The median maximum drawdown

[nonlinear5]

I know, the term "median maximum drawdown" may sound confusing, so let me explain.

Suppose you have a mechanical trading system S which made N trades, with total return R and the maximum drawdown MD. Let's shuffle the trades (i.e. do a Monte-Carlo simulation). The trades are the same, but the order is different. The total return R will be the same, but the maximum drawdown would be different.

Now, the question is, which "maximum drawdown" should be used for the purposes of the trading system evaluation? There are several candidates:

1. The maximum drawdown from the original sequence of trades (that would be MD)
2. The maximum drawdown from the Monte-Carlo simulation (that would be greater or equal to MD)
3. The average maximum drawdown from the Monte-Carlo simulation (that could be greater or smaller than MD)
4. The median maximum drawdown from the Monte-Carlo simulation (that could be greater or smaller than MD)

I thought about this for a while, and it seems to me that measure (4), the median maximum drawdown, is the most meaningful. What it identifies is the most likely maximum drawdown when trades are reshuffled many times.

In this thread, I don't want to argue about the merits of mechanical or discretionary systems. Let's just see if we can figure out the optimal way to measure the system max drawdown. Thanks.

 

[Crispy]

I know, the term "median maximum drawdown" may sound confusing, so let me explain.

Suppose you have a mechanical trading system S which made N trades, with total return R and the maximum drawdown MD. Let's shuffle the trades (i.e. do a Monte-Carlo simulation). The trades are the same, but the order is different. The total return R will be the same, but the maximum drawdown would be different.

Now, the question is, which "maximum drawdown" should be used for the purposes of the trading system evaluation? There are several candidates:

1. The maximum drawdown from the original sequence of trades (that would be MD)
2. The maximum drawdown from the Monte-Carlo simulation (that would be greater or equal to MD)
3. The average maximum drawdown from the Monte-Carlo simulation (that could be greater or smaller than MD)
4. The median maximum drawdown from the Monte-Carlo simulation (that could be greater or smaller than MD)

I thought about this for a while, and it seems to me that measure (4), the median maximum drawdown, is the most meaningful. What it identifies is the most likely maximum drawdown when trades are reshuffled many times.

In this thread, I don't want to argue about the merits of mechanical or discretionary systems. Let's just see if we can figure out the optimal way to measure the system max drawdown. Thanks.

I understand the end goal you are trying to reach. But I can almost guarantee you the maximum draw down across all your tests will probably be the one that happens real time. Whether it happens right off the bat or mid stream wont matter ultimately if you hold fast in the end right? Assume the nuclear worst always.

This is not a flippant answer. I am being sincere.

 

[nonlinear5]

I understand the end goal you are trying to reach. But I can almost guarantee you the maximum draw down across all your tests will probably be the one that happens real time. Whether it happens right off the bat or mid stream wont matter ultimately if you hold fast in the end right? Assume the nuclear worst always.

This is not a flippant answer. I am being sincere.

Thanks, Crispy. I think a lot of people would agree with you, but I believe that assuming the "nuclear worst" leads to suboptimal decisions (and more specifically, to under-allocation of capital to trades).

 

[Crispy]

Thanks, Crispy. I think a lot of people would agree with you, but I believe that assuming the "nuclear worst" leads to suboptimal decisions (and more specifically, to under-allocation of capital to trades).

You are welcome.

Thats a fair assumption. But I dont know how you get around it other than a good position sizing plan. Which is critical anyway.

Good luck! Keep us posted with any findings you have.

 

[nonlinear5]

Thats a fair assumption. But I dont know how you get around it other than a good position sizing plan. Which is critical anyway.

Right. To keep things simple, I didn't want to get into the discussion of position sizing. But the reason I am into this quest of measuring the max drawdown is because it's a measure of risk, which determines the position sizing. So these things are related. I'll post more on this later on.

 

[xelite777]

But I can almost guarantee you the maximum draw down across all your tests will probably be the one that happens real time

True, they say the maximum drawdown is yet to come.

Assume the nuclear worst always.

Yes, but you still need to use some specific value for the maximum drawdown.

Why is that?

Because the maximum drawdown will allow you to calculate the ratio for pyramiding your winning positions and/or compounding your trading account.

In general, robust trading systems rarely exceed 2 times the maximum historical drawdown, if ever.

