The document summarizes a research article that evaluates factors influencing expected stock returns. It finds that beta alone does not reliably explain average returns as the Sharpe-Lintner-Black model predicts. Instead, size and book-to-market equity best capture cross-sectional variation, with smaller stocks and those with higher book-to-market ratios tending to generate higher returns. The results hold across different time periods and robustness tests. The findings imply size and book-to-market may proxy for risk factors, allowing their use in portfolio evaluation and return projections if asset pricing is rational.

1. THE CROSS-SECTION OF
EXPECTED STOCK
RETURNS
RAJU BASNET CHHETRI
28 MAY 2020
A synopsis on

2. Description of the Article
 Title: The Cross-Section of Expected Stock Returns
 Authors: Eugene F. Fama and Kenneth R. French, Graduate School of
Business, University of Chicago
 Journal: The Journal of Finance, Vol XLVII, No. 2, June 1992, pp. 427-465.

3. Background
 Sharpe (1964), Lintner (1965), and Black (1972)’s Asset-Pricing model, also
known as SLB model explains that (a) expected returns on securities are a
positive linear function of their market s and (b) market s are sufficient
to describe the cross-section of expected returns.
 However, there are several empirical contradictions of SLB model like the
“strong negative relation between average return and firm size” by Banz
(1981), “positive relation between leverage and average return” by
Bhandari (1988).

4.  Similarly, there is a positive relation between average return and earnings
to price ratio (E/P) as revealed by Basu, 1983; positive relation between
average return and book-to-market equity (BE/ME) (as explained on US
stocks by Rosenberg et al.,1985 and on Japanese stocks by Chan et al.,
1992).
 Hence, the study was conducted to evaluate the joint roles of
abovementioned variables on expected stock returns.

5. Research Gap/Motivation
 The variables like size, E/P, leverage, and book-to-market equity, all being
scaled versions of price, the study was motivated to explore either all of
them were equally important or some of them being redundant could be
marginalized.

6. Purpose
 The study was conducted to evaluate the roles of market , size, E/P,
leverage, and book-to-market equity in the cross-section of average
returns.

7. Methodology
DATA, ESTIMATION OF VARIABLES, METHODS

8. Data
 All non-financial firms’ return and financial statements respectively was
taken from:
(a) NYSE, AMEX, and NASDAQ, and
(b) COMPUSTAT,
both maintained by Center for Research in Security Prices (CRSP) for
the period 1962-1989.

9. Estimation of variables
 A firm’s market equity at the end of December of year t-1 was used to
compute its BE/ME, leverage, and E/P ratios for t-1, and market equity for
June of year t was used to measure its size.

10. Methods
(A) Two-pass sort on size and 
The two-pass sort on size and  was conducted to see the relationship between average
stock return on size and  respectively. The two-pass sorting on size and  was done as
follows:
1. The stocks were sorted by size (as per Chan and Chen, 1988) to 10 portfolios based
on NYSE breakpoints.
2. “Pre-ranking s” were estimated from 24 to 60 monthly returns based on last five
years data.
3. To allow for variation in  that was unrelated to size, each size decile were again
subdivided into 10 portfolios on the basis of “pre-ranking s” for individual stocks,
making a total of 100 portfolios. Only NYSE stocks were used to establish 
breakpoints.
4. The full-period s were calculated for each size- portfolio, called “post-ranking s”
which were then allocated to each stock in the portfolio.
(B) Fama-Macbeth (FM) regressions
 FM regressions were conducted on time-series averages of the slopes from the
month-by-month cross-section of stock returns on , size, book-to-market equity,
leverage, and E/P.

11. Analysis of data
TABLE I TO VI

12. Table I and II
 The ordering of the pre-ranking and post ranking s for the -sorted
portfolios (explained in Tables I and II) evidenced that variation in , tied
to size, had positive relation with average return, but variation in ,
unrelated to size, had no obvious relation with average return.
 Results were contradictory with the SLB model, which explains positive
relation between  and average return.
 As the results were contrary to the SLB model, validity check was
conducted for 1941-1990 and 1941-1965 (explained in the appendices)
which also showed similar results.

