BENJAMIN M. FRIEDMAN
Harvard University
DAVID I. LAIBSON
London School of Economics
Economic
Implications
Of
Extraordinary
Movements
In
Stock
Prices
MOST PEOPLE AGREE that stock
prices
sometimes behave
in
strange ways.
Going beyond this simple
observation
typically proves
more difficult.
For
at
least the
past quarter century,
economists
have
been well
aware
that
the variation of stock
prices
does not
nicely
match the familiar
bell-shaped
normal distribution.1
The
problem
is too
many extreme
movements.
Very large
increases or decreases would
always
be
possible
even
if
changes
in
stock prices
were
normally distributed,
but
they would
occur
only rarely. By contrast,
actual stock
prices
rise
or fall
by large
percentage
amounts
fairly often-certainly
often
enough
to
raise
serious
doubts
that
the
usual
normal distribution
provides
a
useful
way
to think
about
how
they vary.
Economists
and other
analysts
of the stock market
have
tended
to
react to this problem
in either of two
ways.
The
most common
approach
is simply
to
ignore
it
and
go
ahead
to
analyze changes
in
stock
prices
as
The authors are grateful
to
Daniel
Kessler,
Kenneth
Kuttner,
Andrew
Lo, Robert
Merton, Vance Roley, Neil Shephard, and James
Stock for
helpful discussions. Friedman's
research was supported by the National
Science Foundation, the General Electric
Foundation, and the Harvard Program
for
Financial
Research. Laibson's research
was
supported by
the
Financial
Markets
Group
of the London School of Economics and the
Marshall Aid Commemoration Commission.
1. Application of one
of the
many
central
limit theorems
is
often
used as
motivation
for
the
normal distribution.
Standard
references
that describe the
nonnormality
of stock
returns are Mandelbrot (1963) and Fama (1965).
137
138
Brookings
Papers on Economic Activity,
2:1989
if
they did fit
the normal distribution. Whether
proceeding this way
is
useful clearly
depends on just how far the
reality of stock price
variation
is from the
normal distribution, as well as on the
use
to
which the
results
of the
investigation
are
put.
The
second reaction is
to
characterize
stock
prices by
some alternative distribution
consistent
with a
greater
fre-
quency
of
large
movements
than
under
the
normal
distribution.2 One
drawback to
this approach is
that it
sacrifices the convenient
simplicity
that
makes
most forms
of
analysis based on the normal
distribution
so
attractive in
the first place. Another is
that
no
consensus exists on how
best to model
the
nonnormality
in
equity returns.
The chief contention of this
paper
is
that extreme
movements
in
stock
prices are
potentially important,
both in
practical stock market
contexts
and for
understanding
how the
economy
behaves,
and
that
failing
to take
explicit account
of the fact that
such
extraordinary
movements have
occurred from
time
to time
in
the
past-and
can
occur at
any
time in the
future-is therefore a
serious omission.
In
particular, the paper illustrates
the potential
importance
of
very large
stock
price movements by
two
examples-one
bearing
on the
role
of
the stock
market
(and
of
speculative
asset markets in
general)
in
allocating
the
economy's resources and
one
bearing on how what
happens
in
the market for
stocks (and
other
financial
assets)
influences fluctuations
in
macroeconomic
activity.
Whether
the stock
market
serves
as
an
efficient
mechanism for
allocating scarce
capital
resources
is a
long-standing
issue
central to
the
modern
private
enterprise system.
Prices set
in the
stock market deter-
mine the
actual
cost
of
new
capital
for firms that issue
shares
and,
much
more
important
for the
United
States,
the
opportunity
cost
of
capital
accumulated
by
firms
that retain at
least
part
of their
earnings.
