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A
Behavioral Framework
for
Dollar-Cost
Averaging
Dollar-cost averaging may not be rational behavior,
but
it
is petjktly normal behavior.
Meir
S
tatman
nvestors with cash that
is
destined for stocks often
use a dollar-cost averaging plan. They divide the
cash into segments, and convert one segment at
a
time from cash
to
stocks according
to
a predeter-
The popularity of dollar-cost averaging can be
mined schedule. The alternative to dollar-cost averag-
ing is lump-sum investment.
traced back
at
least
to
the
1940s.
(See,
for
example,
dis-
cussions in Ketchum
[1947],
Solomon
[1948],
and
Weston
[1949].)
And that popularity has never waned.
For example, Clements
[1994]
writes in
a
Wall
Street
journal
column ‘‘aimed:
at
ordinary investors who
want to get their finances going in the right direction”:
I
Tumbling
stock
and bond
prices
can seem
a
lot
less
paintid
if
you
plan
to
buy more. One
of
the
best
ways
of
doing that
is
dollar-cost-averaging,
whch involves shoveling,
say,
$100
into
the
market
every
month,
no
matter
what
is
happen-
ing to stock and bond prices
(p.
Cl).
MEIR
STATMAN
is
professor
of
finance
at
the Leavey
School
of
Business
of
Santa
Clara
University
in
Santa
Clara
(CA
95053).
While popular, the practice of dollar-cost aver-
aging
is
inconsistent with :standard finance. This has
been demonstrated by Ccinstantinides
[1979],
who
shows, within a theoretical li-amework, that dollar-cost
averaging plans are suboptimal. It has
also
been demon-
strated by Rozeff
[1994],
who shows using simulation
that dollar-cost averaging
is
suboptimal.
An analysis of dollar-cost averaging
is
important
for at least
two
reasons, one related to an understandmg
70
A
BEHAVIORAL
WEWORK
FOR
DOLLAR-COST
AVERAGING
FALL
I995
of the behavior of investors, and the other related to the
effects of investor tradmg on security prices. Standard
finance is
a
positive theory,
a
theory that makes predc-
tions about the financial behavior of individuals and
about the outcomes of the interactions between ind-
viduals in financial markets. The practice of dollar-cost
averaging
is
prominent, and the inconsistency between
the practice of dollar-cost averaging and the predictions
of standard finance is too glaring to be ignored.
Moreover, an understandng of the persistence of dol-
lar-cost averaging provides insights into broader ques-
tions, such
as
the overall construction of portfolios.
This article offers
a
behavioral framework that is
consistent with the persistence of dollar-cost averaging.
I describe the roles of four behavioral elements in the
attraction of such plans: prospect theory, aversion to
regret, cognitive errors, and self-control (behavioral life
cycle theory).
Ths
work is part of
a
stream of work that
describes the behavior of investors and the outcomes of
their interaction in financial markets. Earlier work
describes preferences for dividends (Shefrin and
Statman [1984]), the reluctance to reahze losses [1985],
the susceptibdity
to
cognitive errors and the preference
for stocks of “quality” companies [1986, 1995b], the
design of securities
[
19931, the pricing of securities
[
19941, and the construction of portfolios
[
1995al.
“Behavioral investors” make choices in
a
sys-
tematic, if suboptimal, fashion. This is not to advocate
the selection of suboptimal portfolios. But
a
positive
theory must be consistent with the behavior of many, if
not most, individuals.
Some standard finance investors (and academics)
think that behavioral investors can be easily educated
to overcome their limitations. But even if they are
right in their prescription, standard investors wdl be
ineffective
as
teachers if they misperceive their stu-
dents. Behavioral investors are numerous, and they are
difficult to educate. The difficulty in the task of edu-
cation is illustrated in Weston’s [1949] and Sharpe’s
[1981] efforts.
Dollar-cost averaging
calls
for investing the
same dollar amount, rather than the same number of
shares, each period. Thus,
a
dollar-cost averaging
investor buys more shares when the price is low than
when the price is high.
