The Cross-Section of Expected Stock Returns. Authors: Eugene F. Fama and Kenneth R. French.
Source: The Journal of Finance, Vol. XLVII, No. 2 (June., 1992), pp. 427-465
Research question(s):
1. Is there still a valid relation between average return and β? (Does CAPM still apply)
2. Are other (risk) factors related to average returns?
Underlying intuition
The most famous asset pricing model, CAPM, hypothesizes average stock returns are positively
related to β. Fama and French (FF) reinvestigate this hypothesis with more recent data, and an
altered methodology. Multiple claims refute the original findings, and such this paper aims to
falsify these contradictions.
An additional research question follows the research of other authors regarding factors related
to expected returns. This paper aims to add to previous findings by testing average returns with
a CAPM model enhanced with additional factors (three-factor model). The factors are based on
the following company characteristics: Book-to-Market (B/M), Size (M), A/M, A/B and EPS.
Research Methodology & Data
Monthly returns for all from major US exchanges (NYSE, AMEX & NASDAQ) from 1962 – 1990
are used. Financials are excluded, as their leverage is too high relative to non-financial stocks.
Two main methods are used to find information on factors explaining average return: Double-
sorting based on company characteristics, and a cross-sectional regression ran over average
returns using past company characteristics as factors (Fama and MacBeth (FM) regression). FM
regressions used portfolio β’s instead of individual stock β’s as they tend to be more accurate.
An additional issue here is that the beta and the size of a firm have a strong relation. Double-
sorting is used to solve this (using the first method).
Double-sorting in steps:
1. Sort stocks into ten size deciles
2. Take prior data (preceding 24 months - 60 months) to size sorting date to estimate β
per stock, we call these the pre-ranking β
3. Within each size decile, sort stocks into ten β deciles. We now have 100 portfolios
4. Calculate the return of the portfolios over the next year
5. Redo steps 1 to 4 for each year (re-sort the portfolio on a newly estimated pre-
ranking β) in the dataset.
6. For each size-β portfolio, estimate a portfolio (post-ranking) β over the full sample
period.
The second method (FM regression) is used to investigate the relation of a combination of
factors with stock returns. The regression is equal to:
BE A
𝑅"# = 𝛾'# + 𝛾)# 𝛽+",#-) + 𝛾.# 𝑙𝑛(ME)",#-) + 𝛾5# 𝑙𝑛(
)",#-) + 𝛾7# 𝑙𝑛( )",#-)
ME ME
A E E +
+ 𝛾9# 𝑙𝑛( )",#-) + 𝛾:# ( dummy)",#-) + 𝛾@# + 𝜂"#
BE P P ",#-)
Source: The Journal of Finance, Vol. XLVII, No. 2 (June., 1992), pp. 427-465
Research question(s):
1. Is there still a valid relation between average return and β? (Does CAPM still apply)
2. Are other (risk) factors related to average returns?
Underlying intuition
The most famous asset pricing model, CAPM, hypothesizes average stock returns are positively
related to β. Fama and French (FF) reinvestigate this hypothesis with more recent data, and an
altered methodology. Multiple claims refute the original findings, and such this paper aims to
falsify these contradictions.
An additional research question follows the research of other authors regarding factors related
to expected returns. This paper aims to add to previous findings by testing average returns with
a CAPM model enhanced with additional factors (three-factor model). The factors are based on
the following company characteristics: Book-to-Market (B/M), Size (M), A/M, A/B and EPS.
Research Methodology & Data
Monthly returns for all from major US exchanges (NYSE, AMEX & NASDAQ) from 1962 – 1990
are used. Financials are excluded, as their leverage is too high relative to non-financial stocks.
Two main methods are used to find information on factors explaining average return: Double-
sorting based on company characteristics, and a cross-sectional regression ran over average
returns using past company characteristics as factors (Fama and MacBeth (FM) regression). FM
regressions used portfolio β’s instead of individual stock β’s as they tend to be more accurate.
An additional issue here is that the beta and the size of a firm have a strong relation. Double-
sorting is used to solve this (using the first method).
Double-sorting in steps:
1. Sort stocks into ten size deciles
2. Take prior data (preceding 24 months - 60 months) to size sorting date to estimate β
per stock, we call these the pre-ranking β
3. Within each size decile, sort stocks into ten β deciles. We now have 100 portfolios
4. Calculate the return of the portfolios over the next year
5. Redo steps 1 to 4 for each year (re-sort the portfolio on a newly estimated pre-
ranking β) in the dataset.
6. For each size-β portfolio, estimate a portfolio (post-ranking) β over the full sample
period.
The second method (FM regression) is used to investigate the relation of a combination of
factors with stock returns. The regression is equal to:
BE A
𝑅"# = 𝛾'# + 𝛾)# 𝛽+",#-) + 𝛾.# 𝑙𝑛(ME)",#-) + 𝛾5# 𝑙𝑛(
)",#-) + 𝛾7# 𝑙𝑛( )",#-)
ME ME
A E E +
+ 𝛾9# 𝑙𝑛( )",#-) + 𝛾:# ( dummy)",#-) + 𝛾@# + 𝜂"#
BE P P ",#-)
