Arbitrage Pricing Theory

Background

Built on Harry Markowitz's (1952) portfolio theory, William Sharpe's (1964) capital asset pricing model (CAPM) explained expected returns by beta, the sensitivity to a single market portfolio. But CAPM relied on the assumption that investors care only about mean and variance and on an unobservable true market portfolio, which Richard Roll (1977) argued made it hard to test properly. Stephen Ross (1976) proposed an alternative starting from much weaker assumptions. Without specifying investors' utility functions or the market portfolio, he derived a pricing relationship solely from a statistical structure in which returns are generated by a few factors and from the condition that no arbitrage exists.

Theoretical structure

APT assumes that each asset's return consists of its expected return, the products of its sensitivities to several common factors and the unexpected changes in those factors, and asset-specific noise. With enough assets, idiosyncratic noise vanishes in well-diversified portfolios and only factor risk remains. If two such portfolios had the same factor exposures but different expected returns, one could buy one and sell the other for a riskless profit, so absence of arbitrage requires the linear relation: expected return = risk-free rate + Σ(factor loading × factor risk premium). Huberman (1982) gave a concise version of the argument, and Chamberlain and Rothschild (1983) generalized it to an approximate factor structure that relaxes the strict factor assumptions. That APT does not say what the factors are is noted as both a strength and a limitation.

Evidence and the evolution of factor models

Using statistical factor analysis, Roll and Ross (1980) reported three or four priced factors in US stock returns. Chen, Roll and Ross (1986) used macroeconomic variables such as industrial production growth, unexpected inflation, the credit spread and the term spread as factors and found that systematic risk is rewarded. Shanken (1982) argued that with a finite number of assets pricing errors cannot be pinned down exactly, limiting the testability of APT. Connor and Korajczyk (1986) proposed methods for extracting factors from large asset sets. Fama and French's (1993) three-factor model and Carhart's (1997) model adding momentum have different empirical motivations from APT strictly speaking, but they are often interpreted within its multifactor framework. Harvey, Liu and Zhu (2016) highlighted the factor zoo of hundreds of reported factors and proposed stricter standards that account for multiple testing.

FAQ

What is APT in simple terms?

Stock returns are driven by several common risks such as the business cycle, inflation and interest rates, and if there is no free lunch, assets are rewarded in proportion to their exposure to each risk.

How does it differ from CAPM?

CAPM uses a single market factor and strong equilibrium assumptions, while APT allows multiple factors and derives pricing from the weak condition that no arbitrage exists.

Sources reviewed: 2026-10-26

References

1. Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
2. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425–442.
3. Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3), 341–360.
4. Roll, R. (1977). A critique of the asset pricing theory's tests Part I. Journal of Financial Economics, 4(2), 129–176.
5. Roll, R., & Ross, S. A. (1980). An empirical investigation of the arbitrage pricing theory. Journal of Finance, 35(5), 1073–1103.
6. Huberman, G. (1982). A simple approach to arbitrage pricing theory. Journal of Economic Theory, 28(1), 183–191.
7. Chamberlain, G., & Rothschild, M. (1983). Arbitrage, factor structure, and mean-variance analysis on large asset markets. Econometrica, 51(5), 1281–1304.
8. Shanken, J. (1982). The arbitrage pricing theory: Is it testable? Journal of Finance, 37(5), 1129–1140.
9. Chen, N.-F., Roll, R., & Ross, S. A. (1986). Economic forces and the stock market. Journal of Business, 59(3), 383–403.
10. Connor, G., & Korajczyk, R. A. (1986). Performance measurement with the arbitrage pricing theory: A new framework for analysis. Journal of Financial Economics, 15(3), 373–394.
11. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.
12. Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57–82.
13. Harvey, C. R., Liu, Y., & Zhu, H. (2016). … and the cross-section of expected returns. Review of Financial Studies, 29(1), 5–68.