Performance report: missing max drawdown in %!

While trying to see if my Z12 demo is also within it's statistical boundaries, I think I uncovered why that was near impossible to calculate so far. The important piece of information seems to be missing in the performance report!

Taking the Z12 (M/R 50/10) as an example, the performance report says: Max drawdown -2355$ 9% (MAE -3281$ 12%). I suspect that first max drawdown is calculated (in dollar value!), and 9% is just attached, leading to thinking that 9% is the max drawdown. But it is not! Just by looking at the drawdown curve, there could've been a slightly smaller drawdown (say -2000$) but at the time where equity was much smaller leading to a much bigger drawdown percentage-wise (maybe 20% or 30%), yet I don't see that number anywhere in the report. Could this number be added in the future version, please?

I was also thinking along the lines, maybe I could take the biggest dollar amount (-2355$ in the example) and divide it with the required capital (3762$)? This would be a situation where right at the start of trading, the strategy goes in a deep drawdown. But numbers I get that way, ~63% drawdown in the example, are just way too big to be usable or trusted.

To explain from a different angle, to say that my Z12 is still within statistical boundaries, I would need to compare it's current drawdown of about 40% (after taking into account much bigger starting capital) to the max drawdown as calculated by the backtest. If I compare with 9% (or 12% MAE) numbers from the performance report, I could conclude that it should've been stopped ages ago. But if I compare it with 63% calculated above, then it's supposedly OK that it's 40% in drawdown, although it's really not.

I suspect Z12 had about 20-30% max drawdown in the backtest, but there's no number in the performance report reporting that vital information!

All performance analysis software, including Zorro, normally displays the max drawdown in dollars and in percent. But it cannot tell you when the max drawdown will happen, or what is the same, at which equity value it will happen. That is mathematically not possible.

Thus, the equity value at the time of the max drawdown in the simulation is meaningless and can not be used for calculating the drawdown percent value - a drawdown can just happen anytime.

I'm not satisfied with the answer, which means either you misunderstood my question, or I'm missing some detail that you take for granted. I'm certainly not that interested in the time component of the biggest drawdown. But, I want to know what is its value expressed in percentage.

Let me rephrase the question. If performance report says that max drawdown is 9%, can I trust that there certainly was no 10% drawdown at any point in time that the backtest covers?

IOW, are the dollar value and percentage (of max drawdown) in the report independently calculated? And thus can refer to 2 distinct points in time, one when there was biggest drawdown in absolute terms, and the other when the dollar value was smaller, but equity dropped by a bigger percentage?

Maybe an example is in order again:

1)
Eq peak: $1200
Eq valley: $1080

2) (later)
Eq peak: $12000
Eq valley: $11400

Drawdown 1) is $120, 10%
Drawdown 2) is $600, 5%

Obviously max drawdown in dollars is $600, but percentage-wise max drawdown is not 5% but 10%! What numbers would performance report show in the above example?

a) $120/10%
b) $600/5%
c) $120/10%

To me, this still suggests that the drawdown is linked to the prior run up, exclusively. I don't think you can make this assumption. The only way that it can be linked is if the market type changes, e.g. from quiet bull to volatile bear. And that change happens a few times in the backtest period. Generally mechanical trading does not take into account these types of market type changes, or is not good at it. I won't go into the theory as I understand, but it's a Van Tharp concept.

OR, maybe you want to normalise the drawdowns in that case of using a compounding / profit reinvesting feature. Generally a backtest is best done one a none compounding basis. Later, when you are satisfied that it is profitable and robust, you can play with the position sizing strategy to determine how best to compound the result.

The percentage is of course from the total strategy profit, not from the account equity.

And I still have no answer, is it a), b) or c)?

What we're missing here are the 2 extremely important concepts that I can't accomplish unless I know statistical parameters of the backtest, where max drawdown (expressed in percentage!) is probably the most important one.

1) To adapt my personal risk tolerance to a specific strategy, I need to know its max drawdown, so that I can decide how much capital to invest. For example if backtest say 20% is the max drawdown, and I don't accept more than 10%, I need to at least double the minimum required capital (halving the leverage and max drawdown in the process).

2) To decide when to stop trading a strategy, I need a criteria that describes that event. The best advice I find so far is to declare strategy unprofitable when it has reached double it's max drawdown, as calculated by the backtest. So in out example, if MaxDD 20% strategy reaches 40% drawdown, I better stop trading it. Of course, if I applied my money management strategy from the previous paragraph, I would have lost about 20% of capital by then.

Am I getting through?

One more thing, when you jcl say that your Z's are within statistical boundaries, it tells us absolutely nothing. Because, we don't know what's your criteria? You might say it's within boundaries if you still have any capital left in the account you're trading. Or that you have more than a half. We really don't know, so the statement is to be discarded as vague.

Do you want to compare the max drawdown to the max run up as a percent, regardless of whether they occur consecutively or not? That makes sense to me. It is a ratio that is independent of starting point or place in the equity curve.

If not, then I will need to think about what you are asking.

I look at drawdown in its most basic definition. Here, the one from Investopedia is useful: "The peak-to-trough decline during a specific record period of an investment, fund or commodity. A drawdown is usually quoted as the percentage between the peak and the trough."

See, it evens mentions in the second sentence that drawdown is usually quoted as the percentage. But Zorro for some reasons insists on dollar value as more important and adds percentage after, but I'm not sure if that percentage number is really usable and what I'm looking for? That's the whole reason behind this whole thread.

