Normal distribution, arrived at via the central limit theorem, assume that the underlying distributions are independent. They may well approximate independence most of the time, but when extreme events happen, the distributions are correlated, the CLT doesn't apply (not in the simple way it is normally presented), and the overall result is most definitely not normally distributed.
Normal distribution is a terrible model for estimating risk.
The quote isn't the first to confuse bad statistics with some inherent weakness in statistics. Black Swan was a worldwide bestseller based on the same canard.
2) There's probably an appropriate statistical model that wasn't used to come up with the 1 in a billion number, be it some likelihood function, Poisson or Zero-Inflated Poisson, etc... It's up to smart people to understand what statistical model they should probably use.
http://en.wikipedia.org/wiki/Value_at_risk
The "1 in 3 billion years" quote sounds like exactly the kind of line of thinking that was in the Big Short.
It's up to smart people to understand what statistical model they should probably use.
It's not just that their model is wrong -- and VaR is certainly wrong. It's that NO model is right.
That is, the fundamental problem is that they are trying to quantify the unquantifiable. Black swans aren't quantifiable by definition.
If you think there is an "appropriate statistical model", then definitely read the Black Swan. I'm glad it came up many times in this thread, because that means the point has been driven home. If you don't get it, you need the 300 pages of beratement it gives you :)
See chaos theory or google "irreducible complexity". There certainly is a model that is right - an obvious model would be just take all actors, their holdings, and their actions, that trivial model certainly is right. There are even people who have this model available to them : the stock exchanges. In theory, no-one else has it available, and we should be sure they're not using or selling this model, right (heh) ?
Black swans are quantifiable. For instance, calculating the current debt loads of governments will tell you that interest rates aren't going back up without killing social security or something like a 300% (cumulative) inflation. Since we won't be killing social security, a sudden crash (at least 40% drop in SPY) followed by a short-term (~1-2 years) tripling of prices is coming. Alternatively, there could be lots of sovereign defaults, resulting in 10-20% treasury interest rates for 5-10 years. There. Quantified.
Black swans happen because we, as in humanity, have this need to believe that things won't change. When they inevitably do change, the first thing we do is to use capital to get us back to the old situation. But that hardly ever works. When it fails, it requires exponential use of "capital" and the capital is gone (so no-one is ever getting their investment back). A recent obvious example I saw of this is Abu Dhabi : the idea that you can have a lush, green, modern city in the middle of the desert. This is wrong, it's artificial. And every millimetre the city grows comes at exponentially increased energy expenditure, exponentially increased stress on all the systems that support this city, and on a regular (as in weekly) basis a sandstorm comes and makes it blatantly obvious what happens if those systems would fail for even single week. But trillions of dollars are being invested to change this, because it was almost reasonable to do this for a small oasis with a freshwater source. As expected, this city is burning an ever-rising share of the oil income of the state just to keep existing. Black swan coming up, right there.
What does it mean to say that Black Swans are unquantifiable? Take these questions:
1) What is the probability that the S&P will be below 1000 within a month (bigger than 50% drop)? Is it .1%, .01%, .001%, .0001% ? Nobody knows. It's a sufficiently rare event, with so few precedents, that you can't give a useful or reasonable answer, with say an order of magnitude.
2) What is the value of the next YC batch, in 2020? Well if it has a company like AirBnB or Dropbox, it could be $10 B. Or it could be $100M. Nobody knows. (See Paul Graham's Black Swan farming essay.) Although the entire point of the VC industry is to try to make this return more predictable than it inherently is.
3) On September 10, 2001, if I asked you what is the probability that airliners would crash in to the World Trade Center, what would your response be? There was perhaps a prior in the 1993 World Trade Center attack. Still, nobody (outside the State department) could have spoken meaningfully about the probability of this event.
in any case I wonder how much of these price aberrations are caused by bad statistics and not exuberance, overconfidence, or system failures. the latter things can't really be captured by math.