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Energetic
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Posted: 2018-01-08 18:22
I've been surprised as to how much attention people pay to Max DD.

Let's compare two imaginary strategies with equal returns and Sharpes but different DDs. One drops down -50% about once a year and recovers in a week, on average. The other dips -25% every three months and recovers in a month.

Is it reasonable to consider first one riskier than the second or the other way? My instincts are going with the second. If I had money to invest I'd be looking at something like an integral of DD while under water between two high watermarks.

Because DD essentially represents a loss that you'd take if you have to sell at a bad time, correct? (Personally, I disagree b/c it's not really a loss but a paper loss vs. the max that one could realize if sold at the high - kind of nonsensical view, no?) But if max DD is associated with a short narrow trough then your chance of being forced to sell during that particular week is very small. So why worry so much about Max DD instead of more meaningful statistics, like what I suggested above?

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

AndyM


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Posted: 2018-01-08 19:24
If you consider both risk of ruin (even in a world of zero uncertainty) and the impact of Knightian uncertainty, then max DD seems highly pertinent. This is even before you add in psychological factors. You will have many more takers for the second strategy than the first because it affords you the luxury of being wrong; the first doesn't.

I used to be disgusted; now I try to be amused...

Patrik
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Posted: 2018-01-08 20:30
b/c it's not really a loss but a paper loss

Unless one is talking about accounting rules vs "reality", the term paper loss is a bit of a slippery slope. And often signals lots of overconfidence :)

I guess I'm not in love with max DD as a measure, but it or something like it gives some useful rough number to signal when something may have changed and you may need/want to question your assumptions. I.e. if something has been running for 10y with say 10 trades a day and you are starting to approach a DD that is 2x anything you previously experienced - it's natural to question if something has changed. The outcome doesn't have to be that it has, but it at least makes sense to take a look in the mirror. Perhaps you conclude the world has changed and you should throw in the towel (reduce risk allocation, kill it, whatever). To make those decisions relative to a lower max DD is less scary than vs a massive expected DD. Extreme example: for a strategy with an expected DD of 95% once every 5y with a recovery of 1y, if you start to see something worse than that, it's a bad situation to wait for and be in before throwing in the towel..

(obviously these things doesn't have to sit outside the strategy/model, you may have a more adaptive risk allocation process continuously calibrating vs history etc - what I'm getting at is more the intuition as I see it)

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Energetic
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Posted: 2018-01-08 20:52
@Patrik

Paper loss was a bad choice of words. Perhaps, I should have said - imaginary loss.

I'm not at all denying the usefulness of DD as a quantity monitor so I agree the whole paragraph wholesale. I was thinking in terms of strategy evaluation after backtesting stage - deciding whether to invest in it.

@Andy

From what I hear, you're right: more people will prefer second strategy. I just disagree that this is rational.

If you're a hedge fund with a portfolio of strategies then you risk losing no more than what you allocated to this one. Not that it would be pleasant but it won't be a real ruin. At least one should consider max DD in the context of its duration and relative to profitability. That's obviously just my uninformed opinion.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

darkmatters


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Posted: 2018-01-08 23:50
Two points:

1) Max drawdown is like sampling from the tail of a distribution, and in finance a fat-tailed distribution. Even assuming stationarity, the true 'max drawdown' of a PnL distribution is always (much) larger than what has been seen before. That is why it is rational to not prefer that large drawdowns.

2) Max drawdown numbers are very prone to overfitting. Lets say you have a strategy that has some 50% loss in a day or two. There is always some seemingly simple rule that could have you reverse position the day before the big loss that would erase that drawdown. The potential investor would never know you applied it post-hoc either.

NeroTulip


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Posted: 2018-01-09 09:14
Ha, if only MaxDD was a robust statistic, and not highly dependant on the sample...

"Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016)

ronin


Total Posts: 266
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Posted: 2018-01-09 13:21
Energetic,

Say I give you a strategy that makes $1 per day, and loses $ 1 mln every 100,000 days. That is once every 400 years. You backtest it over a ridiculously long time period - say all the way back to 1980s - and you see Sharpe infinity. The strategy is of course negative.

I am exagerating, but only slightly. Have a look at last year's Euromoney hedge fund awards and tell me how much I am exaggerating.

That's the problem in a nuthsell. The notion of "return per unit of risk" is sound. The issue is what the "unit of risk" is.

Standard deviation makes sense as a unit of risk - *if* your return distribution is Gaussian. If you are selling protection like my $1 up - $1 mln down example, it is completely meaningless.

If you are selling protection, then of course maxDD is perfectly meaningful and standard deviation is meaningless. Theoretical maxDD, historical maxDD, simulated maxDD etc - they all have their place.



