Posts this month
A blog on financial markets and their regulation
Among the thousands of pages that I read during my two month long vacation were two papers that show that many of the large number of published asset pricing anomalies (Cochrane’s “zoo”) have withered away over time. The papers are
Hou, Xue and Zhang (2017), Replicating Anomalies, NBER Working Paper 23394 and
Mclean and Pontiff (2016) Does Academic Research Destroy Stock Return Predictability?, Journal of Finance.
Hou, Xue and Zhang show that out of the 447 anomalies that they study as many as 286 (64%) are insignificant at the conventional 5% level. Increasing the cutoff t-value to 3.0 raises the
number of insignificance to 380 (85%). Clearly, there are a lot of Type M errors in the anomalies literature and a few Type S errors as well.
I started wondering what would happen if we imposed an even higher standard of statistical significance. This is where particle physics comes in. While the social sciences are quite happy with significance levels of 5% and 1% (implying cutoffs of around 2 or 3 standard deviations), the significance level required for the discovery of a new particle in physics is 0.0001% or one in a million (implying a cutoff of around 5 standard deviations). For example, when the Higgs particle was discovered in July 2012, the official press release from CERN stated: “Today, both the ATLAS and CMS experiments are beyond the level of around one per million that’s required to claim a discovery.” For more discussion on the 5 sigma standard, see here, here and here.
Asset prices exhibit significantly fatter tails than the Gaussian distribution and that would require raising the cutoff even higher. The statistical quality control world uses a shift of 1.5 standard deviations so that 6 standard deviations (six sigma) are required to achieve quality standards that would otherwise require only 4.5 standard deviations.
I pored over Table 4 of Hou, Xue and Zhang that lists the t-values for all the anomalies that are significant at the 5% level. Not one of these is above 6.0 and only two (Abr1 and dRoe1) are above 5.0. Adjusted for fat tails, there is no anomaly that meets a one in a million standard of significance. By this standard, therefore, markets can be assumed to be efficient. More prosaically, finance is still at the Tycho_Brahe stage of assembling enough high quality data to discriminate between competing theories.