What Practitioners Need
To
Know
.
. . About Factor Methods
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Mark Kritzman
Windham Capital
Management
Financial analysts
are concerned
with factors,
or common sources
of risk that contribute
to changes
in security prices.
By identifying
such factors, analysts may
be able
to control
a ponfolio's risk more
efficiently
and perhaps even im-
prove
its return,
I will describe
in general terms
two approaches often used
to
identify factors.
The first ap-
proach, called factor analysis,
al-
lows analysts
to isolate factors by
observing common variations
in
the returns
of different securities.
These factors
are merely statisti-
cal constructs that represent
some underlying source
of risk;
that source
may or may not be
observable.
The second ap-
proach, called cross-sectional
re-
gression analysis, requires that
we define
a set of security at-
tributes that measure exposure
to
an underlying factor
and deter-
mine whether
or not differences
across security returns corre-
spond
to differences in these se-
curity attributes.
Factor Analysis
I begin with
a nonfinancial, hope-
fully intuitive, example.
I wilt ap-
ply
the insights gained by this
example
to show how we might
go about identifying
the factors
that underlie
the stock market.
Suppose
we wish to determine
whether
or not there are com-
mon sources
of scholastic apti-
tude, based upon
the grades of
100 students
in the following nine
courses—algebra, biology, calcu-
lus, chemistry, composition,
French, geometry, literature
and
physics.
We proceed as follows.
First,
we compute the correlation
between
the algebra grades of
students
1 through 100 and their
grades
in each of the other eight
courses. Then
we compute the
correlations between their biol-
ogy grades
and their grades in
each
of the seven other courses.
We continue until
we have com-
puted
the correlations between
the grades
of every pair of cours-
es—36 correlations
in all. Table I
displays these hypothetical corre-
lations.
That
all these correlations are
positive suggests
the presence of
a pervasive factor, which
is prob-
ably related
to intelligence or
study habits.
In addition to this
pervasive factor, there appear
to
be three other factors,
or com-
monalities,
in performance.
First,
the variation in algebra
grades
is highly correlated with
the variation
in calculus and ge-
ometry grades. Moreover, perfor-
mance
in calculus is highly corre-
lated with performance
in
geometry.
The grades in these
three courses, however,
are not
nearly
as highly correlated with
the grades
in any of the other six
courses. We might thus conclude
that there
is a common aptitude
that underlies performance
in
these three courses.
Second, performance
in biology
is highly correlated with perfor-
mance
in chemistry and physics,
and performance
in chemistry is
highly correlated with perfor-
mance
in physics. Again, perfor-
mance
in these courses does not
correspond
as closely with per-
formance
in any of the other
courses.
We might conclude that
there