Also, I don't understand why time, point or place in the equite curve is coming as a topic in this thread, when I'm specifically interested only in value, not time?

This is one of those topics where I have specific and very simple issue, yet even after many longish explanations from my side, I'm unable to get this simple answers. I had so many such in the past and did really stupid things because I never got my answer. This time I will persist and not continue with anything until this is resolved. I understand there're language barriers, english is not my primary language, and automated trading is complex subject. Yet...

Another example:

Strategy A drawdowns in time (quoted as percentage): 5.1%, 7%, 12%, 3%, 2%

Strategy B drawdowns in time (quoted as percentage): 12%, 7%, 5.1%, 3%, 2%

For strategy A I want to know max drawdown quoted as percentage. It's 12%.

For strategy B I want to know the same thing. It's also 12%.

Notice how the time when the drawdown happened doesn't matter, I simply want to know what's the biggest value.

Notice also how I do not care about dollar value of drawdown, because it is useless without additional context. But value quoted as percentage is useful without any additional info.

Additional examples:

I have this strategy and it has only 10% drawdown, you can trade it as it is (i.e apply full optimal capital to it), because the drawdown is reasonable. I have another experimental one which has 80% drawdown. I wouldn't recommend trading it with more than 20% of your capital, otherwise the risk od margin call is way too high. Do you agree with those statements? Are they simple and understandable enough?

Now third example: I have a strategy that has $55 drawdown. Is it good or not? Would you trade it or not?

Still trying to parse the above...

So, if there's no profit, there's no drawdown? How do I measure drawdown then if I have a loss? If I'm in drawdown (sic!) from my initial capital?

I still do not really understand your problem with the concept of drawdown percentage. Neither of your examples is related to it. DD% is a very simple calculation that is used in most trade platforms and described on many websites:

When a system makes $100 profit with $50 drawdown, its drawdown percentage is 50%. If it makes $50 profit with $50 drawdown, its drawdown percentage is 100%. If there is no profit, its drawdown percentage is infinite.

- As to the check of stratey expiration, we compare the drawdowns so far with the drawdown that is displayed when you click "Test". The algorithm is considered "expired" when the real drawdown exceeds the projected drawdown. You can easily do that yourself with a test run. Only difference is that we check the drawdowns of all Z components separately for removing possibly expired components from the portfolio.

I think I never said I have any problem with the concept of drawdown. Obviously I see it as a very important concept. What I have problem with is Zorro performance report where I don't see max drawdown number quoted in percentage. The number closest to the needed number on the report I don't trust, so I asked for clarification. Here we are on the second page, and the original question has still not been answered. Like we're speaking (writing) in two different languages?!

I have half a dozen very direct questions in this thread already that have all been completely ignored. Instead I now learn that I have a problem with a concept of drawdown. Sheesh... And answering only few of those questions would bring light to this issue. Do I need to extract them and taxatively quote once again, and would you be willing to give direct answers to direct question?

Yes please. What did you not understand with the drawdown percentage and with my simple examples above? Just ask and I'll answer.

If I understand correctly he wants to know why in the Zorro report max drawdown is not shown as a percentage of equity peak at the point it occurred but in dollar values.

As I said repeatedly, it is a percentage of the profit, because using the equity peak amount would simply be wrong.

Incredibly simple question: my Z12 demo is currently $2400 in drawdown. What is the drawdown percentage?

9.17%

And by which magical formula you have arrived to that number?

It's called the "rule of three". Max DD = $2355 = 9%, thus 9*2400/2355 = 9.17%

BTW, did you get this drawdown really with the default settings? It would already exceed our expiration criteria, so we would have to pull this system if we got a similar drawdown.

Huh, now I'm lost completely. It seems that my mind is totally wrapped arround percentages, while you designed Zorro to pay special attention to dollar values. This way we will probably never really understand each other.

But, let me point out one obvious thing that comes out now at the end of this discussion. When I ask about a strategy drawdown expressed in percentage, your answer includes rule with a funky name that includes the number from the backtest of that strategy??? Now that is EXTREMELY weird. Obviously I once again made a mistake and let you do that by choosing a strategy that has known backtest results, but who would've thought it would end like this? How do you then calculate drawdown of the strategy that has not been backtested? Obviously you're missing values for your forumula. Question after question we're just going deeper into the rabbit hole...

I give up. Too much energy for nothing...



No, Margin was at 100 most of the time, so the number should be slightly bigger. At least you finally revealed your criteria for strategy adequacy, so this whole thread was not in vain.

Well, to summarize, my 9.17% answer admittedly did not make much sense in that context because your question didn't either. If you want a percentage of something, you first have to tell the percentage of what.

In a performance projection, the drawdown % is a percentage of the profit. I understand that if you lose some amount x, you might be interested in other percentages, such as how much x is in percent of your current capital. But that, although certainly important for you at that point, can not be predicted by a performance projection of a strategy.

Which "rule of three"? https://en.wikipedia.org/wiki/Rule_of_three

And how is it being applied, exactly?

jcl, I appreciate all your comments, but sometimes they do seem to miss and/or avoid the point. Probably because you're too busy single-handedly (mostly) dealing with all the forum posts along with whatever else you do...

I don't understand why you say the 9.17% doesn't make sense. To me acidburn's question made sense, and should have received a sensible answer...