The
basic
rationale for
an
economy's allocating capital
in
this
way
is the
presump-
tion
that, both
in
the
aggregate
and at an individual firm
level,
the
prices
set in the
stock
market
are
"efficient"
in the
sense
that
they embody
all
available relevant information-or
at least more such information than
any
alternative
capital
allocation mechanism could
bring
to
bear.3 Not
surprisingly,
an
enormous
empirical
literature
has
developed
around
2. Both
Mandelbrot and
Fama
suggested that
stock returns are well
characterized
by
the stable Paretian
distribution. Press (1967), Clark
(1973), and others advocated a
mixed
jump-diffusion
process. More recently Bollerslev,
Engle,
and
Woolridge (1988)
have
modeled asset
returns with an ARCH process.
3.
A
standard
reference is Baumol (1965).
Benjamin M. Friedman and
David l. Laibson
139
this subject, relying on a variety of procedures to test whether stock
rharkets really
are
efficient
in
this
sense.
In
recent years, many such tests
of
market efficiency have turned on
whether the returns to holding stocks exhibit volatility that changes over
time, and even more important, whether changes
in
the volatility of
stock
returns
are
persistent
in the
sense that
greater
or
lesser volatility
observed at any given time implies correspondingly greater or lesser
volatility for at least some
interval
thereafter.
If
shocks to volatility are
persistent, then movements
in the
returns required
to render the demand
for
stocks equal
to the
outstanding supply
will
also be
persistent,
so that
equilibrium asset prices
will tend to
fluctuate
much
more dramatically
than
most standard models predict.4 Empirical analysis presented
in
this
paper, based on an explicit distinction between ordinary and extraordi-
nary movements
in
stock prices, provides
an
explanation for
the
consis-
tent failure of past research to find evidence of long-term persistence
in
the
volatility
of
equity
returns.
Hyman Minsky's
"financial
instability hypothesis"
provides
an
illus-
tration of
the
potential importance
of
extraordinary
stock
price
move-
ments for overall fluctuations
in
the
economy.' Minsky
has
long argued
not
only
that financial
crises play
a
central role
in
causing
fluctuations of
real
economic activity, but also that, as
time
passes after
a
financial
crisis,
behavior
changes
in
such
a
way
as
to reduce the
financial
system's
ability
to withstand shocks
without
sustaining
some
kind
of
rupture,
and
hence
in
such
a
way
that the likelihood of the
next
financial crisis
increases over
time.
Although Minsky's hypothesis
is
typically stated
with
less
than
explicit grounding
in
the
theory
of
economic behavior,
the
analysis presented
in
this
paper
shows
that when the
fluctuation of stock
(or
other
asset) prices
includes both an
ordinary
and an
extraordinary
component,
each with about
the
same dimensions as have
prevailed
in
the
United States since
World
War
II,
behavior
consistent
with the
Minsky hypothesis can
follow as
a
result of
risk-averse
investors
continually using
the
limited information
available
to them to assess the
market's
future
prospects
and allocate their
portfolios accordingly.
Because
the
Minsky hypothesis
is
clearly
about
more
than
just how
investors allocate their
portfolios
between stocks
and
other assets
(at
4. See, for example,
Poterba and
Summers
(1986).
5. See, for example, Minsky
(1972, 1977).
140 Brookings Papers on Economic Activity, 2:1989
the very least,
it
is
about the
choice
of
liabilities as
well
as assets), the
connection between
it and the view
of extraordinary stock price changes
advanced here is obviously illustrative
rather than
direct. The point is
simply
that
conceptualizing
risk
in
the
way suggested
in
this
paper-that
is, as consisting of an ordinary and an extraordinary component-can
readily explain
behavior of
the
kind
hypothesized by Minsky
to
underlie
the irregular occurrence
of
financial
crises with
major negative effects
on nonfinancial economic
activity.
In
the
highly simplified
model
used
below to demonstrate this
point,
the
risk associated
with
holding stocks
is the
only
form of risk considered
and hence
is
a
metaphor
for the far
wider range of
financial and business risks
included
in
Minsky's
rich
descriptions.
The
paper begins by briefly reviewing
stock
price
movements
in
the
United
States, both
since World
War II and
earlier,
and
then
developing
the basic representation
of stock
price
movements
in
terms
of an
ordinary
and
an
extraordinary component.
