How risk multiplier really affects monthly gains and drawdowns

I invented the following values just for the example. Imagine I have an strategy with this expected outcome:

Strategy 1x:
- Monthly gain: 4%
- Expected drawdown: 12%

My understanding is that if I copy-trade that strategy with a risk multiplier based on account equity of 4x, this will be the expected outcome:

Strategy 4x:
- Monthly gain: 16%
- Expected drawdown: 48%

Now suppose that at any given point both strategies have an equity of 10,000$. Then suddenly the max drawdown of both strategies is reached, so Strategy 1x reaches 8,800$ (12% drawdown) and Strategy 4x reaches 5,200$ (48% drawdown). After reaching this max drawdown, the strategies start performing well and reach their expected monthly gains exactly and consistently until they both reach 10,000$ again.

Based on the previous statements I would expect something like seen in equity graph A below, where the green line is Strategy 1x and the red line is Strategy 4x:



However, actual calculations tell me that's not gonna happen. Actual calculations tell me that it will take more time to reach 10,000$ again to the Strategy 4x, that is the red line in graph B above.

The way I calculated it is as follows:
Strategy 1x: 8800 * 1.04^x = 10000, where x is the months until reaching 10,000$ -> x = 3,26 months
Strategy 4x: 5200 * 1.16^x = 10000, where x is the months until reaching 10,000$ -> x = 4,41 months (more time!)

At this point I'm totally confused about what would really happen, A or B, and I hope someone can put some light on the matter.

It comes from your assumption which is wrong. If you win x% and then lose x% (or vice-versa) the result is not BE. Even with 1% you get a negative drift. Say you start with $10000 win 1% then lose 1% your balance is now 9999. It looks like almost the same but $10k is a micro lot and the $1 difference is 1 pip. The drift is equilavent to the spread. The bigger the % the worse the "drift".

I understand what you mean with the drift, but where am I assuming that? Most importantly, which simulation is the correct one according to you: A, B or neither?

This all comes down to math and how percent gain and compounding works. You assume that you make the monthly gain on the amount left from the draw down and compounding works against you in this scenario.

4x strategy:

If you first loose 50% you have to make 100% to BE again.
1000 -> 500 and now you need to make another 500 = 100%!


1000 -> 880 you only have to make roughly 13.7% to recover and there you see the huge huge difference. The more you first loose the actually harder it is to gain it back if you decrease your position size accordingly to your balance.

13.7 % compared to 100%!

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The question is what number are you looking for? Effective monthly gain is what you get after all the losses and this is a complete different number from gain after draw down.

B is correct. The mistake is to say that "if I copy-trade that strategy with a risk multiplier based on account equity of 4x, this will be the expected outcome ...". The gain and DD aren't simply multiplied by four. With any system, at some point you'll get a loser followed by a winner. Say you trade 1%. The result is 0.99x1.01=0.9999. With 2%, the double, the result is 0.98x1.02=0.9996. The difference is four times greater not only twice.

I see. Your examples were really helpful. However if we are right and scenario B is the correct one, is myfxbook.com risk multiplier broken? When you select a risk multiplier of 4x, the expected drawdown increases by 4x, and the monthly gain increases by 4x also, you can test it yourself in AutoTrade demo account.

But according to this it's not so simple. So what I am looking for is now to answer the following question:

What would be a more realistic Monthly Gain (effective) and Drawdown with Strategy 4x given the data of Strategy 1x?

Risk multiplier will not help here. You need to base this on lot multiplier.
However there is a possibility that free marginc may not allow you to use the multiplied lots if drawdown is huge in 4X

I made another two simple simulations (graphs C and D bellow) which involve only two trades. C represents a loser and then a winner and D represents a winner and then a looser. In both cases according to my calculations the strategy that runs at double the risk (red line) ends with a lower equity. See:



At this point I'm still super confused about what trading a strategy with a risk multiplier of 2 or 4 really involves, when it's a good idea and when it's not.

Well what is monthly gain? Is it calculated with the draw down already factored in or without it? Both can be correct but first we should know what we are dealing with. The higher the draw down you have the harder it is to recover.

If you calculate your balance like this increasing both % accordingly will only show an increase in balance if your monthly gain is bigger than your draw down but!! the first question you have to ask yourself is how do you define monthly gain?
You can not scale up gain and draw down just like that.


Begin: 100.
Draw down to 80;
End of the month : 120
In your calculation you would go from 80 to 120 and say it was a gain of 66 %
If you look at the 100 and compare it to the 120 it's a monthly gain of 20%
66% compared to 20 % are not even remotely close numbers.

If I am not mistaken monthly gain and draw down are resulting numbers. You can not multiply them by 4 as they do not scale proportionally. You have to take a look at your trades multiply the lot size and recalculate your monthly gain and draw down over again.

I might post an excel spreadsheet in a few minutes

I'm defining Monthly Gain as the same figure that myfxbook.com displays for the strategies, i.e. the "monthly compound rate of return leading to the total gain". So the draw downs are already factored, everything is already factored. It's the monthly gain you should get on average every month.

I'll also work on Excel to simulate a real strategy based on balance risk multiplier and take a look at what happens if you multiply lot sizes instead.

it's an open office file. You can change the lot multiplier by increasing the average winner / average loose.

While with 50% win ratio

a RR of 1 gives a 50% dd and avg gain +-0

same RR but lot mult by 2

still a RR of 1 : 80 % dd and avg gain +-0
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With 60% win ration and RR of 1 (10/10) you get a avg gain around 100 and a dd of 40%
if we now simply multiply the lots by 2 (20/20) I get a gain of 300 - 400 and a dd of 65 %

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so it hugely depends on the expected values of your system. Maybe it's worth to take the additional risk maybe it isn't. I don't know exactly what fxbook or any trade copier does or mean by multiplication of risks but the way I did it I can understand it and evaluate my position size.

I have run a test with a real strategy traded over months with hundreds of trades and my conclusion is that when the risk is increased by 2x both the Monthly Gain and Draw Down are increased by aproximately 2x. Same thing with any other multiplier. I don't fully understand why but that's what the results show, so I guess that my initial assumption (made also by myfxbook.com) is in fact realistic.