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Portfolio Theory and Quantitative Investment / CAPM and Equilibrium Models

Empirical Tests of the CAPM and Roll's Critique

A model is not a model until it meets the data. The CAPM predicts that expected return is a linear function of a single risk measure — beta — and that beta is the only risk measure that earns a premium. Every unit of diversifiable risk, every unit of total variance beyond the beta contribution, should earn zero additional return. Testing these predictions produced five decades of debate with three headline findings:
  1. The intercept is too high and the slope is too flat. Estimated security market lines have an intercept above the riskless rate and a slope below (RˉM−RF)(\bar{R}_M - R_F) — a pattern consistent with the zero-beta CAPM rather than the standard form.
  2. Residual risk is not priced — but size and book-to-market are. The CAPM's prediction that only beta matters survives early tests (Fama-MacBeth 1973), but Fama and French (1992) showed that once size and book-to-market are added, beta's explanatory power disappears.
  3. Roll's (1977) critique: the CAPM may be untestable. Any ex-post mean-variance efficient portfolio trivially produces a linear return-beta relationship. Since the true market portfolio (including human capital, real estate, and private assets) is unobservable, every CAPM test is really a test of whether the chosen proxy is mean-variance efficient — a different and weaker claim.
These findings have practical consequences. Factor models — from the Fama-French three-factor model to the APT to practitioner risk models — exist because the empirical CAPM fails: they were built to capture what the single-beta model misses.
Learning objectives. By the end of this note you should be able to:
  • describe the two-pass methodology (time-series first pass + cross-sectional second pass) and identify what each pass estimates;
  • state the three testable CAPM hypotheses and what rejecting each one implies;
  • summarise the findings of Black–Jensen–Scholes (1972) and Fama–MacBeth (1973);
  • explain Roll's critique and the logical gap it identifies;
  • state the GRS T2T^2 test and what a large T2T^2 implies about market efficiency;
  • explain why the Fama-French evidence is more damaging to the CAPM than a simple intercept bias.

In this lesson

    1. What is being tested
    1. Two-pass methodology
    1. Early evidence: Sharpe-Cooper and Lintner
    1. Black, Jensen, and Scholes (1972)
    1. Fama and MacBeth (1973)
    1. Roll's critique (1977)
    1. The GRS T2T^2 test and market efficiency
    1. Fama-French challenge (1992)

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