FINANCE Corporate financial policy and R and D Management

APPENDIX 8.A

Multifactor Risk Models

Earlier in Chapter 8, we introduced the reader to mean-variance analysis
and the capital asset pricing model. Accurate characterization of portfolio
risk requires an accurate estimate of the covariance matrix of security re-
turns. A relatively simple way to estimate this covariance matrix is to use
the history of security returns to compute each variance and covariance.
This approach, however, suffers from two major drawbacks:

1.Estimating a covariance matrix for the stocks of the Russell 3000 in-

dex requires a great deal of data; with monthly estimation horizons,

such a long history may simply not exist.

2.It is subject to estimation error. In Chapter 8 we estimated the corre-

lation between two stocks and found that Johnson & Johnson and

IBM have a lower correlation than Johnson & Johnson and DuPont.

One might expect a still higher correlation between Johnson &

Johnson and Pfizer than between Johnson & Johnson and DuPont

because Johnson & Johnson and Pfizer are in the same industry,

health care.

Taking this further, we can argue that firms with similar characteristics,
such as their line of business, should have returns that behave similarly. For
example, Johnson & Johnson, IBM, and DuPont all have a common com-
ponent in their returns in that they would all be affected by news that af-
fects the stock market, measured by their respective betas as we discussed
and estimated earlier in the chapter. The degree to which each of the three
stocks responds to this stock market component depends on the sensitivity
of each stock to the stock market component, as measured by their respec-
tive betas.
Additionally, we would expect Johnson & Johnson and Pfizer to re-
spond to news affecting the health care industry, whereas we would expect
DuPont to respond to news affecting the chemical industry and IBM to re-
spond to news affecting the computer industry. The effects of such news
may be captured by the average returns of stocks in the health care, com-
puter, and chemical industries. One can account for industry effects in the
following representation for returns:

(8.12)

̃ ( ̃ )[ ̃ ( ̃ )]

[ ̃ ( ̃ )] [ ̃ ( ̃ )]

rEr rEr

rEr r Er

JNJ JNJ JNJ M M

H H JNJ JNJ JNJ

=+⋅−

+⋅−+⋅−+

β

10 μ

218 THE USE OF FINANCIAL INFORMATION IN THE RISK AND RETURN OF EQUITY