Risk Arbitrage

People have different risk profiles, and different beliefs about the future. But it seems to me like these differences should probably get washed out in markets, so that as a society we pursue investments if and only if they have good returns using some particular beliefs (call them the market’s beliefs) and with respect to some particular risk profile (call it the market’s risk profile).

As it turns out, if we idealize the world hard enough these two notions collapse, yielding a single probability distribution P which has the following property: on the margins, every individual should make an investment if and only if it has a positive expected value with respect to P. This probability distribution tends to be somewhat pessimistic: because people care about wealth more in worlds where wealth is scarce (being risk averse), events like a complete market collapse receive higher probability under P than under the “real” probability distribution over possible futures.

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