The Probabilty of a Black Swan Event

[Dr. Toad]

After spending a bit of time on these forums, it seems to me that the majority of traders on here are day traders of some variety. My main aversion to day trading to this point is that due to the nature of it, you are often placing a large percentage of your trading capital into a single trade. To me, it seems that the position size of a day trade will in some cases hinge on the ability of the account to survive a black swan event.

For example, one system I am considering implementing myself will set my stop approximately 1% away and my target profit approximately 1% away. My system is a 1 trade a day system with greater than a 50% positive expectancy outcome. So, following "good" money management practice I could conclude that I am safe to place my entire account into this trade. Due to the nature of this system, I think it is more vital to size my position based on the ability to survive a black swan event.

Since black swan events are relatively rare and variable, it is very difficult to get a handle on how to size a position so that an account survives an event such as this. I am trading stocks, so I am most interested to see what percentage movements are typical in these events as related to stocks. Anyone is welcome to share their experiences since I would imagine there are relatively few on here that have experienced (and continued to trade after) such events just please note the instrument you were trading at the time.

I realize that in theory, a long position can decrease to 0, but my thinking is that the probability of this is actually 0 in the day trading context since even if a company declares bankruptcy during trading hours, the stocks will still be traded but I would imagine there will just be a large gap down after such an event.


To help me size my trade position so my account (and lifestyle) can survive such an event, my plan is to risk no more than 2/3's my account on these trades. This is a somewhat arbitrary number and I would like to get a feel for how much drawdown I could expect if/when the black swan event occurs.

So, if you have experienced a black swan event (either positive in the direction of your trade or negative) I would be very grateful if you could provide the following details:

If a negative event:

1. Approximately how far away (percentage wise) from the price at the time of the event was your stop placed?
2. Was your stop order filled, and at what percent was it filled away from the price? I ask this because I am interested to see if anyone was filled before the large drop occurred and how far away their stop was.
3. What approximately was the total percentage drop from the black swan event?

If a positive event, then simply provide approximately the percent increase from the event.


On a related note, I always set stop quote limit orders to protect against flash crashes (and set alerts to tell me if my order has been jumped over), but in a black swan event it would likely be better to have a simple stop order set. Anyone have thoughts on this? What type of protective stop should I have set when day trading?

 

[alexaherself]

After spending a bit of time on these forums, it seems to me that the majority of traders on here are day traders of some variety. My main aversion to day trading to this point is that due to the nature of it, you are often placing a large percentage of your trading capital into a single trade.

It doesn't seem that way to me, at all. I'm a daytrader, myself, but my position-sizes are certainly no higher than they would be if I were trading over longer timeframes (rather the opposite, in fact, if anything).

To me, it seems that the position size of a day trade will in some cases hinge on the ability of the account to survive a black swan event.

With apologies for the "contrary view", I would have thought that both ...

(a) that's probably less true of daytrading than it is of positional trading, and ...

(b) daytraders are in any case far less likely ever to encounter a black swan, simply because the proportion of the time that they're "in the market" is typically so very much less?

For example, one system I am considering implementing myself will set my stop approximately 1% away and my target profit approximately 1% away. My system is a 1 trade a day system with greater than a 50% positive expectancy outcome. So, following "good" money management practice I could conclude that I am safe to place my entire account into this trade.

Far from it: that would be very foolhardy.

Basic probability and statistics predicate that if you have (for example) a 55% strike-rate, over a series of a few hundred trades there's still more than a 50/50 chance that you'll encounter a losing run of 8 consecutive trades somewhere along the way, and that there's more than an 85% chance that you'll encounter a "losing patch" financially equivalent to that caused by a long series of losers interspersed by only a few winners.

my plan is to risk no more than 2/3's my account on these trades.

My own plan for them would probably be to risk no more than 2.5%.

You don't need a "black swan", to have a long losing run: they're statistically normal. What happened with the Swissie in January, thanks to government interference, is a "black swan". A very long losing run isn't.

Strongly recommended reading: "Profitability and Systematic Trading" by Michael Harris (Wiley, 2008)

 

[Dr. Toad]

My own plan for them would probably be to risk no more than 2.5%.