13. Table III
 FM regressions conducted on time-series averages of the slopes from the
month-by-month cross-section of stock returns on , size, book-to-market
equity, leverage, and E/P (explained in Table III),
i. supported the size effect i.e. smaller stocks have higher average returns, in
the 1963-1990 returns on NYSE, AMEX, and NASDAQ stocks.
ii. showed that  does not help explain average stock returns.
iii. BE/ME relation is stronger than the size effect.
iv. the difference between market leverage (A/ME) and book leverage (A/BE)
helps to explain average return, which is given by book-to-market equity
(BE/ME).
v. the average slopes for stocks with positive E/P show average returns
increase with E/P.

14. Average slope = -0.15, -0.17
t-statistic = -2.58, -3.41
Reliable negative relation
(smaller stocks have higher
average returns)
Average slopes are typically
less than 1 standard error
from 0, showing no power to
explain average returns
The two leverage variable slopes are
opposite in sign but close in absolute
values.
Therefore, BE/ME helps to explain
average returns
Avg. slope of E/P dummy variable
0.57% per month, 2.28 standard
errors from 0, indicate firms with
negative earnings have higher
average returns
Similarly, when positive, average
return increases.
(Average return and E/P has U-
shaped relation)
Leverage variables
11 regressions

15. Table IV
 Portfolios formed on values ranked on the basis of book-to-market
equity (BE/ME) and earnings-price ratio (E/P) (explained in Table IV)
showed:
i. strong positive relation between average return and BE/ME and
ii. the combination of size and BE/ME absorbs the apparent roles of
leverage and E/P in average stock returns.

16. Strong positive relation
between average
return and book-to-
market equity
Positive correlation:
Firms with high E/P
tend to have high
BE/ME

17. Table V
 With the above analyses, it was found that  was unable in explaining the
average returns for the sample data, while size and book-to-market
equity captured the cross-sectional variation in average stock returns.
 Hence, further analyses was performed using average return matrix on
portfolios formed on size and BE/ME (explained in Table V).
 It was found that:
i. returns typically increase strongly with BE/ME (with control in size), and
ii. there is negative relation between average return and size (within same
BE/ME groups).

18. Within BE/ME groups:
Negative relation
between average
return and size
Within same size:
BE/ME captures substantial variation in
cross section of average returns

19. Table VI
 Two FM regressions was conducted (explained in Table VI) for two
roughly equal subperiods July 1963 – December 1976, and January 1977 –
December 1990:
i. the cross-section of stock returns on size, ln(ME), ln(BE/ME), and
ii. returns on , ln(ME), ln(BE/ME)
 It was found that book-to-market is consistently the most powerful for
explaining the cross-section of average stock returns.

20. Book-to-market equity is consistently the most
powerful for explaining the cross-section of average
stock returns.
(standard error > 2.95 standard errors from 0,
significant)
Contradicting within two periods

21. Conclusion and Implications
 The results of the test conducted conclude that no reliable relation between  and
average return was found for the sample and period under study, contradicting the
SLB model.
 Similarly, size and book-to-market equity was found to be most reliable variables to
capture the cross-sectional variation in average stock returns associated with size, E/P,
book-to-market equity, and leverage.
 The author explains the assumption of rational asset price framework used in the study
and explains the implications that:
i. If asset-pricing is rational (asset prices reflect the arbitrage-free price of the asset as
any deviation from this price will be “arbitraged away”), size and book-to-market
equity must represent or proxy for risk. Hence, by comparing average returns with
size and BE/ME characteristics, the performance of portfolios can be evaluated, and
similarly, historical data can be used to estimate future projections.
ii. If asset-pricing is irrational and size and BE/ME do not proxy for risk, the author
concludes that the results might still be used to evaluate portfolio performance and
measure the expected returns form alternative investment strategies.

22. Reflection from the article
 The article is methodologically strong with robustness tests and
supporting validity tests attached in the appendix with another set of data
under different time period.
 The results are neatly presented with comparative results of earlier
studies.
 I was able to understand the use of corroborative evidences to support
the findings in the study, and is hopeful to try such methods in my further
studies.

23. Thank you
Suggestions and feedback are welcome.