"People say nothing's impossible, but I do nothing every day" --Winnie The Pooh

Energetic
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Posted: 2018-01-09 17:22
No objections to anything stated here. I didn't mean that max DD can be ignored and I certainly didn't mean that large DD is good. I just don't think that it is necessarily the most interesting statistic (although in some cases it might be).

However I believe an integral measure will be more robust, that's exactly the motivation. In particular, it could partially address the overfitting problem mentioned by @darkmatters.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2018-01-09 20:11
The other thing I will add is that, from a historical perspective, as people searched for ways to evaluate hedge fund performance through the 00's, which was really tricky on both an absolute and relative basis, maxDD became a more important tail risk / ruin metric (survivorship bias notwithstanding). Comparable or coherent risk measures weren't really available or realistic and maxDD is a very simple stat to compute and communicate.

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Energetic
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Posted: 2018-01-09 21:01
See my sig line ;)

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2018-01-09 21:07
Off topic, but remember in the thousands how managers called alpha "skill"? As in "There's 200bps of skill." A recent article, I think it was in the WSJ this past weekend, said that if a strat was employed that (re)invested in the top performing funds ('40 act) of each year since 1991 the return today would be -18% pa.

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finanzmaster


Total Posts: 145
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Posted: 2018-01-22 20:12
I, myself, put a lot of efforts in finding the "best" risk measure.
Of course I didn't find it but:

1) MaxDD is very straightforwardly tangible at least for a retail investor.
I usually communicate it to non-profis like this: image a crisis comes and you lose your job. Additionally, your portfolio reaches the Maximum Drawdown exactly by the time you most acutely need money.

2) Let us consider two scenarios for 3-Year periods:
a. -20%, +25% and then +10% annual returns
b. +25%, +10% and -20% annual returns
In both cases both MaxDD and terminal wealth are equal (we assume re-investment).
But a. will most likely much more painful for an investor than b.

3) Of course the MaxDD shall be considered together with time to recovery.

4) Given, the portfolio returns are not so heavy-tailed and more or less symmetric, one can (approximately) derive the distribution of MaxDD from the volatility.
There are exceptions from this: e.g. a strategy to trade only virtually perfect opportunities: in this case the portfolio value will not change most of time but occasionally will jump up. So the volatility per se is a not an appropriate risk measure here but such (counter)examples are really exotic.

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Energetic
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Posted: 2018-01-23 22:19
Of course the MaxDD shall be considered together with time to recovery.

Thank you. I almost started doubting my sanity.

Here's another idea. In addition to MaxDD and TTR, I started computing annual drawdowns, i.e. MaxDD registered during a given calendar year. Quite revealing, especially when comparing versions b/c instead of one number you get to see many.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

rickyvic


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Posted: 2018-01-29 19:33
Funny enough I am working on something similar for portfolio optimisation.

Just a remark.

Your return is gaussian... (not a bad assumption if volatility is time varying), issue is that DD is not a good measure but just an informative descriptive statistic you look at ex post.
So sharpe and sortino are 2 good measures... ex ante especially, DD only ex post, because it is simply difficult to forecast the number of times you are going to lose in a row, which is your drawdown if you have sound risk management.

Regarding selling protection you are perfectly right, look at the credit funds these days raising bn $... we'll see when they have real DD

"amicus Plato sed magis amica Veritas"

JTDerp


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Posted: 2018-02-06 19:43
I've been reading about ways to account for the tails in the returns and drawdown distributions, in hopes to keep my portfolio running smoothly. In particular:

1) replacing stddev in denominator of a standard Sharpe or Sortino ratio with a 95% CVaR (which may focus a bit too much on the tails...) - people refer to a 'modified Sharpe' in various presentations and papers online

2) looking at CDaR (Conditional Drawdown at Risk)...B. Pfaff has a good book called 'Financial Risk Modelling and Portfolio Optimization with R' which goes into its application alongside an AvgDD and MaxDD.

I still aim to get aggressive with compounding the PnL returns (5/8-7/8 Kelly) but use the CDaR as trigger to reduce the bet sizes...maybe I'm kneecapping myself.

Anyone have experience with modified Sharpe/CVaR, and/or CDaR, & comments?