I too am struggling with Drawdown, Return, and how to maximize return and robustness given the requirements of use of capital, etc.

Thanks.

EDIT: My example was not clear about the peak balance. Corrected.

Clearly you guys are in a different time zone to me! I would like to make some notes, but if I am missing the point, please ignore.

Firstly, Acidburn's cited drawdown definition is correct and that's how one would calculate when live trading. It is dependent on the definition of peak...Peak at the start of live trading is the initial balance of your account. Peak at the start of a back test is usually $0.

A similar example. Suppose your system makes $100 / month in the winning months and loses $100 / month in the bad months. Suppose April is going to be a bad month. If you start trading in January with an initial balance of $100, you will have a run up of $300 to peak $400 balance, then a loss in April of $100. So at the end of April your drawdown will be 25%. If you started trading in February with $100, you would have a run up of $100 to $200 balance and then a loss in April of $100. Thus you drawdown at the end of May is 50%. Same $100 drawdown, two different percentages. In a backtest, the initial balance is $0, so in the two examples above, the drawdown would be 33% and 100% respectively. Four different percentage drawdowns.

I believe this is why jcl finds the question to be confusing. Peak prior to drawdown to calculate drawdown percent depends on the initial balance and how much run up you have before the drawdown.

My solution....Personally, I like expressing all trades in terms of R-multiples (another Van Tharp concept.) Your initial stop is how much you will risk (R). Then the losing trades are -1R unless you move your stop further or closer. The winning trades are some positive decimal of R, e.g. +2R. Essentially you are normalising every trade to the risk. This is useful because you can determine the max drawdown in terms of R multiples and apply that to your risk per trade. E.g. suppose your backtest said that the greatest draw down that theoretically occurred was 20R. If you are risking 1% of your account on each trade, then the greatest theoretical drawdown is 20R x 1% = 20%. Therefore at 1% risk, you stand to lose 20% of your account if you go through the greatest historical drawdown in the future.

Problems with this approach - Firstly, your account goes into draw down, your 1% risk should gradually represent smaller amounts. I.e. First loser 1%, second loser 1% of new balance which is 0.99% of original balance, etc. This actually works for you in that at then end of 20 x 1R losers, you are not down 20% from the peak. You would be down about 17.9%. But it is good for getting a feel for risk and where you are on the equity curve.

Second problem, people come up with complex position sizing strategies. jcl even states that the fixed percent model is statistically doomed. So exactly how to apply R-multiples to the model jcl suggests with OptimalF is beyond me. In fact, when Acidburn was trying to understand OptimalF last year, I was totally clueless (one day I will apply myself to that one.)

Finally, this approach is not adopted in any software I know of. I find it odd as it is the way that I view the world of trading. It is the colour of my glasses, so to speak. Yet so many traders (and software) do not record the stop in the trade log. So you don't have a record of what you were risking. Seems strange to me given that this is a risk management game.

Ok, that's my bit. Hope I have helped a little, at least with my explanation of drawdown percent.

There is another problem with the concept of R multiples. It is intended for manual trading when you don't apply much thought where to place the stop, and always put it at a fixed distance. In atomated trading, stops are usually optimized and depend on volatility. So there is no R, and the system risk is unrelated to the stop distance of a single trade.

Hi all.

DMB, not sure who's in what time zone when (except maybe jcl ), or who has what native language, but at least we can all try to communicate! I'll look at your post later - for now want to try to stay closer to current Zorro...

jcl, I'd appreciate your help with a few things:

a) The manual describes Capital Required (non-reinvest) as the sum of normalized Drawdown and maximum Margin. It describes Annual Return as annualized profit divided by the sum of normalized Drawdown and average open Margin. Why the difference? In other words, why isn't Annual Return calculated as annualized profit divided by Capital Required - presumably the starting capital that return should be based on?

b) I understand your simple ratio calc above to get the 9.17%. I understand that Drawdown % can't be based on an equity value. I understand that total profit is available for an easy calculation, and I can see the usefulness of this % as a measure of the strategy's performance. However, this % has no relevance to strategy expiration, correct?

c) Assuming a strategy is started with the Capital Required, there is some worst-case, small but non-zero probability that it will go margin call immediately, correct? Therefore, should a strategy be started with the Capital Required (CR), 2*CR, or some other amount?

d) If I understand your explanation of strategy expiration, you're comparing actual drawdown with Tested drawdown (not to be unnecessarily confusing, but possibly via the % the former is of the latter), correct? And expiration is triggered when actual drawdown > Tested drawdown (i.e., (actual drawdown / Tested drawdown) > 100%), correct? And to provide the "headroom" for this w/o getting a margin call, the strategy must be started with an investment >CR by some amount (%)...

e) Lastly, for Risk tolerance, if I'm at 20% and there's some small chance a strategy could go full drawdown right out of the gate, then I need to start it with an investment of 5*CR, correct?

Thanks.

a) The return is calculated for the highest likeliness, while the capital is calculated for the worst case. Therefore the average margin is used for the return and maximum margin for the capital. Early Zorro versions didn't use the margin for the return calculation at all.

b) Yes.

c) That is up to you - I normally use CR, but 2*CR is certainly safer. But I would stop a system anyway when CR is lost.

d) Yes, correct.

e) Normally not. Going down to 20% of the CR right at the start is rather unlikely, and could be a sign of expiration of the strategy. In that case it would be better to prepare for terminating the system when it goes down further, instead of investing 5*CR.

