What is known as the characteristic line of modern investment analysis is simply
the regression line obtained from the following model:
rit = ai + ßirmt + ut
where rit = the rate of return on the ith security in time t
rmt = the rate of return on the market portfolio in time t
ut = stochastic disturbance term
In this model ßi is known as the beta coefficient of the ith security, a measure of
market (or systematic) risk of a security.*
On the basis of 240 monthly rates of return for the period 1956–1976, Fogler and
Ganapathy obtained the following characteristic line for IBM stock in relation to
the market portfolio index developed at the University of Chicago:*
rˆit = 0.7264 + 1.0598rmt r^2 = 0.4710
se = (0.3001) (0.0728) df = 238
F1,238 = 211.896
a. A security whose beta coefficient is greater than one is said to be a volatile or
aggressive security. Was IBM a volatile security in the time period under study?
b. Is the intercept coefficient significantly different from zero? If it is, what is its
practical meaning?
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