by that?
  • #16
  • Jun 17, 2023 4:22pm Jun 17, 2023 4:22pm
Quoting yoriz
{quote} Can you elaborate what you mean by that?
Sure my friend! Average "trader" has how much? 200 - 2000$? With min lot size 0.01 (out of 100000$)
so, if you have 200$ you are 50x leverage out of 100, if you have 2000 you are 5x?
Please tell me where is the room for average up/down here?
Here we only have a liquidation engine room due to basic math.
Observer effect
  • #17
  • Jun 17, 2023 4:42pm Jun 17, 2023 4:42pm
My suggestion, take a moment and review the recent ryuryu posts. If you believe them and there is consistency and the posts make sense, continue to follow them. If not, draw your own conclusions.
  • #18
  • Jun 18, 2023 4:50am Jun 18, 2023 4:50am
Quoting ryuryu
{quote} Sure my friend! Average "trader" has how much? 200 - 2000$? With min lot size 0.01 (out of 100000$) so, if you have 200$ you are 50x leverage out of 100, if you have 2000 you are 5x? Please tell me where is the room for average up/down here? Here we only have a liquidation engine room due to basic math.
Do you mean that with a small account there is not enough room to take some draw down? Yes, that is indeed a worry. Using 0.01 lots, each point movement the AUDCAD is worth $0.75. Suppose we have a very conservative leverage of 1:30, then we can handle max. 8000 points on a $200 account. With the settings in the posts above, we would already eat up 6000 points if we hit the SL of the 4th level (200+2*1200+3*600+4*400).

Good point, ryuryu! An averaging down strategy apparently only works with a sufficiently funded or a high-leveraged account!
  • #19
  • Edited 3:29pm Jun 18, 2023 11:21am | Edited 3:29pm
Statistical Optimization (continued)

As discussed in post #13, the randomness of the strategy results in inaccurate parameter optimization. Some of the optimization results will be lucky winners, while others might be better in practice but happen to have bad luck during the optimization. Therefore, instead of selecting the maximum lucky winner, it is better to look at the median values.

I will redo all the steps before, but this time apply statistical optimization using the median results instead of the maximum. To make this practical (i.e. to avoid one full month of running backtests day-and-night), I decided to go for 100 backtests per setting instead of 1000. Probably less accurate, but hopefully good enough.

While the previous experiment was done with a level 1 SL/TP of 200/200 points, I decided to this time use 100/100. Although this gives only 1 hour 49 minutes (see post #2), I realized that only the 50% of trades that immediately hit the TP at level 1 will take 1 hour 49 minutes, but the other 50% of trades that reach level 2, 3, or 4 will take much longer.

So I started this optimization:
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Again searching for the best EntryHour between 1 and 23, but this time combined with RandomSeed 1 to 100. Effectively this runs 100 random tests per EntryHour. These 2300 backtests took quite some time, but eventually gave a nice result:
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We export the backtest results to a spreadsheet and calculate the median profit per EntryHour:
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That looks like a nice smooth graph! Compare that to the erratic looking results we got before in post #3:
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There was no clear winner in the earlier experiment. This time, it is obvious that EntryHour=16 is the best choice!

Optimizing based on the distribution of many optimization runs per setting rather than just one optimization run per setting looks like a more robust approach.

Let's try that same approach for optimizing Level 2...
  • #20
  • Edited 4:44pm Jun 18, 2023 2:09pm | Edited 4:44pm
Hi Yoriz,

I take a similar approach to data analysis (Monte Carlo approach per parameter change) but use Amibroker and Excel. Not quite as elegant as yours though... Looking forward to your next installment!

Best,

Dave
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