Thanks jcl.

a) I don't understand what you mean by "highest likeliness"? If the CR is what I start with, it's 100% likely , and the return should be based on it.

c) If a system is started with CR and it's lost, that's margin call, isn't it?

e) If my Risk tolerance is 20%, I don't want to lose more than 20%. Therefore, I don't want my account going below 80% CR. How likely is <80%CR? Is there a probability curve for drawdown as a % of CR? Linear? S?

a) The return of highest likeliness is defined as the average of all possible returns.

b) Yes. This way the problem solves itself, sort of.

c) Such a curve could theoretically be calculated, although this is not trivial. The Ulcer Index gives a hint as it measures the % of the profit that you'll lose in an average drawdown.

I would think as a percentage of balance peak rather than equity.

Since DD$ is the difference between a balance peak and the lowest subsequent equity valley in account currency units, it would be nice to also have a DD% as the difference between a balance peak and the lowest subsequent equity valley as a % of the balance peak used to calculate DD$.

This, for example, is how myfxbook calculates equity and would be useful for comparing live trading DD results to test DD where the starting capital is different.

If I understand correctly, the DD% that Zorro gives is a % of the final gross profit (not the gross profit at the time of the DD).

Correct, Max DD % is always a percentage of the gross profit of the simulation.

Using a balance peak instead would be not much better than acidburns idea of using an equity peak: Suppose your simulation starts with the first trade winning $10, the second trade losing $20 - a rather normal situation. This would be then a 200% drawdown, regardless if all subsequent trades are won.

Myfxbook is no trading simulator and does not calculate a DD projection at all. It just tells you your current DD. If I'm not mistaken, it also displays the max DD % as a percentage of the profit.

jcl,

linked to bfleming's question:



If this is true, then we need an ability to modify the start and end dates of the back tests.

Also, I have a vague recollection of a discussion of monte carlo simulation, i.e. the ability to reorder and sample from the series of closed trades in the back test would be nice.

Thanks jcl.

a) I don't see how this definition is accurate since a Test doesn't compute all possible returns. But rather than beating this further how about instead adding "Annual Return on Capital Required" to the performance report, since that's directly meaningful to me - the Tested return I can expect on the capital I need to invest.

e/c) A few issues here (with thanks to bfleming! ):

1) From the manual (and rephrasing), Zorro calculates UI as the mean drawdown's % of the maximum equity. This is more optimistic than the manual's noted traditional calculation of the mean of each drawdown's % of previous equity. I actually think I'd prefer the more pessimistic, front-of-the-equity-curve-weighted, traditional calculation... In any case, can drawdown stats (mean, etc.) be added to the report?

2) There is posting above re. not calculating a DD% from the equity / balance peak. Yet, this information is available and could be easily computed, understanding the limit of accuracy due to randomness. Perhaps we could not mix apples and oranges, and keep the existing % as a measure of performance, while adding a maximum (and other stats) % of previous balance as a further, random-qualified measure of risk/ulcer/whatever?

3) Why not incorporate CR in this? Your 200% example above would change dramatically if CR were included...

4) The above relates to "average drawdown", but doesn't really define "an average drawdown"; and doesn't address likelihood of large or maximum drawdown early in strategy execution when equity hasn't built to sustain it. I understand your not trivial comment, but you evidently have either calculations of some kind or gut feel, as you've made statements about what is unlikely. Could you please share what you have in some kind of useful form(s)? For example, "it's <10% probable that drawdown will occur such that 80% of CR is consumed". And, "for those with 25% of CR Risk tolerance, it's >90% probable that drawdowns will not occur that exceed this".

Thanks.

For the performance report figures we have to look at the standards set by other platforms, and at what people normally expect. We can't display strange parameters that no one else could use or understand, even when they are easy to calculate. What would you do with that 200% DD figure and why would you want more weight on the first part of the simulation? Also, many slightly different variants of the same parameter, such as the annual return, would be more confusing than helpful. If you feel that you personally need some additional parameter, you're free to calculate it in your script in the exit run.

That said, I agree that more info about drawdowns would certainly be useful. A parameter provided by some platforms is R2, which informs about how drawdowns fluctuate. I'll put that on our list, and I'am certainly open for other suggestions when the parameter has at least some rational basis.

As to why we don't use CR for a drawdown percentage, well, it would then always be about 100%, because CR basically _is_ the drawdown (aside from the margin).

Thanks jcl.

Aside from the bedside manner issues (which are hopefully language based ), yes and no. Zorro already follows or not as it sees fit standards and what people normally expect. I can't code what I want in the Z strategies, which if you'll recall is what started this thread. What people can understand and what they choose to use are 2 separate issues. I agree with the concerns about report growth and confusion. But different things are important and meaningful to different people, and hopefully your users on this forum are important. Traditional ways of leaving unilateral decisions and providing reporting variety include report writers (probably overkill for Zorro), and report options (possibly via ini settings, for example which drawdown calc to use - Tradition or Zorro).

Thank you for adding more info about drawdowns to the list.

