How do the long-term returns of a high-variance investment compare to those of a low-variance investment?

Question

Variance over the short-term is a useful way of comparing the risk of investments. Got a home purchase or large medical expense coming up? Better not to have too high variance on your invested savings. 20 with a well-paying job and decades until retirement? Sure, risk the high variance for higher returns.
But if you've got decades or centuries in the market, and you're confident your investments won't fold entirely (though they very well may lose a large portion of their value), how do you reason about comparing variances on potential investments?

Aganju · Answer

Typically, the higher the variance, the higher the long-term average returns.
In a graph (x-axis: variance; y-axis: long-term average return), most investments will line up nicely to form an upward sloped line. Investments that fall below the line are considered inferior and might die out; investments above the line simply don’t exist (or everyone would run for them).
As a result, every long-term investor should be in the wildest markets, but - risk adversity typically limits this. Many people can’t sleep well with high variance in their investments, so everyone just goes up to his risk limit. For some that’s global share markets, for some it’s CDs, and fir some it’s cash under the mattress.

How do the long-term returns of a high-variance investment compare to those of a low-variance investment?

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