As
Weston [1949] writes:
In
the
usual
exposition
of
the principle
of
dollar-
cost-averaging, its merit is urged
on
the basis of
a
relationship that holds without exception:
at
any
point
afier
a
fluctuation
in
security
prices
the
average
cost
of
total
shares held is less than
the
average
price
of
the
shares
(pp.
251-252).
Weston exposes the irrelevance of
this
fact: “The
crucial test is whether the shares held can
at
any time be
sold
at
a
gain.
For ths to be possible, average cost must
be less than the current market price per share’’
@.
252).
Similarly, Sharpe [1981] notes that while it is
mathematically interesting that the average price per
share paid by a dollar-cost averaging investor is lower
than the average price per share, it has no economic
significance. Sharpe shows that while high volatility in
stock prices corresponds to large differences between
the average price per share paid by
a
dollar-cost averag-
ing investor and the average price per share, dollar-cost
averaging does not change uncertainty from vice to
virtue. The passage of time since Weston’s 1949 article
and Sharpe’s 1981 book seems to have done little to
dampen enthusiasm for dollar-cost averaging
The world of standard finance
‘is
the world of
frame invariance. Investors care about cash flows, but are
indlfferent among frames of cash flows. The pricing of
options is
a
good example. The price of
a
call option on
a
stock is determined by the fact that the cash flows of
the option can be replicated by the cash flows of
a
par-
ticular dynamic combination of
a
bond and the under-
lying stock. The fact that in the
first
case cash flows are
described in terms of options, while in the second cash
flows are described in terms of bonds and stocks is irrel-
evant to investors in
a
world of frame invariance.
Although the literature of standard finance has
no
relevant role for framing, the behavioral literature is
replete with studes on the effects of frames on choice.
The effect of frames is central in prospect theory,
a
pos-
itive theory of choice by Kahneman and Tversky
[1979], and with it I begin the construction of the
behavioral framework within whch dollar-cost averag-
ing takes place.
PROSPECT
THEORY
Choices of standard finance investors conform
to
expected utility theory. Choices of “behavioral
investors’’ conform better to prospect theory. Prospect
theory investors evaluate their choices in terms of the
potential gains and losses relative to reference points,
while standard investors evaluate their choices in terms
FALL
1995
THE
JOURNAL
OF
PORTFOLIO
MANAGEMENT
71
EXHIELIT
IA
STANIDARD
UTILITY
FUNCTION
Kahneman and Tversky find that
84%
of sub-
jects chose
A,,
the sure amount, in the first problem set.
Yet, 69% of subjects chose
E,,
the gamble, in the sec-
ond problem
set.
This
pattern of choice is puzzling
within standard finance, because standard finance
investors base their decisions on net cash flows and are
never confused by frames. Yet, problem sets 1 and 2 are,
in fact, identical in net cash .flows.
Observe that once the initial $1,000 is integrat-
ed into the choice between
AI
and B, in problem
1,
the
overall choice is between:
Utllity
Total Wealth
A3: A sure gain of $1,500 (the
sum
of the initial
B3: A 50% chance to gain
$2,000
and
a
50%
$1,000
and the sure $500), and
chance to gain
$1,000.
Similarly, once the initial $2,000 is integrated
into the choice between A, and
B,
in problem 2, the
overall choice is between:
of net cash flows
(total
wealth). Moreover, while stan-
dard investors are always risk-averse, prospect theory
investors have an S-shaped value fbnction over gains
and losses that displays concavity (risk aversion) in the
domain
of
gains
and
convexity
(risk-seeking)
in
the
domain
of
losses. (See Exhibits
1A
and 1B.)
The origins of prospect theory
are
in Markowitz
[1952], but
its
development is the work of Kahneman
and Tversky [1979]. To understand the features of
prospect theory, consider an experiment by Kahneman
and Tversky. One group of subjects receives problem
1
:
1.
In addition to whatever you
own,
you have
been given $1,000. You are now asked to choose
between:
AI:
A
sure gain
of
$500, and
B,: A
50%
chance to gain $1,000 and
a
50%
chance to gain nothing.
Another group of subjects receives problem 2:
2. In addition
to
whatever you own, you have
been given
$2,000.
