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Simply put, CAPM is a special case of APT.
The following is from wiki.
The APT along with the capital asset pricing model(CAPM) is one of two influential theories on asset pricing. The APTdiffers from the CAPM in that it is less restrictive in itsassumptions. It allows for an explanatory (as opposed to statistical)model of asset returns. It assumes that each investor will hold aunique portfolio with its own particular array of betas, as opposed tothe identical "market portfolio". In some ways, the CAPM can beconsidered a "special case" of the APT in that the securities market line represents a single-factor model of the asset price, where beta is exposed to changes in value of the market.
Additionally, the APT can be seen as a "supply-side" model, sinceits beta coefficients reflect the sensitivity of the underlying assetto economic factors. Thus, factor shocks would cause structural changesin assets' expected returns, or in the case of stocks, in firms'profitabilities.
On the other side, the capital asset pricing modelis considered a "demand side" model. Its results, although similar tothose of the APT, arise from a maximization problem of each investor'sutility function, and from the resulting market equilibrium (investorsare considered to be the "consumers" of the assets).
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