= Arbitrage pricing theory
{title2=$\mathbb E r_i-R=\sum_j b_{ij}\lambda_j$}
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= APT
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<Arbitrage pricing theory> relates <expected returns> to systematic <factor loadings> and their <risk premiums>. With idiosyncratic noise, a diversification or asymptotic argument needs additional assumptions. With no idiosyncratic noise and spanned factors, the formula is an exact consequence of <law of one price>: <portfolios> matching factor exposures can differ only by a constant payoff, which absence of <arbitrage> forces to be zero.
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