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Explain where the capital asset pricing model falls short

CFA® Level I · Portfolio Management · Portfolio Risk and Return: Part II · PM.4.e

The idea

The model rests on assumptions that do not hold: a single period, homogeneous expectations, unlimited borrowing and lending at the risk-free rate, no taxes or transaction costs, and a market portfolio containing every asset. That last point is Roll's critique — the true market portfolio, including human capital and private assets, is unobservable, so any test of the CAPM is really a joint test of the model and the proxy used for the market. Empirically, size, value and momentum have explained returns beyond beta, which motivated the multifactor models that followed.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which is an assumption of the CAPM?

  1. Investors have different expectations about returnsWhy not: The model assumes the opposite, homogeneous expectations, which is what makes everyone hold the same risky portfolio.
  2. Investors can borrow and lend without limit at the risk-free rate — correct
  3. Transaction costs vary by investorWhy not: The model assumes no transaction costs at all, uniformly.

Unrestricted borrowing and lending at a common risk-free rate is what makes the capital market line a straight line available to everyone.

A harder one

What is the essence of Roll's critique?

  1. Beta cannot be estimated from historical dataWhy not: It is estimated routinely; the critique is about what it is estimated against.
  2. The risk-free rate is not truly risk freeWhy not: A fair observation about government securities, and a separate objection from the one Roll raised.
  3. The true market portfolio is unobservable — correct

Tests of the model are therefore joint tests of the model and the chosen proxy. An index of listed equities omits bonds, property, private businesses and human capital, so a rejection may mean the proxy is wrong rather than the theory.

The hardest tier

Empirical work finds small-capitalisation stocks earning more than their betas predict. What are the two competing interpretations?

  1. Either beta is missing a priced risk factor, or the result reflects data mining and survivorship in the sample — correct
  2. Either the risk-free rate is mismeasured, or transaction costs are too highWhy not: Neither would produce a pattern specific to small companies across long periods.
  3. Either the CAPM is correct, or small stocks have negative betaWhy not: Small stocks have positive betas, usually above one, which makes the excess harder to explain rather than easier.

A persistent anomaly is evidence either for an additional compensated risk — which is what multifactor models assume — or for a statistical artefact. Distinguishing them requires out-of-sample evidence.

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