Predicting the future maximum drawdown...

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pecas

Member
75 6
While my current view that the concept of attempting to calculate future anything is a quite pointless task, I haven’t always been such a miserable curmudgeon and remember being gung ho on all this really interesting stats stuff. So, FWIW:-

Chande’s method involves nothing more complex than multiplying your monthly standard deviation by 5.

But even the more complex manoeuvres in this area still require a nod to standard deviation regardless of whether you are considering a constant or stochastic volatility model so I’m not sure you can so easily disregard SD as bunny suggests.

Mean return and variability of return are key. As is quantity of data of course. While from a professional perspective you would be justified in expending the effort to provide a realistic (LOL) value for this parameter, it is largely meaningless from an operational trading viewpoint and possibly even counter-productive for a retail trader with insufficiently lengthy track record.
You're overestimating what i'm trying to do here, probably it's my ambitious thread title.
When I backtest a system I find a max drawdown value. I want to know if that value was likely to happen, give that sequence of trades, or if it was just a lucky combination (or unlucky, for that matter).
If it happens again in the next cycle, that's definitely hard to estimate, but at least I know what to expect as a likely result if the system continues producing, and I know what an "out of bounds" result looks like, making it easier to identify if/when the system is not working anymore.
 

pecas

Member
75 6
I fixed a bug in the script, regarding the confidence intervals of future profit.
I see there had been only 1 download of my script. Please download again.
The code posted has been edited as well.
Sorry for this.
 

TheBramble

Legendary member
8,395 1,169
When I backtest a system I find a max drawdown value. I want to know if that value was likely to happen, give that sequence of trades, or if it was just a lucky combination (or unlucky, for that matter).
If it happens again in the next cycle, that's definitely hard to estimate, but at least I know what to expect as a likely result if the system continues producing, and I know what an "out of bounds" result looks like, making it easier to identify if/when the system is not working anymore.
Every piece of performance data you extract from any given series of contiguous price data is idiosyncratic.

But even if you choose not to agree with that, it’s rare for any trader to go all the way to the ‘out of bounds’ scenario. Paradoxically, those that do tend to have invested (quite literally) so much into that losing position, they’ll more likely sit on it rather than kill it, or even as DD suggests, simply reduce exposure.

Reaching maximum drawdown or maximum consecutive losing trades (that used to be my favourite) before considering the system a loser overall are the prime benchmarks for evaluation of back-tested systems. But that is an industry in itself and of little relevance to the realities of trading.

Just my view.
 

eegozi

Active member
126 11
Hi,...Nice thread topic. I must tell you that recently I have been studying EXACTLY this and other stats on a trading system I am developing. I have done extensive reading and testing and I will sum up my findings for you about Max DD. BOTTOM LINE,...your Probability win rate determines your max drawdown and risk of ruin. People say that having a HIGH win rate is not important for a winning system and this is true. However, win rate will NOT effect profitability,...It effects draw down and risk of ruin. Take the extremes for example....a lottery like POWERBALL LOTTO with say 1 in 60 million chance of winning $50 Million dollars. IF you are that 1 in 60 million winner you have a large profit...win rate does not effect profit. However, you could spend >60 million dollars (assuming tickets cost $1 each) just to make that $50 mill. THAT is also assuming you make every combinaton of possible ticket numbers ONLY ONCE....However, as in trading you could have multiple losing trades in a row by effectively pulling the same numbers randomly (ie making the same trade...or pulling the same marble/paper out of the bag of marbles). The LOWER THE WIN RATE the HIGHER THE LIKELIHOOD OF HIGH STRING OF LOSERS!!!....that is the key!! Since higher string of losers would ultimately effect a larger drawdown you would have a high risk of ruin with HUGE draw downs as win rate goes down.