You are
now
asked
to
choose
between:
AZ:
A sure
loss
of
$500,
and
B,:
A
50% chance to lose $1,000 and
a
50%
chance to lose nothing.
A4:
A
sure gain of $11,500, and
B4: A 50% chance
to
gain
$2,000
and
a
50%
chance
to
gain
$1,000.
The two problems
are
identical in net cash flows.
EXHIBIT
1B
PROSPECT FUNCTION
Value
(Uthty)
Losses
72
A
BI~HAVIORAL
FRAMEWORK
FOR DOLLAR-COST
AVERAGING
FALL
1995
EXHIBIT 2
Dollar-Cost
Averaging
Amount Price
per
Number of
Period Invested Share Shares Bought
1
$1,000 $50.00 20
2
$1,000 $12.50
80
Total $2,000
100
Average Cost of Shares Held:
$2,000/100
=
$20
Average Price per Share Over
the Two Periods:
(50
+
12.5)/2
=
$31.25
Most of Kahneman and Tversky’s subjects could
not possibly be standard finance investors. Rather, they
are behavioral finance investors. Prospect theory postu-
lates that two distinct cognitive operations lead to
choice, and that these two operations are sequential.
First is framing into mental accounts. Second
is
the
application of specific decision rules to the accounts.
The initial amount, $1,000 in problem
1,
is
stripped away and framed into
a
separate account.
Problem
1
is
then framed in terms of gains and losses
relative to a reference point of zero. The concave por-
tion of the prospect hnction in the domain of gains
leads to a preference of the sure $500 gain over the
gamble, a choice consistent with risk aversion. In prob-
lem 2, the convex portion
of
the prospect function in
the domain of losses leads to a preference of the gam-
ble over the sure $500
loss,
a choice consistent with
risk-seeking.
Consider now framing and choice in the context
of dollar-cost averaging. Imagine an investor who
divides $2,000 in cash into two segments of
$1,000
each, investing one in period
1
and the second in peri-
od 2. The price per share of stock in period
l
is
$50,
and it turns out that the price per share in period 2
is
$12.50. The data are presented in Exhibit 2.
Framing the problem in the standard finance
way, the investor started with $2,000, and now has 100
shares worth $12.50 apiece for
a
total of $1,250. The
investor has
a
clear loss.
Framing the problem as the proponents of dol-
lar-cost averaging would have
it,
the investor bought
the shares at an average cost of $20, while the average
price per share over the
two
periods was $31.25. The
investor has a clear gain. Indeed, framed in the behav-
ioral way, the problem shows
a
gain in
all
cases except
when the stock price never changes. It
is
absolutely
true that the behavioral frame is misleading. It is equal-
ly true that the behavioral frame persists.
Unfortunately, there
is
no comprehensive theo-
ry that explains what makes some frames more com-
pekng the others. (See Fischhoff [1983].) However, the
persistence of the behavioral frame of dollar-cost aver-
aging
is
hardly unique. Consider the public dwussion
about derivatives. Some finance practitioners and aca-
demics frame derivatives in the standard finance way
and know that derivatives can be used with equal effec-
tiveness to increase risk or to reduce it. But framing
derivatives such that they always increase risk is a com-
mon practice, hardly limited to politicians.
A
prominent feature of dollar-cost averaging
is
that it
is
recommended with equal force to investors
with cash who consider converting cash into stock and
investors with stock who consider converting stock into
cash.
This
feature
is
usehl in highlighting the difference
in framing and choice between standard finance and
behavioral finance.
Constantinides
[
19791, who analyzes dollar-
cost averaging within the framework of standard
finance, writes:
Where, then, does the intuitive rationale of dol-
lar-cost-averaging
fail?
