Multi-factor pricing from no-arbitrage

Question

Explain Arbitrage Pricing Theory and how it differs from the CAPM.

Short answer

APT models returns as linear in several factors, $R_i=a_i+\sum_k\beta_{ik}F_k+\epsilon_i$ , and uses no-arbitrage to conclude expected returns are linear in the factor loadings. With many assets the idiosyncratic noise diversifies away, so any mispricing relative to $\lambda_0+\sum_k\beta_{ik}\lambda_k$ could be exploited. Unlike the CAPM it needs no equilibrium or single market portfolio, but it does not say which factors to use.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 11, p.58; question and answer rewritten by SelfMadeQuant.com.

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Mean-Variance Optimisation

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