The opposite is true of HIGH win rate. Say you have a 90 % win rate then your draw down is Very low!! Every time you place a trade you have 90% chance of a win and so your acct will not likely lose money even if you only make a small profit on each trade. Again Win rate does NOT effect profit ONLY DRAW DOWN. I will post information I have posted on another forum on this same topic. In those posts that will follow here I will show you in more detail what i mean and provide solid examples with statistcal analysis to show what I mean.

Also, it is key that you realize that what someone above said about picking a piece of paper and then writing down trade result and then PLACING THE PAPER BACK is absolutely CORRECT. Your prior trades DO NOT effect subsequent trades. If I flip a coin 10 times and the first 4 are all heads does that influence the 5th time I flip a coin....NO....I still have a 50% chance of heads or tails. You can have as many as 10 heads or all 10 tails and obviously any combo in between. So ech coin flip (think trade) has NO bearing on future coin flips. You just know that if you flipped a coin say 2 million times that ON AVERAGE you would have 1 million heads and 1 million tails but there could be strings of each interspersed.

I hope this helps...see my following posts that I will copy from posts I made on another forum.

BTW the statistical analysis you should be doing is a Monte Carlo Simulation wherby you run the same 100 or 200 trades OVER and OVER again 10,000 times. Thats 2,000,000 trades and should give you a distribution of the samples that your system generates. I will refer to these in the future posts with charts I will post.

Good Luck
 
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eegozi

Active member
126 11
Quote from intradaybill:

Irreleavant statistic. The most important ststistic IMO is the profit factor. Must be bigger that 1.75. Then you are doing well. You can have 90% win rate and still get ruined.
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It absolutely is relavant!!! It is MUCH harder to face ruin with 90% win rate than 10%. It all factors together is my point. All of these issues, profit factor, expectancy, and probability of winning trade, and standard deviation between each trade's win and losses also play a role in your overall performance. However, a higher win rate reduces drawdown which HELPS reduce your volatility of your account's equity. The more times your trade is a winner (even if small) will minimize your string of losses and minimize drawdown. With lower probability trades you need bigger profit wins to make up for the multiple losses in a row you would face. I would MUCH rather have a system with 0.3R expectancy and 90% win rate than a 0.4R expectancy and 10% win rate.

Lets say you have a system that has 0.3R expectancy so in 10 trades you have 9 that make on average 0.44R and one 1R loser with total win of 3R in 10 trades = 0.3R Now take a system with 9 losses in a row of 1R each. Your last win would have to be 13R to make up for the 9R losers and make4R divided by 10 trades = 0.4R expectancy in 10 trades. However, because each trade is INDEPENDENT of what occurred on the prior trade it does not matter whether the prior trade won or lost as the prior trade does NOT INFLUENCE the next trade. So your chance of a loss is STILL 90% on the next trade. You easily could rack up 20+ losers in a row with this system and likley only rack up a max of about 2-3 winners in a row. Over 10,000 trades this may all even out but few of us would have the conviction to trade a 90% losing system with HUGE drawdowns of 20 losers in a row or more. Do a Monte Carlo analysis on a system like this and you will see what I mean. This is a poor system to trade...you are better off flipping a coin (50:50) for your trade direction.

This has been explained in GREAT detail in "The Definitive Guide to Position Sizing" by Dr. Van K Tharp for those that are interested in reading more about this.

Again, probability is NOT the end all be all of trading but it sure as hell helps!!!

(If you have read this far notice that I was having a discussion about reducing risk per trade to 0.1% per trade and 1% per trade. Some one suggeted that this would reduce drawdown and volatility. NOtice that 0.1% risk on a low win rate does NOT effect volatility of the system equity.)
 
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eegozi

Active member
126 11
OK,...here is a MC Sim for 2 different systems. BOTH systems will have a 0.4R Expectancy and assume a starting capital of $100,000. The first system has a win rate of 10% and the second 90%. These are the ONLY differences in the systems. Both MC simulations are done and posted below. Both simulations are of 200 trades simulated 10,000 times!!! This is 2,000,000 trades.