Its
rationale is that the
investor
replaces
one
major gamble on
a
tempo-
rary
she
of
prices by
a
number of
smaller
gam-
bles and thus diversifies risk. The fault of
this
argument is misrepresentation of
the
state
of
the
world, before
a
decision is made. Dollar-cost-
averaging implies that
an
investor with
all
hs
endowment in
asset
A is in
some
way
different
from an investor with all
his
endowment in
asset
B, but otherwise identical. Dollar-cost-averaging
ignores
the simple fact that the latter investor
may costlessly
convert
his endowment from asset
A
to
asset
B before he considers the optimal
investment decision. Both investors face the
same
prospects
irrespective of the composition
of
their endowment, and any claims
of
gambles
on
temporarily overpriced
or
underpriced prices
are
simply fallacious (pp.
447-448).
Imagine two investors, A and
B,
who are iden-
tical except that
A
has
$1,000
in cash and
B
has $1,000
in stocks.
A
faces
a
choice between keeping his wealth
FALL
1995
THE JOURNAL
OF
PORTFOLIO MANAGEMENT
73
in
cash
or converting it into stock while
B
faces
a
choice: between keeping her wealth in stock or con-
verting it into cash. Framed in the standard finance
way, the choice problems of A and
B
are identical
because
B
can costlessly convert her initis stock
endowment into cash. Therefore, their choices are
predcted to be identical.
The frames and choices of
A
and
B
are likely to
be difierent within the framework of behavioral
finance. The two are identical in their beliefs,
so
they
agree that the return on cash is zero, and that the value
of stocks
at
the end
of
the period
will,
with equal prob-
abilities, either increase to $1,300 or decrease to $860.
The expected gain on stocks is $80, while the expect-
ed
gain
on cash is zero.
How would A frame the choice? Assume that
the reference point for A is the $1,000 in cash,
a
posi-
tion he has adapted to, and that he frames the choice in
terms of gains and losses relative to the $1,000 reference
point. If
so,
the choice
is
between:
Cash A. A sure gain of zero, and
Stock
B.
A
50%
chance to gain $300 and
a
50%
chance to lose
$140.
Assume that the reference point for
B
is $1,000
in stocks,
a
position she has adapted to.
If
so,
the choice
is betureen
Cash A. A
50%
chance for an (opportunity)
gain of
$140
and
a
50% chance for
an (opportunity) loss of
$300,
and
Stock
B.
A sure (opportunity) gain of zero.
The problems faced by A and
B
are framed
differently, and the choices are thus likely to differ.
The concavity of the prospect function in the
domain of gains, and the convexity of the prospect
function in the domain of losses, is likely to cause
A
to hold onto his cash, and it is likely to cause
B
to
hold o’nto her stock.’
The purported advantages
of
dollar-cost aver-
aging involve,
as
Constantinides demonstrates,
mis-
leading frames. Framed in the standard finance way,
a
dollar-cost averaging investor only replaces one
major gamble, embedded in
a
lump-sum investment,
with
a
number of smaller gambles, embedded in dol-
lar-cost averaging. But frames are important, and
they a:ffect choice.
AVERSION
TO
REGRET’
The purchase of stock for
$1,000
will result in
$1,300
at the end of the period, or it will result in $860.
The monetary gain is
$300,
and the monetary
loss
is
$140,
but monetary gains and losses are not
all
that
affects choice. The joy of pride and the pain of regret
matter. Kahneman and Tversky E19821 describe regret
as
the frustration that comes, ex post, when
a
choice
results in
a
bad outcome.
If the
$1,000
purchase of stocks results in
$1,300,
the
$300
monetary gain is supplemented with
the pride that comes from what is framed
as
buying
$1,300 worth of stock for
$1,000.
If the
$1,000
pur-
chase of stocks results in $800, the
$140
monetary
loss
is supplemented with the regret that comes from what
is framed
as
buying $860 worth of stock for
$1,000.
The dstinction between
1)
gains and losses in
terms of money and 2) gains and losses in terms of
pride and regret is akin to Thaler’s [1985] distinction
between acquisition utility and transaction utility. In
Thaler’s framework, the total utility of the purchase is
composed of acquisition and transaction utilities.
Acquisition utility depends Ion the difference between
the value of the product and the outlay. Transaction
utdity depends on the “barg,Gn” value of the purchase.
In this framework, the bargain value corresponds to
pride and regret.
