You can derive what sort of variance a person will tolerate if they have a "utility function" quantifying the marginal value of each dollar. If you are risk averse (which people usually when they have a small net worth) then your utility curve will be concave. Think like sqrt(x) function.

OTOH, insurance companies can afford to have a roughly linearly utility function (because, as pointed out, they play the game much more often than others), which is why they are in business.