5 ms·

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

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.

nickles 8y ago
> 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-a577-00144feab7de https://www.ft.com/content/5a06ef16-b5e4-11e4-a577-00144feab...
darkerside 8y ago
I'd assume that statement presupposes a normal distribution. Is the stock market return normally distributed?
- shakethemonkey 8y ago
  It's a power law distribution (Mandelbrot's work). That's why these numbers are outlandish.
- airstrike 8y ago
  Stock returns are modeled based on the assumption that they are lognormal. Whether they really are is a different story.
jayalpha 8y ago
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/B0086PPXLM 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 8y ago
  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?
  - throwawaymath 8y ago
    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.
  - btilly 8y ago
    Nassim Taleb famously thought so, and made a killing in 2008 on this theory. But his fund does lose money in most years.
  - jayalpha 8y ago
    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 8y ago
      4. miscalculating
  - pjc50 8y ago
    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 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.
jeffdavis 8y ago
Standard deviation only has meaning for a normal distribution.
- raverbashing 8y ago
  In this context yes, especially since it assumes distributions are normal. The strict statistical meaning of a standard deviation applies to any statistical distribution

nickles 8y ago

> 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-a577-00144feab7de https://www.ft.com/content/5a06ef16-b5e4-11e4-a577-00144feab...

darkerside 8y ago

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

shakethemonkey 8y ago
It's a power law distribution (Mandelbrot's work). That's why these numbers are outlandish.
airstrike 8y ago
Stock returns are modeled based on the assumption that they are lognormal. Whether they really are is a different story.

jayalpha 8y ago

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/B0086PPXLM 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 8y ago
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?
- throwawaymath 8y ago
  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.
- btilly 8y ago
  Nassim Taleb famously thought so, and made a killing in 2008 on this theory. But his fund does lose money in most years.
- jayalpha 8y ago
  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 8y ago
    4. miscalculating
- pjc50 8y ago
  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 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.

jeffdavis 8y ago

Standard deviation only has meaning for a normal distribution.

raverbashing 8y ago
In this context yes, especially since it assumes distributions are normal. The strict statistical meaning of a standard deviation applies to any statistical distribution