You don't need a "black swan", to have a long losing run: they're statistically normal. What happened with the Swissie in January, thanks to government interference, is a "black swan". A very long losing run isn't.

Strongly recommended reading: "Profitability and Systematic Trading" by Michael Harris (Wiley, 2008)

Thanks for the comments, I am well aware of losing patches and am running through probability calculations on the system right now. The values I quoted were more hypothetical for the sake of simplicity. The strategy I am looking at has closer to a 75% w/l in theory, so a string of 10 losses in a row is on the order of 1 in 1,000,000 (0.25^10) if I'm not mistaken. This would result in a drawdown of approximately 8% assuming my stops are hit for the actual system I am investigating which is easily survivable.

I would like this thread to focus more on the black swan event probability and not so much the strategy as I will be posting the details of my strategy as well as the analysis I am going through on it in depth in my trading journal later today when I finish the analysis. I would very much appreciate your input on that though once I have posted it, and we can continue the discussion of the points you bring up in there at that time.


One point you do mention though is that you would risk no more than 2.5%. Is this to say that if your account is $100,000, you would trade no more than $2,500 worth of the item in question or that you would set your stop so you would lose no more than that amount. If it is setting your stop then perhaps my initial post wasn't very clear since we are actually talking about the same order of magnitude of risk. I would be risking approximately 0.67% of my account (2/3's of my account with a 1% stop on the trade).


I agree with your point that a day trader is less likely to experience a black swan event. However, since day trading (to my understanding) involves concentrating a large portion of your capital into one item, the impact a black swan event will have on your account is far more substantial that with longer term trading since comparatively the position size (of the long term trade) would be smaller due to a wider stop loss.

 

[alexaherself]

The strategy I am looking at has closer to a 75% w/l in theory

Ok, that's very different, I see.

"Numbers of consecutive losers" aren't really what you need to be looking at, though. Those are incredibly rare.

"Long bad patches" are hugely more common, where you have a few losers followed by one winner, then another few losers followed by one winner, and so on. Those are the real danger.

With a strike-rate of 75% (not necessarily the same thing as "nearer to 75%", of course), I'd be allowing for a losing patch equivalent to nine straight losses, myself, and (allowing for a 50% loss of my entire account) on that basis, I'd be staking no more than 7%.

I hope I won't offend you at all (not my intention!) by mentioning, though, that if I thought I'd discovered a method of trading with a 75% strike-rate at a 1:1 reward-to-risk ratio, I probably wouldn't be trading it at all, because I don't believe that's possible, at any level of trading, and I'd be re-examining very closely both the parameters from which that "conclusion" was derived, and the ways in which it was derived from them. It doesn't sound at all plausible or credible, to me. Sorry, but long experience of dealing with such calculations has taught me that there almost always turns out to be "something wrong", when the outcome's anything like that.

Be aware that when you prove something's the outcome, with a 95% probability, that means there's still a 5% probability that the figures were screwy for unknown reasons. Or, to put that another way, if you assess the predicted outcomes of trading systems on a basis of 95% certainty, you're going to get one totally wrong one time out of every 20. Call me a skepchick, but I can't help wondering, on the basis of the statements you've made, whether this system is that one out of twenty where "something went wrong". Absolutely no criticism implied at all, but I think it would probably be very naive not to wonder.

One point you do mention though is that you would risk no more than 2.5%.

I was looking at a strike-rate of 55%, when I said that. I had taken your "over 50%" as meaning "just over 50%". Sorry.

Is this to say that if your account is $100,000, you would trade no more than $2,500 worth of the item in question

No. It's not a simple as that.

With $100,000 in your account, to risk 2.5% of your account on each trade means that if you lose as much as is possible on the trade, it can't possibly cost you more than $2,500. Things like leverage also have to be factored in.

since day trading (to my understanding) involves concentrating a large portion of your capital into one item

Sorry, but you really are completely mistaken about that: it doesn't mean (or imply) that, at all. If anything slightly the opposite, as I explained above.

