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(I'm not in finance, so pardon my ignorance)

In The Big Short (2015), there is a little story about Cornwall Capital's early trading strategy:

Their strategy was simple and brilliant. Jamie and Charlie found markets will sell options very cheaply on things they think will never happen. So when they were wrong, they were wrong small, but when they were right, they were right big.

There must have been a lot of such unlikely events that occurred, since their fund turned \$110K into \$30M in a few years.

What I don't understand is why the market would systematically underestimate the probability of many unlikely events? Presumably, such estimates were based on some mathematical models, and not someone's gut instinct. Why would a bias such as this exist?

Is it safe to assume that Cornwall Capital's strategy wouldn't work now, since it's been made public?

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    $\begingroup$ "their fund grew from \$110K to \$30M in a few years" This could be new customers putting fresh money in, not necessarily from high returns. Or some good returns plus some fresh money. $\endgroup$
    – nbbo2
    May 16, 2020 at 0:17

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It’s a nice story and it makes for nice headlines and good reading (it’s a great book and movie) but it’s not necessarily that simple. You may or may not have the same view as your counterparty regarding the probability of some remote event and one of you may be “mispricing it” but the fact that it (or a few of them) happens and makes your fund $30m doesn’t imply the option was underpriced in the first place. It may have been, or it may actually have been expensive but the event occured nonetheless and you still made 100x your money even though at the fair price you would have made 200x.

The only way to know is to repeat the same experiment many times. Obviously with rare events happening in the real world, it’s not that easy as it’s not a controlled experiment. It’s entirely possible that these types of funds are just lucky three times, ten times, in a row. There is not enough information to conclude that such or such option is mispriced.

From experience though, certains classes of rare events like market crashes tend to be overpriced: equity skew is “too high” and “cliquet crash puts” are “too expensive” by most measures against history and there are good theoretical reasons for that (see the chapters on put selling and similar strategies in the fantastic Expected Returns by Ilmanen). The (small subset of) behavioral finance literature I’m familiar with also points to the possibility effect (or lottery ticket effect) for low-probability events which should result in the same observation (see for example Kahneman).

In any case even with a mathematical model, assumptions are made. They may or may not reflect reality. Biases occur then.

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  • $\begingroup$ Your answer is a very valid and i can't argue with it. but it needs to be caveated that that is how it is today - a lot of this will come from institutions being required to keep their VaR below some arbitrary level, so they find some otm options and buy them to fix their VaR problems - they don't mind paying over the odds for them since they have to anyway, and paying 2% rather than 1% for an otm put is better than overpaying atm. The important thing to note is that this was not always the case, and historically smiles have been very flat - the wings were underpriced - i.e. no fat tails. $\endgroup$
    – will
    May 17, 2020 at 9:47
  • $\begingroup$ Yes that’s very true. Things do and have changed over time as markets adapt to events, risk appetite fluctuates, and as regulatory considerations arise. $\endgroup$
    – Ivan
    May 17, 2020 at 10:36

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