I wouldn't do anything with the 200% DD figure per se. I was pointing out that if your example started out with CR rather than 0, the 200% goes way down... I realize that CR ~= DDmax, but DDmax only causes margin call if it happens at the beginning of the strategy (assuming the striven-for monotonically increasing equity curve). That, Traditional DD calc, etc. are in the same vein as the unanswered probability question and acidburn's concern - finding some basic, solid understanding of the Risk Management going on here, esp. with the Z strategies. You say it's unlikely that DDmax will happen at strategy start, and supposedly back that up by running strategies internally starting with CR (although there's been no evidence published of that, despite requests). Questions:

1) How unlikely? How is this likelihood determined, exactly?

2) How does a given individual's Risk tolerance factor in? You may be comfortable going with CR and possibly losing it all in 1 account - it may not be your personal funds. But out here in the user community, we're not. We need to know how to identify and manage that Risk.

3) While it may be unlikely (whatever that means) on an individual basis, as more and more people use Zorro, isn't it more and more likely that some poor soul is going to experience it and get totally wiped out?

4) You watch for this manually, but isn't that just the opposite of what Zorro should do? Shouldn't Zorro - at least the Z strategies - have a fail-safe circuit breaker that aborts the strategy if DD > x% * CR?

Thanks.

1) You can estimate the likeliness of DDmax right at start as roughly (0.5 * length of DDMax) / (Simulation time).

2) Hard to answer - there is no simple formula.

3) This is almost certain. No matter how profitable a strategy is, at some day there will be a drawdown that exceeds the DDmax of the simulation.

4) When I think about it, yes, this could make sense, maybe as another flag in the .ini file. But the phantom flag is a better method, as it stops losing components much earlier.

jcl, I get what you're saying.

When you run a test on Zorro it gives you the $DD as the biggest $ drop. So when you're running the same system live, you can expect the same absolute $ drop, regardless of starting capital or balance. % doesn't matter.

So, for example, I'm running Z12 on $50K demo account with Margin = 100, Risk = 25. The test results show:

Max drawdown -5148$ 9% (MAE -6948$ 12%)
Capital required 8017$

But capital, as we know, is irrelevant to the equation. What matters is that so far my demo has had an actual DD$ of -3386, which is still well within the historically largest DD. So I can consider the system to be performing within its expectations.

This also explains you're approach of trading a system with Zorro's stated minimum CR and considering it expired when the capital is gone. Makes sense to me.

I think it's simply a question of analytics. That is, myfxbook shows DD as % drop in balance. It doesn't show absolute DD$, I had to calculate it from peak balance to equity valley using a calculator (no big deal, but extra steps for the lazy haha). (BTW, I didn't see where mxfxbook shows DD as % of profits.)

It would be a helpful addition to Zorro to also have DD as % of balance, which necessarily has to include starting capital into the equation. That is:

Let's take your example of the first trade winning $10 and the second trade losing $20, but with a starting capital of $100. Your balance after the first trade is $110 and after the second trade, $90, giving you a max DD of 18% ($20/$110), not 200%.

This 18% calculation isn't actually necessary for understanding the expected DD, as we saw above, but for easy comparison to analytical tools such as myfxbook it would be helpful.

By the same token, it would be helpful to have, for example, a starting capital slider for the Z systems so as not to have to do successive tests with different margin settings.

It's just a matter of looking at the same thing from different angles.

(BTW, for sake of comparison, let's look at the above example with DD as % of profits. Again, we start with $100 and the first trade wins $10 and the second losses $20, and all subsequent trades are winners. For convenience's sake let's say there are 98 subsequent winning trades, all winning $10. This gives us a final profit of $970 (99 winners - 1 loser = (99 x $10) - (1 x $20) = $970) and a drawdown of 2% ($20/$970). It's this figure that's misleading to people I think.)

Adding the start capital would not solve the basic problem: It is not possible to predict when a drawdown happens, and therefore also not possible to express projected drawdown as a percentage of the current balance.

Consider this: any strategy encounters DDmax at some random point in the simulation. If right at the start, your balance DD would be 100%, because you just used DDmax for your start capital. If it happened at the end, the balance DD would be maybe 10%. So you would get with the same strategy a balance DD between 10% and 100%, dependent on the simulation start date. This % value would tell you nothing about what you should do when you're getting a real drawdown of say 30% of your current balance.

What you could theoretically do is using a linear balance curve and calculating the balance DD at any point of the curve. So it would start with 100% and end with 10%, and if your current drawdown exceeds the percentage at the current point of the curve, you should pull out. But that would be just a complicated equivalent of simply pulling out when the real drawdown in $ or pips exceeds the predicted drawdown.

The problem with a capital slider is that the margin/capital relation is normally nonlinear, due lot granularity and trade skipping. So you can easily calculate the capital from a given margin, but you can not directly calculate the margin from a given capital.

Got it, makes perfect sense to me. Easier just to break out the ol' calculator

@bfleming - For question (2) above, it was suggested that if the CR is an expected future drawdown event, than that amount should represent the portion of your account you are willing to lose. E.g. CR is $10k and you are willing to lose 20% of your account in drawdown. Then your account balance should be $10k / 20% = $50k. Of course this 'dilutes' the expected return to 1/5th as well. So your 200% return on CR is really 40% of $50k. And that is the backtest prediction, not real life. Sobering!

Thanks jcl, bfleming, DMB.

jcl, re. 1), it seems you're saying the probability is linear? If DDmax is equally likely to start during any bar in the Test, why wouldn't that be 1 / ((Test period) - (length of DDMax))? Of course, all this changes using the traditional calc and early term focus...

