Recently the whole "if your p(doom) is high, you should short the market" thing has been going around. Let's say the market prices in a 0.1% chance of extinction per century, and you think there's a 50% chance we're dead in the next 25 years. This is about 12 bits of evidence.
How much profit is it even reasonable to expect someone to make from 1 bit of evidence?
Is this a constant function of the bits which is calculable like e.g. a Kelly bet? Or does it depend on the market?
If the latter, does it ever make sense to short things at all based on p(doom)? I assume not, since shorting is generally stupid high-risk for an uninitiated trader (as I understand it).
Consider: everyone else thinks a company share has a 0.1% chance of being worth $10 tomorrow and a 99.9% chance of being worth $0. I think the chance is 50:50. Therefore the stock price is $0.01 today. If I have $100 in the bank, I maximize expected log(money) by spending fully half of my money on it. By my reckoning the maximum log-expected money is $1581, which corresponds to about a 16-fold increase over $100. Which is not 10 bits of alpha!
PS not looking for investment advice here, just looking for maths.
Recently the whole "if your p(doom) is high, you should short the market" thing has been going around. Let's say the market prices in a 0.1% chance of extinction per century, and you think there's a 50% chance we're dead in the next 25 years. This is about 12 bits of evidence.
Consider: everyone else thinks a company share has a 0.1% chance of being worth $10 tomorrow and a 99.9% chance of being worth $0. I think the chance is 50:50. Therefore the stock price is $0.01 today. If I have $100 in the bank, I maximize expected log(money) by spending fully half of my money on it. By my reckoning the maximum log-expected money is $1581, which corresponds to about a 16-fold increase over $100. Which is not 10 bits of alpha!
PS not looking for investment advice here, just looking for maths.