 

[Izzy Fuente]

I would like this thread to focus more on the black swan event probability

That is an oxymoron. A Black Swan event is by its very nature probabilistically incalculable. You mention "simple stops". There is nothing simple or guaranteed about stops. They won't necessarily by triggered at the price you state if the market has taken fright. Trading anything more than 5% of your capital in any one trade or 25% at any one time across effectively correlated assets will eventually diminish your trading position without any need for a Black Swan.

 

[Dr. Toad]

Ok, that's very different, I see.

I hope I won't offend you at all (not my intention!) by mentioning, though, that if I thought I'd discovered a method of trading with a 75% strike-rate at a 1:1 reward-to-risk ratio, I probably wouldn't be trading it at all, because I don't believe that's possible, at any level of trading, and I'd be re-examining very closely both the parameters from which that "conclusion" was derived, and the ways in which it was derived from them. It doesn't sound at all plausible or credible, to me. Sorry, but long experience of dealing with such calculations has taught me that there almost always turns out to be "something wrong", when the outcome's anything like that.

Believe me, even though I developed this I am every bit as skeptical as you are. I am aware of one factor that may cause the system to fall on its face when live testing, and am going through the statistical calculations mainly so I know when this has occurred and when to dump the system.

I do not understand completely all of the points you made, but lets continue this discussion in my trading journal after I post the system I am looking at because I am interested in understanding some of the points you have made.

*directs the train back onto the rails*

 

[alexaherself]

Believe me, even though I developed this I am every bit as skeptical as you are.

I hear you ... I'll be watching with interest and am wishing you nothing but "well" with it.

 

[0007]

Dr. Toad - an interesting topic and I look forward to reading more of your journal. I can't answer your questions because fortunately I have never experienced a true BS event – plenty of gaps and adverse movement but not the real thing. Even if this post doesn't directly address your points I hope it may be useful to others. I have thought about the subject quite a bit, I'm not an expert on it but have just tried to apply some ordinary common sense as follows. As has already been pointed out a true Black Swan event is very different from a statistically expected run of unfavourable trades – these can and should be allowed for in risk management. By its very nature the Black Swan event is unpredictable both in form and extent but the best we can do as traders to defend ourselves against adverse price movement is to make sufficient allowance within reasonable expectation – and even that of course might not be good enough.

For my BS planning I assume (1) no stops / limits or any other kind of requested prices will be available or honoured (2) the trading desks will be closed (3) my open trades will be subject to the full effect of the BS. As far as risk management goes I research my market historically and take into account (4) largest adverse movement of the index (5) largest adverse movement of any one instrument (6) largest adverse gap – possibly not a true BS event but it can seriously hurt you. I then feed this information into my risk management spreadsheet so that I always know my risk with regard to: (a) the worst effect if just one of my positions is subject to a BS event (b) the worst effect if all my open positions are subjected. The problem with this is that if you are long then the effects can be absolutely devastating e.g. in the aftermath of 9/11 some major stocks fell by about 50% – would a (possibly overleveraged / over position-sized) account be able to withstand that? It's evident from the recent Swiss FX fiasco that some couldn't.

Having spent much time looking into the effects of inadequate risk management especially when long in swing trading, I now trade short because I consider the risk to be more manageable and the most probable (but not certain) BS is likely to benefit the trade. I think the whole area of BS risk management is a difficult one because you are dealing with unknowns but all you can do is make the best arrangements possible based on past experience. There is a lesson to be learned from the Victorian engineers who had a similar problem of assessing necessary strength for bridges and other large structures. They didn't have the technical facilities we have today so they just did the best they could and added a safety factor – this worked well most of the time but the occasional BS e.g. the Tay Bridge disaster caught them out (similar sort of thing in 1940s Tacoma, USA I also recall) and to a certain degree we are in the same predicament. So with all my risk assessment I tend to over estimate the risk.

What I do find surprising is that to blow up an account or 2 (most likely caused by inadequate risk management?) is almost seen (and possibly this is an over exaggeration by me) as a badge of honour in some quarters. As far as I'm concerned risk management is the most important aspect of trading: you can probably screw up on the rest and come back to fight another day but maybe not so easily with bad risk management.

 

[tomorton]

Good timing, as I've just been reading Nicholas Taleb.

