Welcome to another post on reproducibility in finance literature!
A couple of days back, Robeco quant researcher Matthias Hanauer tweeted his latest work (joint with David Blitz) on size premium in the “Settling the Size Matter"1 paper. It’s a relatively short paper and attempts to address the basic question if (and how) size factor matters at all.
Does Size Matter? Check out our brand new paper on the size premium (joint work with David Blitz).
It was a quick fun exercise reproducing the results using Python 🐍. All the code is available on Github
settling-the-size-matter
Data
Almost all the data used in the paper is publicly available from following sources (except for their self-constructed size factor based on 2x3 independent sorts on size and the ex ante beta of a stock towards the QMJ factor (SMB_beta_QMJ))
Exhibit 1: Regression results for US SMB_3F factor
There exists a “raw size” premium of 0.19% per month in the US but fades away after controlling for market exposure as well as popular factors of value (HML) and momentum (WML)
Size premium rises significantly after considering additional factors exposures such as Fama-French’s profitability (RMW) and investment (CMA), AQR’s quality-minus-junk (QMJ) and extended q-factors of investment-to-asset (IA), return on equity (ROE) and expected growth (EG) respectively
Original Paper Table
Reproduced Table
Exhibit 2: Regression results for international SMB_3F factors, Kenneth French regional data
Internationally, the size premium remains absent – discretely as well as when considered with other factor exposures such as HML, WML, RMW and CMA
Europe
Original Paper Table
Reproduced Table
Asia Pacific ex-Japan
Original Paper Table
Reproduced Table
Japan
Original Paper Table
Reproduced Table
Emerging Markets
Original Paper Table
Reproduced Table
Exhibit 3: Regression results for international SMB_3F factors, AQR regional data
Results are similar to Exhibit 2 (i.e. no existence of significant alpha), although it slightly improves after controlling for QMJ factor
Europe
Original Paper Table
Reproduced Table
Pacific
Original Paper Table
Reproduced Table
Exhibit 4: Regression results for international SMB_3F factors, AQR country data
For most international markets, the size premium is statistically insignificant with the sole exception of the US (but only after controlling for QMJ factor exposure)
Original Paper Figure
Reproduced Figure
Exhibit 5: Regression results for different versions of the US SMB factor
Considering different versions of quality-controlled ex-ante size factors (as opposed to ex-post in the earlier case) doesn’t alter the results to a significant extent
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Exhibit 6: Regression results for US SMB_3F on either the long legs or the short legs of other factors
The size premium results are promising but limited only to short leg of other factors
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Exhibit 7: Regression results for standard factors on alternative factors with 10% instead of 50% weight to small-caps
Size factor plays a key role to fully expose the benefits of other factors such as value and momentum
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Original Paper Table
Reproduced Table
Summary
The key message of the paper is quoted from the last line of the abstract
“Size is weak as a stand-alone factor but a powerful catalyst for other factors”
