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Since the early 1960s, several models have been developed to explain the expected
returns of stocks. Following the seminal work by Markowitz (1952) on efficient portfolio
selection, Sharpe (1964) and Lintner (1965) developed the Capital Asset Pricing Model (CAPM).
Under this approach, the expected return of an asset is linearly related to the market risk
premium through a measure of systematic risk called the asset's
beta. Differences in expected returns between different securities should be totally explained by the difference in their
systematic risk or beta.
As opposed to the CAPM which models the expected
return of a stock as linearly dependent on a single factor (the market), the
Arbitrage Pricing Theory (Ross, 1976) allows the expected return of a
security to be a function of several (macro) factors. Stock's
expected return is thus a function of the sensitivity of the stock's return to several factors
which are assumed to reflect systematic risk.
In the 1980s, some empirical analyses found the existence of some anomalies with
regard to the CAPM. Among these anomalies, Banz (1981) found that the average returns on
small (large) companies are systematically higher (lower) than predicted by the
CAPM leading to the existence of a `size effect'. Furthermore, Rosenberg et al. (1985) found a significantly positive relationship between average return and book-to-market ratios. Building on
these observations, Fama and French (1992) proposed their well-known three-factor
model. Expected returns are modeled as a linear function of the risk premium on the market,
the premium related to the size of the company and its book-to-market
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