 

[Crispy]

True, they say the maximum drawdown is yet to come.



Yes, but you still need to use some specific value for the maximum drawdown.

Why is that?

Because the maximum drawdown will allow you to calculate the ratio for pyramiding your winning positions and/or compounding your trading account.

In general, robust trading systems rarely exceed 2 times the maximum historical drawdown, if ever.

OK.

I use a static method. 1 car for every 2500 in capital for ES intraday as an example(volatility adjustment is another can of worms but lets assume normal volty range). My drawdown period position size is adjusted as per the ebb and flow of cap base. So, drawdown occurs, size is smaller. And vice versa.

What im saying is that isnt position sizing method more organic that way than assuming some backtested max drawdown from day one? Or am I missing something? Frankly what works for me works for me and probably wont change in the near future. But I am really curious how others approach the subject.

Thank you.

 

[nonlinear5]

OK.
What im saying is that isnt position sizing method more organic that way than assuming some backtested max drawdown from day one?
Thank you.

I think there is something more organic than simply using a static allocation (such as $2500 per contract, as in your case). I believe the capital allocation (i.e. position size) should be based on the risk/reward profile of your strategy.

To illustrate, consider the results from one of the systems that I have:

Leverage	MaxDD	NetProfit
10		20	1100
12		24	7030
14		28	12890
16		32	184200
18		36	227500
20		40	274200
22		44	304500
24		45	329200
26		49	346200
28		53	360900
30		57	372000

It's the same intraday ES system in 11 different reincarnations, or 11 different levels of leverage.

The leverage is defined as
Leverage = ES contract size / capital per contract
For example, if the ES is trading at 1900, then contract size is
1900 * 50 (contract multiplier) = $95000
Let's say the leverage level is 14. Then capital per contract is
$95000 / 14 = $6785

The Max DD is the maximum drawdown in percents. The NetProfit is the terminal profit.

As can be seen from the table above, as leverage is increased, MaxDD goes up, and NetProfit goes up, as well. That is pretty much what we expect. Now, the question is, at what level of leverage would you trade this system?

 

[dom993]

I think you are making things difficult for yourself.

Make a 10,000 run (MonteCarlo simulation) for 1 year worth of trade (if your system averages 500 trades / year, that's what you simulate in those MC runs). Use a fixed position size of 1 contract, or a fixed $$$ risk per trade.

For each run, capture the Peak P&L, Ending P&L, max DD $, max DD duration.

Look at the distribution of your max DD. Compute its average & stdev. If trading results where a normal distribution, you could safely use 2 stdev away from the average as your system max. possible DD. Unfortunately, tradings results are not a normal distribution, you'll have to use a few more stdev as a buffer (I use avg + 5 stdev as a starting point).

Add the margin requirement for 1 contract to that amount, and you have your min account size for 1 contract for that system. You don't need any more funds for that 1 contract, and using less than that might have you run out of funds during a severe but "normal" DD.

I like to look at where the max historical DD stands in the MC max DD distribution - most often times, it is right at the average, or within +/- 1/2 stdev ... if it further away than 1/2 stdev, you might want to look at that period of time, and find out why your system was underperforming through that period.

 

[nonlinear5]

Make a 10,000 run (MonteCarlo simulation) for 1 year worth of trade (if your system averages 500 trades / year, that's what you simulate in those MC runs). Use a fixed position size of 1 contract, or a fixed $$$ risk per trade.

For each run, capture the Peak P&L, Ending P&L, max DD $, max DD duration.

Look at the distribution of your max DD. Compute its average & stdev. If trading results where a normal distribution, you could safely use 2 stdev away from the average as your system max. possible DD. Unfortunately, tradings results are not a normal distribution, you'll have to use a few more stdev as a buffer (I use avg + 5 stdev as a starting point).

Add the margin requirement for 1 contract to that amount, and you have your min account size for 1 contract for that system. You don't need any more funds for that 1 contract, and using less than that might have you run out of funds during a severe but "normal" DD.

Your approach makes sense to me. There is something missing, though, which is the consideration of the gains with respect to the trading size. In your calculations, you appear to use the drawdowns along. I think every system has an optimal level of leverage that it can be used with, and I think that level is the one at which the following ratio peaks:

ratio = ln(net profit) / medianDD

where ln is the natural logarithm.