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Explain where the capital asset pricing model falls short

CFA® Level I · Portfolio Construction · 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 one tangency portfolio.
  2. Investors can borrow and lend freely at the risk-free rate - correct
  3. Investors pay taxes at different rates on their returnsWhy not: The model assumes no taxes and no transaction costs, so every investor faces the same after-cost returns.

The CAPM is a model of how risk and expected return relate, and it rests on simplifying assumptions. One is that every investor can borrow and lend any amount at the same risk-free rate (the return on a safe asset). That is what lets everyone reach a straight line of choices, the capital market line. The model also assumes investors share the same expectations and that there are no transaction costs, so the other two choices state the opposite of the model.

A harder one

Tests of the CAPM use a stock index as a proxy for the market portfolio. What is the essence of Roll's critique?

  1. Historical data are too short to estimate a betaWhy not: Beta is estimated routinely; the critique is about what the index stands for, not the data length.
  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

The CAPM refers to the market portfolio, which holds every asset in the world, including bonds, property, private businesses and even people's future earning power. Nobody can observe that. Tests therefore use a stock index as a stand-in, called a proxy. Roll's point is that a test then checks the model and the proxy together. Example: if an index fails to explain returns, the index may be a poor proxy and the theory may still be fine.

The hardest tier

Parisa Naidoo, an analyst, regresses the average returns of 500 stocks over 20 years on their betas, which she estimated against a broad domestic equity index. The relationship is weak, and she concludes that the capital asset pricing model is invalid. A colleague says the conclusion is premature. Which objection is most valid?

  1. Returns should have been regressed on standard deviation, not betaWhy not: The CAPM prices beta, so beta is the right measure to test. Standard deviation is total risk, which the model does not reward.
  2. The index may be a poor proxy for the true market portfolio - correct
  3. The model describes portfolios, so individual stocks cannot be testedWhy not: The security market line applies to individual securities as well as portfolios.

The CAPM's market portfolio holds every risky asset, including property, private firms and human capital (people's future earnings), and it cannot be observed. Any test uses a stand-in such as an equity index, so it tests the model and the stand-in together. This is known as Roll's critique. A weak link between beta and return might mean the model is wrong, or only that the index is a poor proxy, so the betas were measured against the wrong benchmark. The model prices beta rather than standard deviation, and the security market line applies to individual stocks, so the other objections fail.

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