Let me tighten up my argument a bit. Assume two businesses with an 80% chance of success, where success is worth $1000, and a 20% chance of failure, where failure is worth -$2000. But of course these are stocks, so they can't be worth less than zero, so the expected value of each is $800.

But the expected value of the combined company (where all outcomes are floored at zero) is only $1280 (not $1600), because there's a real chance that one business blows through the profits of the other.