"How dreadful...to be caught up in a game and have no idea of the rules." - C.S.

finanzmaster


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Posted: 2018-02-07 17:24
@rickyvic, returns are often non-normal, esp. for a portfolio of derivatives.
Here is a very good example of two low-volatility portfolios, one of which has already ended up in plain-zero and other has "merely" suffered a sudden loss of -45%.

https://letyourmoneygrow.com/2018/02/07/wikifolio-proreturn-45-greedy-german-pays-price/

But the maxDD would be in this case be a very representative number.
Moreover, since wikifolio does keep all trading statistics open, the maxDD could have been accurately simulated for both cases!



www.yetanotherquant.com - Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students

Energetic
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Posted: 2018-02-07 18:28
Actually, the second portfolio is a good illustration of what I had in mind. If (if!) this is a rare event (say, decadal) then I'd be happy to trade 35%/yr growth for a 45% maxDD.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

finanzmaster


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Posted: 2018-02-07 19:11
@Energetic,
Well, the rare event in this case is the performance of 35%/yr, rather than 45% maxDD.
As a matter of fact this portfolio performed so good due to extremely low volatility of the underlying (DAX) :)







www.yetanotherquant.com - Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students

ronin


Total Posts: 266
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Posted: 2018-02-08 15:31
> I'd be happy to trade 35%/yr growth for a 45% maxDD

It's a good example. 35% is a function of leverage, and 45% is a measure of how lethal leverage is in the long run.

In this particular example, it takes 2 years to recover from from the 45% dd at 35% return. Leverage it some more, and you can't recover.

"People say nothing's impossible, but I do nothing every day" --Winnie The Pooh

Energetic
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Posted: 2018-02-08 18:02
What if there were no leverage?

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

finanzmaster


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Posted: 2018-02-08 22:30
@Energetic,

Today again -43%, entering loss zone!
https://www.wikifolio.com/en/int/w/wf000prore

>What if there were no leverage?
In a sense, incorrect question since this bonus cap certificates are complicated.
If the Underlying (the DAX in our case) touches a certain barrier, the "bonus" is away.
If the DAX grows over a certain cap, the pay-off of a bonus cap certificate does grow anymore.

www.yetanotherquant.com - Knowledge rather than Hope: A Book for Retail Investors and Mathematical Finance Students

loltrading


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Posted: 2018-02-17 03:14
It's rational for backers to care about this for a couple reasons:

1. You could be selling tail risk. Lots of ways to hide it but if you have massive DD over a long track record it will be made obvious. Sure there are a lot of charlatans who haven't yet had such a DD, but it's sensible to protect yourself from those who have.

2. They want to keep you working and hungry. Imagine you get paid a % of your annual profits. Your strategy does great every day of the year until Dec 31 where it takes a massive hit, taking you underwater, making $0 bonus. You won't get a bonus next year until you cover your losses from last year.

Are you more likely to talk to those recruiters spamming your LinkedIn? If your current firm likes you/your strategy, they'll probably lose even more money throwing you a decent stub bonus to keep you from walking away.

3. It's simply easier to manage strategies with more normal profit profiles. Taking a nasty hit will have the other LPs, board, GPs, etc. asking uncomfortable questions with no good answers. People don't want the stress and hassle. Their ideal world is pay you a nice cut, have a solid stream of profits result from your work, and go home to wife & kids on the weekend without anxiety.

Energetic
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Posted: 2018-02-20 20:26
@FM

I meant to ask this question generically: what IF there is an unleveraged strategy with 35%/yr growth for a 45% maxDD?

@LT

1. Yes, you're right, and I'm not saying that maxDD is unimportant. I just disagree with the weight given to it.


For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

rickyvic


Total Posts: 120
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Posted: 2018-03-01 20:01
In your definition of DD you say that the loss is unrealised.... "Because DD essentially represents a loss that you'd take if you have to sell at a bad time"
DD is normally calculated on mk2mkt PnL, which is the sum of unrealised and realised PnL.
So it makes sense to look first at the sampling frequency (10 msec drawdown might not be that relevant for a long term investor but might be for a HFT), second at the time to recovery (as correctly mentioned), reinvestment of profits and finally at the capital consumption that max drawdown creates. The last is the most important of all, once you lost money you don't have it for margin and to absorb further losses, meaning higher probability of ruin during a DD.

Now if this is % of peak or just max loss in $ it does not matter.

Regarding a Calmar ratio of 0.5 to 1 this would be interesting for a CTA, or investors that look at daily to monthly horizons and need large capacity.
Buy side and sell side traders with short term horizons look at more 2-3 and up also because they dont need large capacity.
These numbers tend to converge to sharpe and sortino ratio, less true for short vol strategies.


I hope this helps a little to clarify some points...

"amicus Plato sed magis amica Veritas"

nikol


Total Posts: 439
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Posted: 2018-03-26 18:41
Might be of interest
"Maximum DD" by by Amir Atiya in "Risk"
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