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How do you quantify investment risk?
The standard measure of risk is the variance of the asset. The return on investment of the asset is understood as a random variable with a particular distribution. One can make inferences about the underlying distribution using historical data. As you say, this is what the quants do. There are other, more sophisticated measures of risk that allow for such things as skewed distributions and Markov switching. If you are interested in learning more, I suggest starting with the foundations of Modern Portfolio Theory: "Portfolio Selection" by Harry Markowitz and "Capital Asset Prices" by William Sharpe.