We all fear Black Swans. But there are positive Black Swans too. Making sure you're exposed to these is a way to perhaps cushion the impact of a negative Black Swan. e.g. small positions in oil explorers, biotech developers etc.?

I've even been wondering also about placing short entry orders well below current price ranges. What do we think about a trailing short entry order on the Dow at x% below current closing prices? Maybe other indices /instruments are more sensitive to negative Black Swans, so better for shorting?

 

[tar]

I've even been wondering also about placing short entry orders well below current price ranges. What do we think about a trailing short entry order on the Dow at x% below current closing prices? Maybe other indices /instruments are more sensitive to negative Black Swans, so better for shorting?

Hence they are stops orders then most likely you will get slipped big time , otherwise there is no need to get concerned about black swans just use a stop .
I recall a thread here about a trader complaining how they executed his stop to sell EUR/CHF at 0.96 ish instead of 1.20 .

 

[Lightning McQueen]

Hence they are stops orders then most likely you will get slipped big time , otherwise there is no need to get concerned about black swans just use a stop .
I recall a thread here about a trader complaining how they executed his stop to sell EUR/CHF at 0.96 ish instead of 1.20 .

wasn't it etx? shifted the goal posts and changed his profit to a big loss?

 

[tar]

wasn't it etx? shifted the goal posts and changed his profit to a big loss?

Saxo bank

 

[Dr. Toad]

Plenty of gaps and adverse movement but not the real thing.

This is probably more what I should be concerned with. As far as the black swan event goes, I can just conservatively assume my entire trade will be wiped out and limit my size for surviving this.

What are some of the worst (or best if you were on the winning side) intraday gaps you have experienced? In your experience, about how often do these occur?

(6) largest adverse gap – possibly not a true BS event but it can seriously hurt you.

How do you determine this besides scouring through hundreds of hourly charts of what you are trading. I suppose I could conservatively assume the largest day change in the instrument I am trading constitutes the largest expected gap. This would be simple enough to determine from looking at a daily chart with about 2 years of data.

 

[Lightning McQueen]

Saxo bank

yes, that would be it. there were so many different discussions at the time it's difficult to recall all the situations and issues raised.

 

[0007]

NB. My comments are based on my experience as a swing trader using EOD data.

This is probably more what I should be concerned with. As far as the black swan event goes, I can just conservatively assume my entire trade will be wiped out and limit my size for surviving this.

Sensible. And if you have had a trade in place for some time that has been going in your favour then the damage may not be very serious. That's why it's important to review risk regularly (daily in my case trading SP 500 shares).


What are some of the worst (or best if you were on the winning side) intraday gaps you have experienced? In your experience, about how often do these occur?

Without going into the stats, off the top of my head, gaps in general happen reasonably often. However, my entry & exit rules keep me out most trades that develop adverse gaps. Evaluating my rules against S&P 500 back data I find that 20% is a sensible worst case gap metric - but this could easily be different for other markets and trading instruments. Obviously no problem with a favourable direction gap but what happens the other way? A recent short trade I had which fulfilled my entry rules gapped up by 14%. Fortunately I had been holding it for a while and had been trailing my stop; when the gap occurred I was stopped out beyond my registered stop but still ended up with a profit multiple against risk of 1.35 (i.e. £1.35 back for every £1 risked) – a fortunate outcome but helped by being in a good trend identified by my rules. As an exercise in post-trade analysis I looked at the situation of entering the trade (which still conformed to my rules) the day before the gap up. In that case I would have experienced a profit multiple of minus -2R(isk) – annoying but easily coped with due to adequate risk and position sizing management.

How do you determine this besides scouring through hundreds of hourly charts of what you are trading. I suppose I could conservatively assume the largest day change in the instrument I am trading constitutes the largest expected gap. This would be simple enough to determine from looking at a daily chart with about 2 years of data.

