cutoffs to define our test portfolios.
2.3 Factor Model
In estimating abnormal returns, we use the Carhart (1997) four factor model
to adjust for the influence of the systematic risk factors of Fama and French
(1993) and Jegadeesh and Titman (1993):
Ri,t — Rb,t = ai + βi,M ∙ (RM,t - Rp,t) + βi,sMB ∙ SMBt
+βi,HML ∙ HMLt + βi,WML ∙ WMLt + εi,t, (1)
where the dependent variable is the excess return of portfolio i in month
t, Ri,t, over the return of some benchmark in the same month, Rb,t. In
our basic tests we will use the risk-free asset as benchmark, i.e., Rb,t = RF,t.
RM,t -RF,t denotes the excess return of the market portfolio over the risk-free
rate. SM B is the return difference between small and large capitalization
stocks. HML is the return difference between high and low book-to-market
stocks. WML is the return difference between stocks with high past returns
and stocks with low past returns.7
The market portfolio and the SM B , HML, and WML factors are based
on the entire CRSP universe of stocks. We first want to make sure that
Model (1) captures the relevant risk factors for our universe of investable
stocks, which consists of all S&P 500 and S&P 1500 stocks, respectively.
Therefore, we analyze whether it correctly prices portfolios containing all
of these stocks. If the model is correctly specified, the intercept αi in (1)
should not be statistically significant different from zero.
7The market, the size, and the value portfolio returns were taken from Kenneth French’s
Web site: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french, while the mo-
mentum factor was kindly provided by Mark Carhart.
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