Both MC sim are done using ONLY 0.1% capital at risk per trade. Notice that this is considered EXTREMELY conservative by most standards as most would say 0.5-2% risk is typical for trading. The ONLY reason I have included this 0.1% risk MC Sim is to show that at 0.1% capital at risk you could still have significant draw downs and wide possibilities of outcomes in trading with a 10% system. This 0.1% was also the amount of risk that intradaybill mentioned in a prior post as if that is somehow going to prevent draw down. It does not. It only reduces the rate of bleed and possible ruin. Realize also that everyone has a different definition of ruin. For me 20-25% draw down I would consider ruin. For others this number may be 50% or 100%. Everyone has to decide for themselves what that number is.

Notice that the 10% system has a PEAK of $37,000 GAIN and nearly -$12,000 LOSS. Also notice that the longest string of losers is 33!!!! The longest string of winners is 2!! NOTICE THAT AVERAGE WIN WAS $9500 OVER THE ENTIRE SIMULATION!!!! THIS IS IDENTICAL TO THE AVERAGE WIN FOR THE 90% SYSTEM.

(sorry about the ALL CAPS,..I can not figure out how to bold something here..LOL)

Compare that to the 90% system. Peak win is certainly lower but so is the peak draw down. This system has a max Draw down of -$370. Also notice that ALL of the simulations produced a NET profit even the MINIMUM profit was $7,000 (7%). Point is that the 90% system has less draw down and ZERO possibility of ruin and 100% chance of a winning year.

The obvious question is now for the 90% system with ZERO chance of a losing year am I risking too little per trade? I would say the answer is YES. You could do MUCH better with this system by only changing the amount risked per trade. Lets see what happens with 1% at risk,....to be continued below.

First pic is 10% system at 0.1% risk. Second one is 90% system at 0.1% risk.
 

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eegozi

Active member
126 11
Ok so now lets look at the SAME systems with a 1% risk of capital per trade. Again lets assume a $100,000 starting capital. Again 200 trades simulated 10,000 times.

Notice that now the risk of draw down goes up even with the 90% system. However, also notice that in the 90% System the MINUMUM is still a $50,000 Win. Thats 50% folks!! Nothing to sneeze at as a MINUMUM win. MAX is $103,000. This suggests that even more risk could be taken with this system and maximize gains.

Notice that the 10% system has a MAX Draw down of $101,000!!! YIKES!!. MIN P/L with this system is -$100,500 LOSS!!! That is complete RUIN by anyone's definition. I do realize that the MAX Gain is higher with this system but that is only because of the higher profit of the winners when they occur. This is the same a intradaybill was describing "Trend Following Mutual Funds" that have trades that win for months & years (large R gain) for MANY small (1R) losses. Again the AVERAGE win for BOTH systems is about $80,000 (give or take a little)

So,...Probability of win IS RELEVANT!!! Realize one last thing that ALL MC Sim assumes the trader will trade the system EXACTLY the same as when the stats were collected and that the stats are a good representation of the market that will come in the future. It also assumes that you will trade it 100% mechanically and that your emotions will not falter. I dare say that anyone's emotions would come into play after a string of 33 losses with the 10% system. So your results will likely be less than the MC simulation. So with a 90% system you have room for error,...NOT SO MUCH with 10%.

I hope this clears things up a bit....Good Luck!

First = 10 % system at 1% risk and Second = 90% system at 1% risk.
 

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JRP2891

Established member
752 125
So with a 90% system you have room for error,...NOT SO MUCH with 10%.[/B]

I hope this clears things up a bit....Good Luck!

First = 10 % system at 1% risk and Second = 90% system at 1% risk.
The only 90% systems i know of, are the ones that go by names like; "Forex Robot Destroyer", "Forex Predator", "I'm going to eat your lunch for you - MK2", and "Here Comes the Big Bad Wolf Money Hoover".
 

