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Weighting Conventions in Fama–French and Carhart Factors

Article Quant Q&A · Author: incognito
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Summary

The document explains the weighting structure of the market, SMB, HML, and momentum factors commonly used in Fama–French and Carhart regressions. The market factor is described as a value-weighted return across eligible US firms. For SMB, HML, and momentum, the underlying size, book-to-market, or prior-return portfolios are value-weighted, while the long–short factor is formed by taking equal-weighted averages or differences of those portfolio returns.

This distinction clarifies why descriptions of the factors may refer both to equal and value weighting: the weighting applies at different stages of construction. The answer cites factor definitions and established papers, but provides no new performance analysis. The original question raises whether equal weighting might influence estimated alpha; understanding the construction helps frame that concern, though it does not determine how much any particular regression result depends on the weighting scheme. The discussion focuses on the standard US factor portfolios and does not compare alternative factor implementations.

Key ideas

  • The market factor is constructed as a value-weighted return over eligible US stocks.
  • SMB averages value-weighted size portfolios with equal weights across the component returns.
  • HML combines value-weighted book-to-market portfolios through equal-weighted component returns.
  • The momentum factor similarly uses value-weighted portfolios and equal weights across component returns.
  • Factor construction has multiple weighting stages, so calling a factor simply equal-weighted or value-weighted can be imprecise.

Tags

EquitiesFactor investingStatisticsUS markets
Full text
# Are the FFC factors equal or value-weighted?


# Are the FFC factors equal or value-weighted?












As the title already reveals: I need to know whether the Fama-French (carhart) factors are constructed by using equal-weight sorting or value-weight sorting.

On Kenneth F. website it says the portfolios are are constructed using the 6 value-weight portfolios formed on size and book-to-market.

However Cremers et al. (2012) argue in their paper, that FF use equal-weighted sorts?

This is relevant as it may reveal that the alpha that shows up from a regression upon the FF factors is due to equal-weighting rather than actual 'skill' alpha.

## Answer by skoestlmeier (score 5, accepted)

https://quant.stackexchange.com/a/48992

Regards FFC, you refer to four portfolios, which are formed by using different weightings:

- The market portfolio, which is a value-weighted return with end-of-previous market cap. as weights: The excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).

- The SMB portfolio, which is the equal-weighted return of value-weighted portfolios, i.e. the six sub-portfolio returns are value-based, and the hedge-portfolio is based on equal-weighted returns of these sub-portfolios: SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios.

- The HML portfolio, which is (as SMB) the equal-weighted return of value-weighted portfolios. Here, the return of four sub-portfolios are value-based, and the final HML return is the equal-weighted difference return of these sub-portfolio returns: HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios.

- The WML (or MOM) portfolio, which is updated each month, and similar the HML is the equal-weighted return of four value-weighted sub-portfolios (see Jegadeesh/Titman (1993)). MOM is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios.

References:

Carhart (1997). On Persistence in Mutual Fund Performance, The Journal of Finance.

Fama/French (1993), Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics.

French (2019), Data Library.

Jegadeesh/Titman (1993), Returns to buying winners and selling losers: Implications for stock market efficiency, The Journal of Finance.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.