Ch. 6: Security Offerings 347
5.3.3. Average monthly abnormal returns using factor pricing regressions
In this section, we use empirical asset pricing models to generate portfolio expected
returns. An asset pricing model is estimated using monthly returns, with the intercept
term in the pricing model (also referred to as “Jensen’s alpha” fromJensen (1968),or
simplyα) as the measure of the average monthly abnormal return. The most commonly
used empirical asset pricing models in this literature are of the multi-factor (APT) type
in general, and the three-factor model ofFama and French (1993)in particular.^53
The factor pricing analysis proceeds as follows. Letrptdenote the return on issuer–
portfoliopin excess of the risk-free rate, and assume that expected excess returns are
generated by aK-factor model,
E(rpt)=βp′λ, (8)whereβpis aK-vector of risk factor sensitivities (systematic risks) andλis aK-vector
of expected risk premiums. The return generating process can be written as
rpt=E(rpt)+βp′ft+ept, (9)whereftis aK-vector of risk factor shocks andeptis the portfolio’s idiosyncratic risk
with expectation zero. The factor shocks are deviations of the factor realizations from
their expected values, i.e.,ft≡Ft−E(Ft), whereFtis aK-vector of factor realizations
andE(Ft)is aK-vector of factor expected returns.
Regression equation(9)requires specification ofE(Ft), which is generally unob-
servable. To get around this issue, it is common to replace the raw factorsFwith factor
mimicking portfolios. Specifically, consider the excess returnrkton a portfolio that has
unit factor sensitivity to thekth factor and zero sensitivity to the remainingK−1 fac-
tors. Since this portfolio must also satisfy equation(8), it follows thatE(rkt)=λk.
Thus, when substituting aK-vectorrFtof the returns on factor-mimicking portfolios
for the raw factorsF, equations(8) and (9)imply the following regression equation in
terms of observables:
rpt=βp′rFt+ept. (10)Equation(10)generates portfoliop’s returns, and inserting a constant termαpyields
the alpha measure of abnormal return.
We estimate alphas using two models which include theFama and French (1993)
factors as well as two additional characteristics-based risk factors:
rpt= (11){
αp+β 1 RM+β 2 SMBt+β 3 HMLt+et,
α′p+β 1 RM+β 2 SMBt+β 3 HMLt+β 4 UMD+β 5 LMH+et,whererptis the excess return to an equal-weighted portfolio of issuers, RM is the excess
return on the CRSP value weighted market index. SMB and HML are theFama and
(^53) See, e.g.,Connor and Korajczyk (1995)andFerson (2003)for extensive surveys of multifactor models.