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Lumifer comments on Open thread, Aug. 17 - Aug. 23, 2015 - Less Wrong Discussion
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The financial markets allow you to bet on such things. If you actually believe that 50% probability, you can place a bet in the markets at what would look to you like VERY favourable odds.
Would this involve shorting stocks? That seems dodgy, given that the default is for stock to rise. And if my probability distribution is about 50% crash, 40% surge upwards, 10% stability, then shorting isn't a particularly good idea.
Or maybe its time to buy some bitcoin...
You can express quite complicated views in financial markets.
That distribution doesn't look like "the default is for stock to rise" :-) Besides, a 2008-magnitude crash would probably drive the equity markets to what, half of their current value? You can't expect a "surge upward" to give you symmetrical gains on the upside, so your expected distribution is very lopsided.
Let's make things even simpler -- you believe that in half a year we'll end up in one of two states -- either, with a 50% probability, the equity markets will crash to half price, or, with a 50% probability, the markets will stay the same or go up. If this is so, you can take a position in the markets which is guaranteed to make you money, either a lot (in the first case) or a little (in the second case). Guaranteed, that is, if the markets will do one of these two things.
Its not - stocks rising is the prior, this is my posterior.
Exactly what instruments would guarantee this return? A mixture of shorts and options?
The simplest would be a put spread. You would buy deep out of the money puts and write (sell) other OOM puts much closer to the current price. You will buy more deep OOM puts than sell shallow OOM puts, however because you will be buying cheap puts and selling expensive ones you will start with a positive balance. In the case of markets going nowhere or up, both sets of puts expire worthless and you keep your difference in premium (you earned a little money). In the case of the crash, both sets of puts expire in the money, but you are long more puts than you are short, so you make a lot of money.