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An analysis of fama and french's (1993) three-factor asset pricing model, which is an extension of the capital asset pricing model (capm). The authors test the efficiency of the market by examining the relationship between risk and return using size and book-to-market ratios as additional risk factors. The results show that the three-factor model explains the cross-sectional variation in stock returns better than the capm.
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2(t)
3(t)
1(t)
m(t)
0(t)
1
CAPM, Multifactor Models and APT
cross sectional data
Sample
July
to Dec.
(monthly data)
โsize and valueโ sorted portfolios, monthly time series returns on
stocks are explained by a
factor model R it
1i
mt
2,i
t^
3i
t Rbar i^
m
1i
SMB
2i
HML
3i where R i^ = excess return on asset i R m = excess return on the market Rbar = mean return
For the
portfolios
sorted (i.) by size and (ii.) value (BMV) and (iii.) by value
and size.
Market betas are clustered in range
and
is correct
expect positive correlation)
Sorting portfolios by book to market rejects the
(see graph)
Success of Fama
French
factor model can be seen by comparing the predicted (average) returns with the actual returns (see graph)
Average Excess Returns and Market Beta 0 0.8 0.6 0.4 0. 1
0
1
Beta on Market Excess return Returns sorted by BMV,within given size quintile Returns sorted by size,within given BMV quintile
Fama and French (1993) Findings (Cont.)
2
stage procedure to test
Empirical test on
use portfolios to minimise the errors in measuring betas
beta explains the difference in average (cross
section) returns between stocks and bonds, but not within portfolios of stocks
Fama and French book to market and size variables should be included as additional risk factors to explain cross
section of average stock returns