Yamato

Legendary member
9,840 245
This is a very useful thread for me, so I hope it will keep going. I think a question mark should have been added at the end of its title, because as I have been studying a little bit of probability (being math illiterate), I have increasingly realized that it's not possible to predict the future maximum drawdown, which is potentially infinite. After a lot of thinking, and losing, I have understood the problem is:
1) how to appraise the probability of x future maximum drawdown
2) how to build a portfolio so to optimize (reduce the probability/size of) the... "most likely" future maximum drawdown

I just found a related link on the subject:
Reliability of the Maximum Drawdown
...For this reason, it is better to judge risk from observed volatility than from observed maximum drawdown.
I understand little of what it says, but it's definitely related to this thread and maybe similar to something Vince says, and, even though I didn't read almost anything by him (just a few lines), he seems to say that drawdown is not very useful. Here's two links to his books in .pdf (which hopefully I will be able to read within the next few years):
Portfolio Management Formulas - Ralph Vince..pdf
http://www.fxf1.com/english-books/MathematicsMoneyManagement.pdf

The math discussed on this thread is too advanced for me ("montecarlo simulation", etc.) but I hope the discussion will continue (hopefully simplified or I won't understand), so I can learn something more. It was useful for me to read here (more than one person said it) and understand how previous trades do not affect subsequent trades, as in a coin toss experiment. At first it didn't seem right, but later I was convinced of this, even though I'd like to point out that it holds true only as long as we're not talking about a system that only goes long on a future like the SP500, because in that case, the more it falls and the more it's likely to rise. In that case, we could not say that previous trades do not affect future trades.

Here's some more good links related to this thread:
Risk of Ruin
Risk of Ruin Index
TraderFeed: How to Avoid Risk of Ruin in Trading
 
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bradypreston

Newbie
5 0
Have you ever tried using statistics to determine the expected drawdown, in place of using the backtested drawdown. Statistical worst case scenario will usually give you a more accurate measurement of future drawdown.
 

Yamato

Legendary member
9,840 245
Yes, I think I've been trying to use something similar maybe (according to what I've understood of your post). I'll try to explain my idea. I've been noticing that the concept of backtested maximum drawdown is not as useful as the concept of... variability, of the frequency of falls, in other words of the (backtested, once again) drawdown from every point on the (backtested) equity curve to the subsequent lowest point. For example, I would say that, always within backtested data, a portfolio of systems (or a system) whose maximum fall peak-to-trough is 10k but has no other >9k falls, could still be better than a portfolio of systems (or a system) that has a smaller max fall, but a lot of >9k falls. With my limited math knowledge, i can see this is related to the way sharpe ratio measures performance and variability, but I see that sharpe ratio gives me a ratio of profit vs variability, and that it doesn't give me the same information as to my risk of blowing out with a given capital, according to the past behaviour (back-tested data).

Anyway, once I started to think in terms of probability theory (which I ignored completely until recently), and once I understood that maximum drawdown is not a guarantee of future performance but only an approximate indication, I also realized that there's other, more accurate, ways to forecast my probabilities of success/failure.
 

donaldduke

Experienced member
1,665 251
You can control max drawdown size through position sizing.. however you cant control how long a drawdown will last ( at least not without abandoning your system).

Here is a chart of Dunn Capital fund performance, long term trend following.. note the 7 year long drawdown starting around year 2004.
Prior to that the largest drawdowns were 'only' about 2 years long. This is reason long term trend following is so hard to do without giving up, most people cannot take even a 1 year drawdown let alone a 7 year one.

 

Earthling

Junior member
14 3
I have just finished listening to an audiobook: “Fooled by randomness”, by Nassim Nicholas Taleb, that discusses maximum possible historical drawdowns / trading disaster scenarios, tying it in to montecarlo analysis, survivorship bias etc. No formulas in it though, just general explanations. It was interesting to me because he talks about the traits of potentially ruinous risk taking and of conservative risk management, I could physically point at examples of both as I was listening to it.
Sorry – I know its just another book, but its an audio book, so its good for a walk or something. (Its 10 hours though, so thats a long walk.)