Re. 2), a few things:

From 1) there's an idea of the probability of DDmax. However, I still prefer the traditional calc since the focus here is on Risk and not being blown out of the water by an early margin call.

From the R2 you mentioned there's a better idea of the drawdowns profile. From this we might be able to get a better idea of the strategy's danger zone?

And from that either at least a comfort zone and what to watch for (manually), or (better) some way to automatically monitor the strategy's execution & drawdown.

In reflecting further I think there may be a language issue regarding "safe". The manual says CR is the amount to safely trade the strategy. However, is 100% loss really called "safe"? It seems CR is the amount needed to (hopefully) just barely survive the low-probability worst-case scenario, at least as far as the strategy's Test results show. And it can be worse than all the math and stats, once the real world takes over.

And there are obviously more than 1 of us who think "safe" means maximum loss is quite a bit less than 100%...

Which leads to 3): If it's certain someone(s) will get wiped out, say so clearly; and say how best to protect oneself. Don't use words like "safe"!

And 4): Regardless of how good the phantom flag is, it seems to me there should be an overriding fail-safe circuit breaker, possibly user-configurable via .ini, that will stop the strategy if drawdown exceeds a certain value. If the phantom flag works as advertised (and is used), this would never be hit - but if not, it'd sure be good to have...

Thanks.

Thanks for the suggestion. Yes, financial trading can indeed result in a loss even when you invested the recommended capital. I'm not sure whether you really did not know that before, but I'll mention this more clearly in the manual.

I've also put your suggested emergency flag on the list.

Hi all,

I think we might be confusing different things, trading for income and trading for capital appreciation. The z strategies appear to be trading for income. In that context, it would be unwise to invest 100% of your capital in any z strategy considering the risk of full drawdown of CR on bar 1.

The decision is more like:
In backtests of this strategy $Y bought a cashflow of $x per month over z years. Can I tolerate risking $Y to buy the Net Present Value of the cash flow of $x per month over z years. Considering the z strategies do not reinvest and are designed for income, I would withdraw the monthly income while maintaining the CR (+ possibly a buffer built up out of profits).

I'm not convinced analyzing drawdown as if using a traditional capital appreciation model looking at % risk per trade, and return and drawdowns as a % of overall capital works in this context.

Thanks jcl, and now swingtraderkk!

jcl, yes, I realized from the start that 100% loss was possible, and didn't start trading Real until I'd Demo'd to a point of some satisfaction. However, I'm still uncomfortable because I don't feel I yet have a good understanding of the likelihood of that 100% loss, or 50%, or even 25%, nor how to best protect against it, preferably in an automated way consistent with the theme of Zorro.

swingtraderkk, I think your distinction is somewhat useful. On the flip side, though, there need to be ways to determine and manage the risks - I don't see that as any less necessary because of an income vs. capital distinction. I hope no one is putting 100% of their capital into any single thing - be it a Zorro strategy or whatever! Whether for capapp or income, we're putting some portion of our capital at risk. Without RM as acidburn tried to point out we're gambling - worse even, 'cause at least with gambling you can compute the odds.

Thanks.

Ddlv,

In my income view, the risk is fully managed, it is the initial CR, all of it. It is the amount I fully tolerate to lose and I set my margin and risk sliders appropriately. I tolerate that risk on the basis that the potential return is worth it, the NPV of the monthly income cash flows over the period of backtest (adjusted down naturally on the sensible basis that real diverges from backtest results). If everything stays within parameters I'm happy to let it run.

Things I would find useful are an ability to see Monte Carlo simulations of the test trades, but anyone who can program could do this from the testrades.csv. Someone programatically challenged like me would also like to be able to custom select a timeperiod for running the test, but I think that may be possible by using the simulate script on the testrades.csv edited to remove time periods not of interest.

Thanks swingtraderkk.

It seems our areas of potential divergence are:

I don't consider "fully tolerate" to be equivalent to "fully managed".

I don't see how "everything stays within parameters" is being determined, or even that the tools to determine it exist.

So, as you point out re. MC, etc., there's yet room for improvement!

Thanks.

I am late to this party. Certainly not qualified to discuss any high-level math here.

But I do have a (stupid?) question: why has nobody mentioned the MAE%? I prefer to use that as my gauge. As I understand, it is the most pessimistic measure of "what could happen" with regard to drawdown. Is that incorrect to think that way?

My rudimentary trigger, to know when a bot has gone haywire would be either:
1) exceeds or approaches simulated MAE% drawdown, as measured from highest balance peak;
or possibly 2) exceeds the Capital Required figure

There may be other measures that could more proactively "red flag" a problem with a bot, but certainly those 2 above are definite.

What am I missing here?

Yes, using the MAE is not good IMO. The MAE is normally higher and thus using it as a DD limit is a bit more risky.

There is no simple formula for a red flag. A system can exceed its historical MaxDD anytime and can still be profitable and recover. But you have to draw a border somewhere.

In the end it comes to personal outlook at what is lose'able or how much are you are ready to risk to make a given amount of money. CR, 1.5*CR or higher. personal lenses.

I use MAE% more as a comfort measure when designing the bot. If the MAE% during simulation makes my stomach turn, then I know the bot is too risky.

On the other hand, if I look at the MAE% during rigorous simulation and I think "pfffftt!" then I know the bot is for me.

How's that for scientific?

Hi all. Another thought has occurred that I'd like to run by jcl & you all. If the objective is Income, how does removing profits change the measures of risk, etc.?