Standard finance investors are affected by neither
pride nor regret. Pride and ‘regret, however, do matter
to behavioral investors. If the joy of pride is equal to the
pain of regret, behavioral irivestors who choose stock
over cash without considerations of pride and regret
would not alter their choice once pride and regret are
introduced. If the pain of regret is sufficiently larger than
the joy of pride, however, behavioral investors would
choose
to
keep their holdnp in cash rather than suffer
the pain of regret that will come if stock prices decline.
Kahneman and Tverslry note that there is
a
close
association between regret and the level
of
responsibil-
ity for
a
choice. Actions taken under duress entail little
responsibility and bring little regret. Following
a
rule
is
one way to reduce responsibihty. Choice under
a
strict
rule is choice under duress. Dollar-cost averaging
involves
a
strict rule that specifies amounts
to
be invest-
ed
at
particular points of tinie. The abdity of
a
dollar-
cost averaging plan to reduct: responsibdity is especially
helpful for investors who are concerned about their
exposure to regret.2
74
A
BEHAVIORAL
FRhMEWORK
FOR
DOLLAR-COST AVERAGING
FALL
1995
COGNITIVE ERRORS
AND
SELF-CONTROL
Dollar-cost averaging is
a
non-sequential or
non-contingent investment policy. The non-sequential
nature of dollar-cost averaging is manifested in
a
com-
mitment
at
the initiation of the plan to invest
a
partic-
ular amount in each subsequent period, regardless of
any information that might become available after the
initiation of the investment plan. Constantinides
[1979]
notes that the non-sequential nature of dollar-
cost averaging is considered by its proponents
as
the
key to its success.
Constantinides
[1979]
shows that dollar-cost
averaging is dominated by
a
sequential optimal invest-
ment policy,
a
policy that takes into account informa-
tion that arrives after the initiation of the investment
plan. He adds that, in light of this result, it seems iron-
ic that proponents of dollar-cost averaging go to great
lengths to emphasize that investors must have the
courage to ignore new information
as
they follow the
inferior non-sequential investment policy.
A
policy that is suboptimal within standard
finance might nevertheless be attractive to behavioral
investors.
One
advantage
of
the non-sequential
nature
of dollar-cost averaging for behavioral investors is that
the non-sequential rules of dollar-cost averaging reduce
responsibhty and regret. But the advantage of follow-
ing rules extends beyond
a
reduction in responsibility.
The rules of dollar-cost averaging serve to combat laps-
es in self-control
as
cognitive errors influence investors
to terminate their investment plans.
To understand the roles of self-control and cog-
nitive errors, consider the description of dollar-cost
averaging by Cohen, Zinbarg, and Zeikel
[1977],
quot-
ed by Constantinides
[1979]:
The important
thing
is
to
stick
to
your
sched-
ule-to buy,
even
though the
price
keeps
fang,
which, psychologically,
is
usually
hard
to
do
....
To
engage in dollar-cost-averaging
successfully,
you
must
have both
the
funds
and the courage
to
continue buying in
a
declining market when
prospects
may seem bleak.
As
Cohen, Zinbarg, and Zeikel note, investors
find it dfficult to continue to buy stocks following
stock price declines. But why do investors find it
dffi-
cult? The answer is that investors generally believe that
recent trends in stock prices wdl continue.
The tendency of investors to extrapolate recent
trends in stock prices is
a
reflection of representative-
ness,
a
cognitive error, and that tendency is well-docu-
mented. For example, Solt and Statman
[1988]
find that
investment advisors become optimistic about the
prospep of stocks after increases in stock prices and
pessimistic after declines. They
also
find that there is no
relationship between the sentiment of investment advi-
sors at one particular time and the performance of the
stock market in the subsequent period.
Suppose
a
dollar-cost averaging investor starts
the investment plan with the expectation that there
is
an equal chance for an up-market or down-market in
the coming period. Once several down-periods occur,
the investor revises the probabilities
so
that the proba-
bdity
of
a
down-market is higher. The investment plan
that was attractive by the old probabilities might no
longer be attractive by the new ones, and the investor
might choose to abandon the plan and stop buying
stocks. Here is where the self-control role of dollar-cost
averaging is most important.
