my deepest apologies then. either way steel balls!
This is good for bitcoin.
“…in that channel.”
Ok, boomer! 
I hate when people reference something as a 3/4/5/6/whatever-sigma event from a probabilistic perspective. Market outcomes DO NOT follow a normal distribution. I’m sure the spike in volatility from the coronavirus was a 10+ sigma event… the likes of which traditional finance models would have predicted to happen once every million years. I’m pulling these numbers out of my ass but you get the point. It’s why LTCM failed and why you should never be short vol. Thank you Taleb and Mandelbrot for shining a bright light on this perpetuated bull ■■■■ people call traditional finance theory.
Pretty sure almost everyone is short vol except some hedge funds and certain specialist or retail investors…
It depends on the context. There are plenty of reasons to refer to things by sigma. For instance in the Munger example i reference above they were referring to the distribution of return persistence. Not sure how they modeled it in that specific EMH context but probably something binomial. It’s absolutely correct that context to refer to someone’s persistence of returns by a “sigma” event and frankly to your point if the distribution did not fit, that would have exactly made Munger’s point, except in this case reinforcing an inefficient market.
If we’re arguing about specifically market returns as in the case you cited, then sure the point stands. But outside of market returns or other known non-normal distribution there’s nothing wrong with the practice when properly applied.
What I said applies to any distribution of continuous outcomes (i.e. not a coin flip or 6-sided die roll). Basically, if there isn’t a discrete set of outcomes and you try to apply a normal distribution or a confidence interval, you’re just giving yourself a false sense of security. A great example (source: Mandelbrot but expanded on by me for illustrative purposes) is if you can’t swim and you try to cross a river that you knew beforehand had an average depth of 2ft. You get half way there having only hit depths of 1-3ft. Then suddenly you step off a cliff. This, according to a normal distribution of outcomes, was a 100 sigma event (hyperbole). Now you’re dead because you trusted the bell curve. 
Are you saying a normal distribution isn’t meant for a continuous variable?
Not necessarily. My point is that the usage of “that was an x-sigma event” or measuring risk based on std dev of returns or VaR calculations is naive and dangerous.
I just re-read what I wrote and yes I said “any”, but my point wasn’t to corner the application of statistical distributions. Hopefully my point wasn’t lost over a semantic technicality.
Yeah, I’m sorry what you’re saying is a complete misunderstanding of what mandelbrot meant based on some pop sci book as well as an abomination w/r/t basic mathematics. It’s interesting because I’ve often said Taleb is the most often misquoted and misunderstood writer. I’m not even sure you understand distributions properly because you keep referring to everything as a normal distribution and assuming confidence intervals can only be applied to normal distributions. You’re also conflating the use of non-normal distributions with normal proxies with the use of any pdf and relegating all of stats to pmf’s.
What is your academic math / stats background?
I’m not trying to be rude despite appearances, you just came in pretty cocksure and hot and I’m not sure you really understand what you’re saying or that comparing a return persistence distributions is not the same as comparing return distributions. As an aside, I coined myself Black Swan over 10 years ago because of the impacts Taleb’s books had on my early career, so it’s not as if I need a lecture on Taleb or Mandelbrot, I just think you’re miscasting the point.
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I’ll admit I don’t have a stats or math background so please ignore my misused terminology. My original comment was also not directed at the Munger comment or return persistence.
I am curious what your takeaways were from Mandelbrot’s (mis)behavior of markets? For me, a major takeaway was that the tail risk of market volatility has historically been much fatter than options pricing models would suggest. In my mind this was directly connected to Taleb’s viewpoint that the magnitude of changes in volatility is notoriously underestimated in “Extremistan”.
Did I misinterpret the above?
No, this part is exactly correct. I assumed you were talking to the Munger quote which would be misinterpreting the point of Mandelbrot and Taleb. Their point wasn’t so much that you can’t ever use normal curves to approximate continuous distributions accurately (like breaking point of a strip of steel from a sample, or heights of people) it was that you shouldn’t use normal distributions to model things that are not normal and that it is dangerous to do that in situations where the risk of those tails has such downside. So Taleb’s books IMO were written from best to worst and the trilogy is best read like Fooled By Randomness, which is pretty much talking about how we like to attribute patterns to random behavior. It’s almost a behavioral book and focuses on randomness. Black Swan digs into the idea of misapplication of normal distributions to extrimistan type things. Then the third was Antifragile which looks at structures from a robustness perspective.
Together you can think of it as like “you don’t understand the world as well as you think” (Fooled by Randomness), “people routinely view things that aren’t normal through a normal distribution lens because our brains aren’t equipped to deal with tail probabilities” (Black Swan) and then “banks shouldn’t have 50x leverage given the above and other insights about building organizations with these facts in mind”.
You’re not far off, but I think you started over applying it to the point of saying “any application of normal distributions against functions with continuous distributions is wrong” which is not really the case.
Solid synopsis. What a great trilogy.
If this makes sense, while what you said I said above is exactly what I said, it’s not what I meant haha
I was trying to find the term to represent non-normal distributions and continuous variables came to mind… noted to not use that term in the future.
Have you read anything on power laws? Scale by Geoffrey West or Zipf? Crazy stuff.
I haven’t read those, tbh, the last few years I’ve been so buried at work reading industry peices and doing grad work people kept buying me books because it was the one Christmas idea everyone knew I’d like so I’ve got a full scale library in the basement I haven’t touched. I believe west is in there. If you liked Taleb I’d guess you’d really enjoy “Thinking Fast and Slow” if you have some extra time.
Point was not lost.
My hesitation wasn’t that you said “any”, but rather that the idea of a normal distribution is for a continuous variable with a range of (-inf, +inf), so your comment was a bit odd when discussing “if there isn’t a discrete set of outcomes…”. Just thought your wording was a bit hazy (i.e. discrete outcomes meaning something that only has certain possible outcomes? or do you mean a finite set of outcomes?).
This is proof to me the CFA curriculum (stat/quant) portion fails its audience. Distributions and kinds of variables and data types are all different ideas. You can have a non-normal distribution like Poisson for a discrete random variable like number of loan defaults in one year (not continuous, discrete integer valued variable) and you could have a Weibull distribution for a continuous random variable like time to default on a loan (continuous). (And then there is the possibility that these things can be approximated by a normal distribution under certain conditions!)
Looking for a way to say, non-normal-- you already hit it on the head! I wouldn’t shy away from calling something a continuous variable unless it is not continuous (i.e. age is continuous and we switch the resolution from year to days to… but something like fingers on a hand is discrete and not “cut off” due to our resolution capabilities).
This was somewhat my point based on his post, but you hit it harder than I did.
I’ve read it, thanks for the rec though BS.
Fair criticism tickersu. I didn’t want to say “non-normal distributions shouldn’t be assumed to be normally distributed.” It’s like “no ■■■■…” I was more trying to describe what makes the distributions non-normal. To which I clearly failed. Let me try again without attempting to use statistical jargon… What comes to mind for me are variables without limits that may be subject to feedback loops or that can take values orders of magnitude higher than the average.
We get that, but really you’re just restating the point about the risks of using gaussian dist to approximate non-normal functions. Getting mixed up with limits and continuous variables really starts to go off topic and starts to undermine the point, because a true normal distribution mayor many cases really go off with no limit and that’s not a problem as long as the density in the tails stays true to a normal distribution.