Obviously one can't remove the MI each month, since the equity curve isn't linear and that would definitely risk margin call. But how about the limit case where one removes any net profit after every trade is closed such that the account balance is never more than CR? (Equity might be due to open trades...)

Wouldn't this change DDmax (based on account balance), CR (recursion, anyone? ), UI, & everything else? I.e., removing profits increases risk, doesn't it? Are the current measurements adequate for the stated Income objective?

Thanks.

What you do with your profits does not affect the performance parameters of a strategy.

But for the reasons mentioned in the manual, don't remove all your profit. Keep the square root of your capital growth. F.i. when your capital doubles, remove only 60% of your profit, and let 140% of the initial capital stay on the account. 140% = square root of 2.

Thanks jcl.

However, your statements are contradictory. Clearly what I do with the profits affects the performance of the strategy if I remove more than the square root of the capital growth.

But, I actually don't follow what you're saying. The manual talks about the square root in terms of reinvesting profits, and says the Z strategies don't. Why, then, for a Z strategy or any strategy which doesn't reinvest, can't 100% of the profits be removed?

Also, if it's the other way around and the square root thing applies to removing profits in non-reinvesting strategies, then the Monthly Income displayed by the Performance Report is not correct, is it? Since only 60% of that amount is available to be removed...

By removing the excess of the square root requirement, are we not opening up the system for a future margin call event?

Yes. It does not matter for the square root rule what you do with the profit: If you use it for reinvesting or remove it from the account has the same consequences for the same reason. Your non-reinvested capital must rise at least with the square root of time for keeping pace with the rising drawdown expectancy.

This is important for trading and should be understood, otherwise you're living risky even with a profitable system.

"square root of TIME"? (emphasis added) Now I'm even more confused... Please confirm that's some kind of typo...

Please also bear with some baby steps:

a) Is it true that the square root rule applies to all strategies whether they reinvest profits or not?

b) Is the application of the square root rule different for a strategy that reinvests profits vs. one that does not? (I.e., for the former does more Capital need to remain?)

c) I assume the square root rule is referencing the CR from the Performance Report, correct? (I.e., regardless of what additional Capital one may wish to add as a safety margin.)

d) The exact formula is Cmustremain = max(CR, CR + 1.414 * (AccountBalance - CR))? Or is it Cmustremain = max(CR, sqrt(AccountBalance/CR) * CR)?

e) When profits are reinvested this creates a new CR but the above formula sill applies? Even though the reinvestment happens at a later time?

f) Again, if these profits are not available to be removed without jeopardizing the strategy, then how can they be included in any Income figures? IOW, the Income figures on the Performance Report are all 40% too high?

g) What happens when I stop Trading, close all trades, and restart Trading? Does this accomplish a reset of the strategy and it is safe to withdraw all profits > CR before the restart?

Thanks.

a) yes b) yes c) yes d) neither, it's CR*sqrt((CR+Profit)/CR) e) yes f) no g) no.

Some feeling tells me that the answers won't help either and you have now questions h) to z). But it makes not much sense that you try to learn a formula what to withdraw in which situation. You must understand the _reason_.

Look in the manual about money management - there is everything explained. I've also added an example for withdrawing. http://manual.zorro-trader.com/kelly.htm

Thanks jcl.

d) Then in AccountBalance terms, the formula is Cmustremain = CR * sqrt((max(CR, AccountBalance) / CR)?

e) Is CRnew = CR + ReinvestedProfits?

f) I'm really not understanding something here. If the Performance Report shows Monthly Income of $100 and I remove $100 every month, haven't I violated the square root rule?

g) Why not? How does the restarted strategy know whether it was run before or not? Or if it was run more than once before?

Thanks.

No, it's CR+profit, not AccountBalance. Naturally, the account balance is smaller when you withdraw profits.

The answer to f) is yes and to g) that the God of statistics knows everything. You cannot deceive him by pretenting you just started the system the first time .

It is the trading time that matters. How often you restart the system is irrelevant.

Thanks jcl.

d) Ah, I see. It's based on running total profit since strategy start, irrespective or withdrawals, not incremental profit since the last withdrawal.

f) Then something's wrong, at least with the word choices. If it's only partially available to me, then only that part of it is Income. Put another way, if the posted figures are the Income I want from the CR invested, then to support that the Return/Profit must be way higher.

g) Still struggling with understanding this. Say 3 years ago I ran a strategy, made some profits, and withdrew them. At the time I stopped 3 years ago Cmustremain = 2 * CR. Now 3 years later I want to run it again. I run a WFO and lo and behold the CR is the same CR as originally Tested over 3 years ago. GODstatistics really knows I ran it before and now requires 2 * CR and will margin call me for restarting with only CR? Can you point me to a link that specifically describes how this works?

Thanks.

Hi jcl,

2 other questions:

1) (Variation of the last question:) For any run of a strategy, how does GODstatistics decide if it's the 1st time I'm running it and to treat me right, or that I've run it before and to margin call me? Would appreciate a reference link to help sort this out...

2) How is all this different for Z4/5?

Thanks.

I do not understand your second question, but as to the first, the god of statistics can treat you right because he counts the number of trades that you entered with that sytem.

When you roll the dice, your chance to suffer three losses in a row is much higher when you roll them 30 times, than when you roll them only 3 times. Same for trading. I have no reference link, but can find an introduction book to statistics in the links page of the manual.

