The Arbitrage Theory of Capital Asset Pricing

Source: Ross, S. A. (1976). Journal of Economic Theory 13(3), 341–360.

TL;DR

Introduces Arbitrage Pricing Theory (APT): if returns are driven by a few common factors, then

no-arbitrage alone implies expected returns are linear in the assets' factor loadings — without

needing the market portfolio, mean-variance preferences, normality, or quadratic utility. APT is the

theoretical license for multi-factor asset pricing.

The Sharpe–Lintner–Treynor mean-variance CAPM gives E_i = ρ + λβ_i, but its linear relation rests on

mean-variance efficiency of the market portfolio, which in turn needs hard-to-justify assumptions

(normal returns or quadratic preferences). Ross asks: can the same intuitive linear risk–return

relation be derived from a far weaker premise — the mere absence of arbitrage?

Returns follow a factor model: R̃ᵢ = E_i + β_i δ̃ + ε̃ᵢ (eqn 2; generalized to k factors), with δ̃ a

mean-zero common factor and ε̃ᵢ idiosyncratic mean-zero noise independent enough for the law of large

numbers to apply. The argument: (1) form a zero-wealth ("arbitrage") portfolio, well-diversified so

each weight is order 1/n; (2) by the law of large numbers its idiosyncratic noise vanishes for large n;

(3) choose weights with zero factor exposure — a riskless, costless portfolio must earn zero. This

forces expected returns into the linear span of the betas:

E[Rᵢ] ≈ ρ + Σⱼ βᵢⱼ λⱼ, where ρ is the riskless (or zero-beta) rate and λⱼ are factor risk premia.

Expected return is (approximately) linear in factor loadings; the relation holds for most assets,

with pricing errors that vanish as the number of assets grows.

No role for the market portfolio, mean-variance preferences, or return normality.

Idiosyncratic risk is diversifiable and unpriced; only common-factor exposure earns a premium.

The number and identity of priced factors is left unspecified.

The foundation for essentially all multi-factor pricing — macro-factor APT (Chen–Roll–Ross 1986)

and characteristic factors (Fama–French 1993, q-factor, and the "factor zoo").

Frames performance and risk as exposures to priced factors.

Because the theory does not name the factors or their count, empirical implementations rely on

factor-analytic or theory/characteristic-motivated choices, and identification is fragile in small

samples.

APT says nothing about what the factors are or how many — leaving the door open to data-mined

factors.

The pricing relation is approximate: it holds in the limit / for well-diversified portfolios, and

bounds the average (not every) pricing error.

Empirical content depends entirely on the factor specification chosen by the researcher.

Ross, S. (1976) — The Arbitrage Theory of Capital Asset Pricing — Journal of Economic Theory

Chen, N.-F., Roll, R. & Ross, S. (1986) — Economic Forces and the Stock Market — Journal of Business

Fama, E. & French, K. (1993) — Common Risk Factors in the Returns on Stocks and Bonds — Journal of Financial Economics

Sharpe, W. (1964) — Capital Asset Prices — Journal of Finance

Provenance: verified/generated from the paper's full text.