[shakethemonkey]

The 1987 market crash (October 19, 1987, single-day loss of 23% in the S&P 500 index) was a 25 standard-deviation event. Mind you, an 8 standard-deviation event is an event that should occur once every 3 trillion years. And 25 standard-deviation events are unfathomable given the age of the Universe.

[jayalpha]

Describing market moves in "standard-deviation events" does not really make sense. It is something for normal distributions and "random walks".

It has been known for a long time that his is not the case: https://www.amazon.com/Fractals-Scaling-Finance-1st-First/dp...

The conclusion is: due to faulty mathematics, far out of the money options are underpriced. Or, who Mandelbrot concluded, "investing on the stock market may be riskier than you think".

[jliptzin]

Not disagreeing with you, but would buying far out of the money options be a viable strategy if you wait long enough for the black swan event?

[jayalpha]

No, because timing.

But if you have a few bucks to spare and want to gamble you could buy far out of the money options for a downturn. VIX gets priced in, don't know how it looks currently.

Or you can gamble with "paper money" at Thinkorswim.

If you see a 25 standard deviation you are either

1. Incredibly lucky

2. Incredibly unlucky

3. Or don't have a standard distribution (but a fat tail distribution or Levi flight or whatever)

[fnord123]

4. miscalculating

[lmm]

In principle yes. If far out of the money options are systemically underpriced then just buying a bunch and holding them should make money on average, by definition.

In practice there are a bunch of concerns. You have the gambler's ruin problem: even if your bets are positive expected value, it's very easy to go bankrupt. Since your fund makes all of its money from crises you have a bunch of counterparty risk along a risk of regulatory intervention etc.. Your fund will lose money in most years and it's very difficult for potential investors to know whether you're actually positioned to make money from a crisis or just wasting all their investment. See Keynes' line about sound bankers.

Taleb endorses and advises a fund that tries to bet on "black swans"; it's explicitly advertised as a fund that will lose 5% of its value every year in "normal years", but hopefully pay off in exceptional years. You can invest in it if you want. In theory it should work, but no-one will really know until after we have one of those exceptional years.

[btilly]

Nassim Taleb famously thought so, and made a killing in 2008 on this theory. But his fund does lose money in most years.

[pjc50]

The trouble with this is that you need to have enough of a black swan to trigger the options but not enough that it prevents them paying out, e.g. due to counterparty risk or some kind of systemic collapse.

And "the market can stay irrational longer than you can stay solvent" - by definition this produces few, rare payouts.

Far better to employ the LTCM strategy and write a lot of out of the money options: https://en.wikipedia.org/wiki/Long-Term_Capital_Management

The trick is to do that with other people's money, on which you initially get huge returns. You can then collect large managment fees. The collapse takes out the fund, but it's an LLC so the staff get to keep their bonuses from previous years.

[throwawaymath]

Generally not, because the price of the option is going to rise commensurate with the uncertainty of it being in the money.

It gets more and more difficult to accurately forecast that as uncertainty increases, which is why they're not priced as efficiently farther in the future. But since this is somewhat well known, you need to have some kind of edge to make it work - buying options haphazardly won't.

[nickles]

> The 1987 market crash (October 19, 1987, single-day loss of 23% in the S&P 500 index) was a 25 standard-deviation event.

Adding to this, the Swiss Franc revaluation in 2015 was called a 20 standard deviation event [0].

[0] https://www.ft.com/content/5a06ef16-b5e4-11e4-a577-00144feab...

[jeffdavis]

Standard deviation only has meaning for a normal distribution.

[raverbashing]

In this context yes, especially since it assumes distributions are normal.

The strict statistical meaning of a standard deviation applies to any statistical distribution

[darkerside]

I'd assume that statement presupposes a normal distribution. Is the stock market return normally distributed?

[shakethemonkey]

It's a power law distribution (Mandelbrot's work). That's why these numbers are outlandish.

[airstrike]

Stock returns are modeled based on the assumption that they are lognormal.

Whether they really are is a different story.