The original factor theory, dating back to the 1960s, is the capital asset pricing model, or CAPM, which predicts that the only determinant of an asset's expected return is how strongly its returns move (or, in technical terms, covary) with the market's.
The strength of the relationship is summarized in a variable called beta. A beta of 1 indicates that for each percentage point the market moves, an asset's price moves in the same direction by a percentage point. CAPM predicts asset returns are linearly related to market beta.
However, since the 1970s, academics have known that stock returns don't seem to be related to beta. This finding spurred many fruitless or convoluted attempts to explain how market efficiency could be squared with a world in which CAPM didn't work.
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