The data
presented
show that
the
familiar
finding
of too
many
extreme
price
movements
to fit the
normal
distribution
emerges regardless
of
the
period
chosen.
Moreover,
over
the postwar period
these extreme movements
overwhelmingly consist
of
market
crashes,
not rallies.
The model introduced to
represent
this
process uses some simplifying assumptions
to
identify
the
magnitude
and
timing
of the
movements
that it
is
possible
to
regard
as
extraordinary.
As
it
turns
out,
all
of
these
extraordinary
movements since World War
II
have been
price
declines.
Further,
each of the
crashes
pinpointed
in
this
way
is a familiar
episode
in
market
history, and, except
for
the one
in
1987,
each coincided
with
some
independent
event
that
potentially
could have
caused
it.
Surprisingly,
the estimated
magnitude
of the
extraordinary
crash
component
is
identical
in
each of these
episodes.
The next
section
of the
paper illustrates
the
implications
of
this two-
part representation
of
stock
price
movements
for
the
question
of volatil-
ity persistence (and, ultimately,
market
efficiency).
The
analysis
here
relies
in
part on
the familiar
ARCH
model
developed by
Robert
Engle.6
But
it
also
introduces
a more
robust
form of this
model-MARCH
(for
"modified
ARCH")-designed specifically
for
this
purpose.
The
result-
ing
estimates shed
additional
light
on the
time
series
properties
of
equity
returns, including
in
particular
the
question
of
persistence
of
volatility.
6. See Engle (1982); Engle,
Lilien, and
Robins
(1987); and Bollerslev, Engle, and
Woolridge (1988).
Benjamin M. Friedman and
David I. Laibson
141
The last section takes up the Minsky hypothesis
to illustrate
the
relevance of extreme movements
in
stock prices
to
fluctuations in
nonfinancial economic activity. Using empirical estimates
of
the
extraor-
dinary component
of
stock
price changes analogous
to
those
presented
in
the first section of the paper,
the
analysis
shows how the behavior of
investors trying
to allocate their
portfolios
as
best
they can, using
whatever information they have available
at
any
time, can cause the
overall
financial system
to become more
fragile
with
the
passing of time
after
the most recent
market
crash, just
as Minsky has suggested.
Especially
in
this context, however,
it
is appropriate
to question
a
central
assumption maintained (purely for convenience)
throughout this paper-
specifically,
that the
ordinary
and
extraordinary
components
of
stock
price changes occur independently
of one another. The paper concludes
with a brief discussion of the interesting, though difficult
to investigate,
possibility
that the
two may
be related
in an
important
way.
Stock Returns: Ordinary and Extraordinary
Since the
end
of World War
II,
the
average pretax
return on
stocks
traded in U.S. markets has been positive
in 28
years
and negative
in 15
years.
The
average
rate of return
during 1946-88,
measured
by
the
Standard and Poor's
500,
was 12.62
percent
a
year.
Compared
with 4.75
percent
a
year
for
Treasury bills,
the
average
excess return on
stocks
during 1946-88
was 7.86
percent
a
year.7
Figure
1
plots
the
excess
returns on stocks over
Treasury bills for
1946-88 using the quarterly time unit that is standard
for most macro-
economic
analyses
of the
postwar
era.
Two features of the data stand
out.
First,
in
several quarters stock prices
moved
far
enough-either up
or
down-to
render the total excess
return
very
large
or
very
small
compared
with the
usual
range
of variation.8 More
specifically,
the
kurtosis of the excess
returns
series
is
1.41, statistically
significant
at the
7. All returns data are computed from
Lbbotson
and
Associates (1989).
8.
Because dividends tend to move
so much more
smoothly than stock prices, the
identification of extraordinary returns
and extraordinary price changes, as implicitly
maintained throughout this paper,
is
entirely legitimate. For the post-World War II data
analyzed below, the quarterly standard
deviation of
the total
return series for
equities is
0.0770.
The
standard deviations
of
the
underlying price change
and dividend
series are
0.0761 and 0.0036, respectively.