Alphas in disguise: A new approach to uncovering them

The Carhart 4-factor model has become the academic standard for explaining returns; however, recently passive indices have been shown to have non-zero alphas in their 4-factor models, which should not be so for passive indices that represent the market.  Either the wrong factors are being selected or there are errors in the calculations of those factors used. 

Previous studies have suggested that one error may be the SMB calculation: some small funds may actually have big companies in them, because, since big companies are small relative to the whole market, causing a biased positive SMB estimate.  This goes for the other winner/loser, value/growth factors as well.  To mitigate that error, other studies have reduced alpha in indices by including only only US Equities in the market portfolio, make the HML and SMB portfolios be value-weighted instead of equal-weighted, separate value/growth stocks and small/big stocks, and make the sizes more granular (such as large-cap, mid-cap, small-cap, etc.).

The authors study 1,383 US equity mutual funds over the period January 1992 to October 2013, who designate the S&P 500 as their benchmark.  They then make adjustments to the Carhart 4-factors (obtained from Ken French's website) that will bring the alpha to zero.  In their calculations, they find both active and passive funds perform worse on an adjusted alpha basis than what is implied by the unadjusted Carhart 4-factor model. 

Also noted is that the passive tracker funds performed the worst over the period, showing significant negative alphas; which is counter-intuitive, considering a passive tracker fund should have a zero alpha.  Active mutual funds perform outperform in some periods and under-perform in others.

Chinthalapati, V., Mateus, C., & Todorovic, N. (2017). Alphas in disguise: A new approach to uncovering them. International Journal of Finance & Economics, 22(3), 234–243.