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
is a
common source
of
ap-
titude associated with biology,
chemistry
and
physics.