Size Factor Comparison
The small-cap premium is an excellent example of the difficulty in discerning, in real time, the integrity of an established factor. The anomaly has failed to establish a meaningful new high since it was originally published in 1981. Only in the last decade—nearly 30 years later—have the tides of the industry finally seemed to turn against it as an established anomaly and potential source of excess return.
The remaining broadly accepted factors—e.g., value, momentum, carry, defensive and trend—have all been demonstrated to generate excess risk-adjusted returns across a variety of economic regimes, geographies and asset classes, creating a great depth of evidence supporting their existence.
What evidence, then, would make us abandon faith from the Church of Factors?
Testing Each Factor
To explore this question, we ran a simple experiment for each factor. Our goal was to estimate how long it would take to determine that a factor was no longer statistically significant.
Our assumption is that the features of each factor’s return pattern will remain the same, but the forward average annualized return will be zero since the factor no longer “works.”
Toward this end, we ran the following experiment:
- Take the full history for the factor and calculate prior estimates for mean annualized return and standard error of the mean.
- De-mean the time-series.
- Randomly select a 12-month chunk of returns from the time series and use the data to perform a Bayesian update to our mean annualized return.
- Repeat the previous step until the annualized return is no longer statistically non-zero at a 99% confidence threshold.
For each factor, we ran this test 10,000 times, creating a distribution that tells us how many years into the future we would have to wait until we were certain, from a statistical perspective, that the factor is no longer significant.
Based on this experience, 67 years is the median number of years we will have to wait until we officially declare price-to-book (known as HML) to be dead (we are ignoring historical and forward evidence, or counter-evidence, found in other geographies). At the risk of being morbid, we’re far more likely to die before the industry finally sticks a fork in price-to-book.
We perform this experiment for a number of other factors—including size (“SMB”), quality (“QMJ”), low-volatility (“BAB”) and momentum (“UMD”)—and see much the same result. It will take decades before sufficient evidence mounts to dethrone these factors.