monthly value-weighted security prices in the CRSP index, an index of all
publicly traded securities. Most security betas are estimated using five
years of monthly data, some 60 observations, although one can use almost
any number of observations. One generally needs 30 observations for nor-
mality of residuals to occur. One can use the Standard & Poor’s 500 index,
the Dow Jones Industrial Average (DJIA), or many other stock indexes.
The JNJ beta is 0.11 when estimated using the value-weighted Standard &
Poor’s 500 index, the traditional index for estimating betas. The t-value of
the JNJ beta is 1.36, which is not statistically significant (at the 10 percent
level, the critical t-value being 1.645). One must be careful, because the
t-value allows one to reject a null hypothesis that the beta is zero. The JNJ
beta versus the CRSP index, composed of some 8,000 securities having
stock returns in 2003, is 0.11, and its t-value is 0.80. Betas should be esti-
mated using value-weighted indexes. JNJ is a defensive security, having a
beta less than unity. An aggressive security has a beta exceeding 1. If the
market is expected to rise 10 percent in the coming year, we should expect
JNJ stock to rise about 1.1 percent.
The corresponding betas for IBM and DD are:
Security Value-Weight CRSP Value-Weight S&P 500
IBM 1.32 1.45
(t) (6.00) (6.47)
DD 0.80 0.93
(t) (4.55) (5.24)If a security’s expected return exceeds the required rate of return from
the CAPM and its beta, then the security should be purchased. Purchasing
such a security drives up its price, and drives down its expected return.
The total excess return for a multiple-factor model (MFM) in the
Rosenberg methodology for security j, at time t, dropping the subscript t
for time, may be written:
(8.10)The nonfactor, or asset-specific, return on security jis the residual risk of
the security, after removing the estimated impacts of the Kfactors. The
term fis the rate of return on factor k. A single-factor model, in which the
market return is the only estimated factor, is obviously the basis of the cap-
ital asset pricing model.
ERjjkkjf e
kK
()=+ ̃ ̃
=∑β
1