Beta serves as a measure of risk because it can be used to derive a probability distribution of returns based on a set of market returns.

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Beta is a measure of systematic risk, which is the risk that cannot be diversified away. It is calculated by comparing the volatility of a stock's returns to the volatility of the market as a whole. A beta of 1 means that the stock's returns are perfectly correlated with the market's returns. A beta of less than 1 means that the stock's returns are less volatile than the market's returns, and a beta of greater than 1 means that the stock's returns are more volatile than the market's returns.

Beta Serves as a Measure of Risk Because It Can