# 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!

• I think the phrase you're looking for is the "Joint Hypothesis Problem". In particular, any abnormal risk-adjusted returns can be interpreted either as an inefficiency in the market, or as an additional risk factor that should be included in your risk model. – Evan Wright Dec 16 '14 at 20:27
• Yes! Would you mind turning that into an answer? – Constantin Dec 16 '14 at 22:14

## 1 Answer

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.