The Joint Hypothesis Problem in Tests of Market Efficiency
Summary
The document explains why a test for market inefficiency cannot cleanly distinguish a genuine return anomaly from a flaw in the model used to define expected or risk-adjusted returns. This is the joint hypothesis problem: testing whether prices are efficient also tests the chosen asset-pricing model. For example, a positive, statistically significant alpha under a factor model could reflect an exploitable anomaly, or an omitted source of risk that makes the model’s benchmark incomplete.
The response uses the history of the Fama–French portfolios as an illustration. Their abnormal returns relative to CAPM can be read as evidence against market efficiency if CAPM is assumed correct; alternatively, the returns may indicate that the portfolios capture risk factors missing from CAPM. The example clarifies interpretation rather than offering a procedure to settle the issue. The document gives no new empirical tests and does not establish which explanation is right, so conclusions depend on model choice and supporting evidence.
Key ideas
- An empirical efficiency test also depends on the asset-pricing model used to define abnormal returns.
- A significant alpha may indicate mispricing or an incomplete risk model.
- Fama–French portfolio returns challenge CAPM benchmarks but may also reflect additional risk factors.
- Statistical significance alone cannot determine whether a return pattern is an anomaly.
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# What are the empirical limitations to testing market efficiency? # What are the empirical limitations to testing market efficiency? I have encountered a rather elegant argument about the limitations of empirically testing for market efficiency, involving the central point that we do not know whether a result is due to the "true behaviour" of the market or due to the model used to simulate that behaviour. Unfortunately I have not been able to retrieve this argument online, nor any publications relating specifically to this, which may be due to the fact that I do not know how this argument is typically referred to in the literature. In particular, I would like to understand how we can interpret any empirical results regarding market anomalies or market efficiency when taking into account the above important limitation. Say, for example, we use the Fama-French-Carhart model in order to examine whether a particular portfolio formation strategy leads to abnormal returns. If our $\alpha$ is positive and significant, how can we know this is due to an actual anomaly (on which we have based our portfolio formation), rather than a bias in our model, which has underestimated market returns (other than the fact that the model usually has a decent predictive power)? I greatly appreciate any clarification or resources! ## Answer by Evan Wright (score 9, accepted) https://quant.stackexchange.com/a/15905 This the "Joint Hypothesis Problem". Basically, any test for abnormal returns is also implicitly a test of the model you use to define "abnormal". If you see a significant and positive $\alpha$, that could either mean that you actually are generating excess risk-adjusted returns, or it could mean that your risk model is incomplete. This is basically what happened with Fama-French. If you assume that CAPM is true, then Fama and French showed that the market is inefficient, since certain portfolios have abnormal risk-adjusted returns. However, since "everyone" now knows about the Fama-French portfolios, and they still show excess returns over those predicted by CAPM, it's more reasonable to interpret their results as having discovered new risk factors.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.