FINANCE Corporate financial policy and R and D Management

where = JNJ’s realized return

= realized average stock market return

= realized average return to health care stocks

= realized average return to health care stocks

E[·] = expectations

βJNJ= JNJ’s sensitivity to stock market returns

μJNJ= effect of JNJ-specific news on JNJ returns

This equation simply states that JNJ’s realized return consists of an
expected component and an unexpected component. The unexpected
component depends on any unexpected events that affect stock returns in
general [r~M– E(r~M)], any unexpected events that affect the health care in-
dustry [r~H– E(r~H)], and any unexpected events that affect JNJ alone (μJNJ).
Similar equations may be written for IBM and DuPont.
By beginning with our intuition about the sources of co-movement in
security returns, Rosenberg (1974) made substantial progress in estimating
the covariance matrix of security returns by presenting the covariance ma-
trix of common sources in security returns, the variances of security specific
returns, and estimates of the sensitivity of security returns to the common
sources of variation in their returns, creating the BARRA risk model. Be-
cause the common sources of risk are likely to be much fewer than the num-
ber of securities, we need to estimate a much smaller covariance matrix and
hence a smaller history of returns is required. Moreover, because similar
stocks are going to have larger sensitivities to similar common sources of
risk, similar stocks will be more highly correlated than dissimilar stocks.

BARRA Model Mathematics

The BARRA risk model is a multiple-factor model (MFM). MFMs build
on single-factor models by including and describing the interrelationships
among factors. For single-factor models, the equation that describes the
excess rate of return is:

(8.13)

where = total excess return over the risk-free rate

Xj= sensitivity of security jto the factor

= rate of return on the factor

u ̃j = nonfactor (specific) return on security j

f ̃

j

r ̃j

rXfu ̃jjjj=+ ̃ ̃

r ̃JNJ

r ̃H

r ̃M

r ̃JNJ

Appendix 8.A 219