You need two things: (1) data supply (2) software to process (scan) the data. EOD data is easy to source – I use Yahoo and download it with a very useful utility called ML Downloader. This data isn't always perfect and sometimes needs tidying up but it's free and available and perfectly adequate for EOD trading. Intraday data usually needs to be paid for but it's available from numerous sources. For scanning there are quite a few programs out there and there are suggestions in this forum if you do a search. Some charting packages include scanning facilities but you might be required to have a basic knowledge of programming to get the best out of them. I use an old version of Metastock (V9) which I really like because it does everything I want easily & clearly. Its scanning facility at a basic level is based on a scripting language which is not too difficult to learn if you have some basic programming knowledge. Another possibility is Amibroker which can do almost anything if you are clever enough. A further possibility is to use Excel which can easily import data but you would really need some basic grounding in programming or constructing formulas to get what you need from it. Matlab is also very good but you need to know how to use it. I believe the Rolls-Royce solution is Tradestation which is priced accordingly, but you still have to be able to use it's programminglanguage.

I would find life a lot more difficult without a scanning facility and believe it is an essential tool to enable me to work quickly and efficiently. If you are not knowledgeable in programming and don't have the time or inclination to become so, then I suggest finding a scanner where you just dial in what you're looking for and the software does the rest. I believe there are packages that do this and perhaps others can advise better than me. Once you get into the habit of using a scanner you will wonder how you ever managed without it. You can also go searching for all sorts of things that you didn't know were of use to you!

.

 

[Dr. Toad]

Ah, I think we are talking about different things 0007, I am interested in intraday gaps not interday gaps. I have experienced enough of interday gaps to know they are quite common and can be substantial. What I want to know is with regards to a day trading strategy what gap can be expected and how often. For example perhaps a 5% gap within about a minute of a substantial news event of a particular stock during the trading day. Or perhaps a gap of this magnitude and time frame is absurd...I really have no idea but would like to get an idea of it.

 

[0007]

Ah, I think we are talking about different things 0007, I am interested in intraday gaps not interday gaps. I have experienced enough of interday gaps to know they are quite common and can be substantial. What I want to know is with regards to a day trading strategy what gap can be expected and how often. For example perhaps a 5% gap within about a minute of a substantial news event of a particular stock during the trading day. Or perhaps a gap of this magnitude and time frame is absurd...I really have no idea but would like to get an idea of it.

Apologies for misunderstanding you but perhaps my blurb will be of use to a beginner somewhere. I suspect there are some interesting stats lurking related to your question but they are right out of my knowledge since they just get subsumed within my style of trading. Someone must know but I've never seen it revealed here. I've always had the impression that Daytraders watch their screen like a hawk on low TFs and don't let it get to the stage where gaps take adverse effect. But we are talking Black Swans and its outside my experience. So I await a knowledgable answer with interest.

 

[Mr. Charts]

Black swans are surprisingly common. There are a lot in Dawlish, Devon.

As a day trader I can only remember two or three in 15 years of full time trading of US stocks and on every occasion the situation corrected itself with seconds or minutes. No problem. In any case, risk is there to be managed and strictly limited.
Of course that doesn't mean to say it couldn't happen, it's simply my personal experience. As has been said, as a day trader I am in the market for less time so the odds are more on my side.

 

[0007]

Black swans are surprisingly common. There are a lot in Dawlish, Devon.

As a day trader I can only remember two or three in 15 years of full time trading of US stocks and on every occasion the situation corrected itself with seconds or minutes. No problem. In any case, risk is there to be managed and strictly limited.
Of course that doesn't mean to say it couldn't happen, it's simply my personal experience. As has been said, as a day trader I am in the market for less time so the odds are more on my side.

That's very helpful. It also says to me that day trading properly managed is not as dangerous as some would have you believe. As a balance to the intense concentration required during the trade (I'm guessing here on the concentration bit because I've no experience) it must be nice not carry any out of hours risk.

 

[Dr. Toad]

Black swans are surprisingly common. There are a lot in Dawlish, Devon.

As a day trader I can only remember two or three in 15 years of full time trading of US stocks and on every occasion the situation corrected itself with seconds or minutes. No problem.

This is very helpful. As a follow up, do you know what the cause of the large drops were? Were they flash crashes or legitimate "bad news" drops that reverted back for a short time?

This seems to point to my current stop technique of a stop quote limit order being the correct one to use when day trading as protecting against flash crashes is the very reason I use it.