Thanks jcl.

Some things may be finally sinking in. Your dice example helps, and should probably be added into the manual.

I'm still not understanding a few things, though...

Why is the 0 profit square root rule used rather than the + profit rule? Because the square root rule is more pessimistic?

If the Test period was, f.i., 3 years, why isn't the square root rule already accounted for over an equivalent Trade period, and kicks in after that?

Shouldn't Test match Trade? IOW, if I'm planning to take out Income, shouldn't the Test be run with those removals? This would change DDs, etc.

Let's say I have $15k to risk on all this. Is it more risky to run, say, Z12 on one account with the entire $15k? Or 3 Z12's on 3 accounts with $5k each?

Re. the 2nd question, all of this applies to WFO and such Trained and Tested strategies, correct? Aren't Z4/5 by nature different and all profit removable?

Thanks.

The 0 profit square root rule is used because it errs on the pessimistic side and requires no further assumptions about the system. Otherwise one had to calculate the system expectancy, which however in turn depends on DD, so we would get a loop of iterations that does not always converge.

The square root rule is nowhere built in in Zorro, except for drawdown normalization. Aside of that it's just a recommendation in the manual. What you do with it is completely up to you and your script. The same goes for reinvesting, taking out profit etc.

One Z12 with $15K or 3 Z12s with $5K are the same risk.

Z4/Z5 are indeed exceptions insofar as the drawdown is limited by the price cap. It won't grow with the square root of time. So you could theoretically remove all profits. Still, there is no hard limit in the other direction, so it's more safe to treat Z4/Z5 like any other system.

Thanks jcl.

You've mentioned time again. Please clarify: Whether the doubling occurs over 2 months or over 2 years, the same 41% must remain? Or does time enter the calculation in some way that makes the % different for one or the other?

Still don't understand why it's OK to Test one way and Trade differently. That seems to violate a fundamental rule of Testing, doesn't it?

For the same level of risk, Z4/Z5 seem to have a clear advantage in terms of profit removal, a.k.a. income, true?

Thanks.

Remember that when we mostly start testing out a system we don't test with a starting capital. We usually run the backtest with flat lots and the capital requirement suggestion after is based on the normalized drawdown and largest margin requirement during the testing period. To simulate what would have happened if you had started out with a fixed capital with re-investment, you can program in this

Where the 250 is the capital you would have started with.

Thanks liftoff.

Sorry - I evidently haven't explained very well. Since Zorro's focus is on "enabling a large audience to get a regular income through automated trading", I've been trying to understand how that regular income really works. The Performance Report shows Return and Capital Required, but doesn't cover removing profits for Income (that's now dealt with elsewhere in the manual).

Among other quandries, there's this:

At the forest level, if Zorro's focus is Income, shouldn't Testing be aligned with that, and be done with some profits regularly removed (which would affect subsequent drawdowns, etc.)?

At the trees level, shouldn't the Testing and Performance Report be structured for that? Shouldn't it include the strategy's estimated Monthly (or whatever timeframe) Income that doesn't cause margin call, doesn't violate the square root rule, lives within the calculated Capital Required, etc.?

Thanks.

I see what you mean. The way it is advertised and the way one subsequently learns to use it are completely different. I doubt there is any strategy on here that can bring in regular income.

I think it's in fact possible with some strategies to produce a monthly income on button press - but that's not Zorro's focus.

Zorro's focus is to _enable_ you to achieve a regular income by _understanding_ to develop and use strategies. It helps you to accumulate the money, but does not tell you what to do with it.

You can of course program a script that does all this for you, but that's not a part of the Z systems or of the performance report. The report is about the strategy, not about your bank account. That's why figures like "your monthly salary by square root withdrawal" don't appear on the report. If you think you need that, just calculate and add it.

I think it's in fact possible with some strategies to produce a monthly income on button press - but that's not Zorro's focus.
I completely agree on this part.
But does it also mean the Z systems have not being designed with regular income in mind?

If you mean a monthly regular income: in my opinion this requires a system that is not purely mechanical, but also uses some fundamental information. But that's just my personal opinion, it's no hard fact. Z1-Z3 are mechanical systems and thus have inherent long drawdown periods, much longer than a month. Only the newer Z4 and Z5 systems, or similar systems, can really produce a monthly regular income. But still, they just trade, and leave it up to you to withdraw or reinvest the profit wisely.

I agree with your position. (Y) .. The use of "regular" changes a lot.

Thanks jcl.

I don't mean to detract from what Zorro brings to the table, and don't want to beat this to death, so I'll probably take a break after this post or soon (hopefully to go work some more on strategies! ).

But I do think it's important to look at this from a slightly different perspective. I agree about _enable_, but f.i., the Z systems are supposed to be _examples_ of this enabling. To wit, they're supposed to work, satisfy the objective of generating income, illuminate what Zorro offers, and encourage your users to embark on their own _enable_ quests.

To me, it detracts when Tested return figures aren't what can actually be withdrawn - ha ha - fooled you! It detracts when they don't perform (defined as an equity curve that doesn't deviate too much from Test). It detracts when vague words like "wisely" are used repeatedly, and your users are left to figure out what's really meant, and what the true parameters, statistics, etc. are. (Note that this is totally different from expecting/requiring your users to figure out what they want to do once a clear understanding of functioning is achieved.)

FWIW, HTH.