The standard theory is that risk--properly defined as the omnipresent, nondiversifiable, priced risk---is something that generates a linear payoff for everyone. If you take 2 units, you will receive 2 units of the risk premium regardless of who you are. Thus, if you think the equity risk premium is 5%, then investing in stocks with twice the equity beta should generate a 10% annualized premium, and stocks with a 0.5 beta should generate half the beta. Properly defined, it's all about the quantity of the dollar betas at work. After 45 years of intense search, no one has found a beta that has this property.
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