Arbitrage pricing theory

Arbitrage pricing theory prices an asset's expected return as a linear function of its sensitivities to several risk factors, extending the CAPM's single market-beta model to multiple factors.

ByHoang TruongUpdated July 5, 2026

See it move

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A two-factor model prices a stock off a 3% risk-free rate, plus its beta to each factor times that factor's risk premium. With a 1.2 beta to a 2% interest-rate premium and a 0.8 beta to a 1.5% inflation premium, expected return is 3% + 2.4% + 1.2% = 6.6%.

Where it fits

TopicRisk, Return & the CAPMAdvancedSubjectCorporate FinanceAdvanced

The formula

LaTeX

E(R_i) = R_f + \sum_{k=1}^{n} \beta_{ik} \times RP_k

Variables

$E (R_{i})$: Expected return on asset i (decimal)
$R_{f}$: Risk-free rate (decimal)
$β_{ik}$: Asset i's sensitivity (beta) to factor k (dimensionless)
$R P_{k}$: Risk premium associated with factor k (decimal)
$n$: Number of priced factors (count)

Prices asset i's expected return as the risk-free rate plus compensation for its exposure to each of n systematic risk factors.