Investors who allocate funds between savings
and consumption often face difficulties because con-
sumption is
tempting.
Rules
are
useful in enforcing
a
savings plan. Shefrin and Statman
[1984]
show how
rules such
as
“consume from dividends, but don’t dip
into capital” help investors manage the self-control
problem when
a
myopic “agent” within the individu-
al wants to consume now, but
a
forward-looking
“principal” considers savings for the future
as
well
as
current consumption. “Don’t dip into capital” is
a
rule that the principal uses to constrain the consump-
tion of the agent.
The task of the principal in enforcing savings is
especially difficult after
a
period of losses, whch
is
when the strict rules of dollar-cost averaging are most
effective. The rules of dollar-cost averaging help
investors “continue buying in
a
declining market when
prospects may seem bleak.”
CONCLUSIONS
Investors who employ dollar-cost averaging have
their wealth in one asset, such
as
cash, and consider
transferring it into another asset, such
as
stock. They
can transfer wealth from one asset to the other in
a
lump sum. Instead, they transfer wealth in increments
over time according to
a
predetermined plan.
It has been known
at
least since Weston
[1949]
FALL
1995
THE JOURNAL
OF
PORTFOLIO MNAGEMENT
75
that the practice of dollar-cost averaging is inconsistent
with standard finance. Yet dollar-cost averaging seems
as
popular today
as
ever. The persistence of dollar-cost
averaging is an embarrassment to the role of standard
finance
as
a
positive theory of financial behavior.
:Dollar-cost averaging is significant even if it is
followed only by small investors,
as
the aggregate of
small investors is large. Moreover, the early literature on
dollar-cost averaging, such
as
Cottle and Whtman
[1950], suggests that dollar-cost averaging plans were
then popular among institutional investors. There is no
evidence of
a
decline in that popularity.
Dollar-cost averaging is consistent with the pos-
itive framework of behavioral finance. I have described
the role
of
four elements of the theory: prospect theo-
ry, aversion to regret, cognitive errors, and self-control.
Choices that involve transfers of wealth among assets
are framed and evaluated within prospect theory to
show that dollar-cost averasng transfers are appealing
to investors who find lump-sum transfers unappealing.
Considerations of pride and regret affect transfers of
wealth among assets. The susceptibhty to cognitive
errors, in particular the tendency to extrapolate recent
trends in stock prices, explains why investors find it &f-
ficult to continue dollar-cost averaging plans after
a
period
of
stock price declines, and the need for rules to
facilitate self-control explains the non-sequential
nature
of the rules that govern dollar-cost averaging.
.Dollar-cost averaging joins financial products
such
as
covered calls and LYONS, described by Shefrin
and Statman [1993],
as
products that
fit
poorly with
standard finance yet fit well with behavioral finance.
Indeed, it belongs in the general area
of
portfolio con-
struction. Shefrin and Statman [1995a] show that
investors generally construct portfolios in ways that
deviate from standard finance theory but are consistent
with behavioral finance.
Much
of
dollar-cost averaging takes place in
a
framework where choice is not explicit.
A
feature of
the implementation of defined-contribution pension
plans, such
as
401(k)s, is that employers and employees
contribute cash to the pension plan on each payroll
date, and the cash contribution is converted on that
date into stocks or bonds. Any choice between lump-
sum and dollar-cost averaging in defined-benefits pen-
sion plans, however,
is
only implicit because employees
are not given an explicit choice between contributions
in portions over the cause of
a
year and
a
lump-sum
contribution
at
a
point during the year.
Suppose an employer does offer employees
a
choice between dollar-cost averaging contributions
coinciding with payroll days during
a
year and
a
one-
time lump-sum contribution of the total annual
amount
so
that the present kalues of the cash flows in
the two options are identical. The prediction of stan-
dard finance is that employees will be indifferent
between the dollar-cost averaging option and the
lump-sum option. The prediction of behavioral finance
is that employees would prefer the dollar-cost averaging
option. While
I
know of no employer who offers such
a
choice
at
present, it should be possible to test
this
hypothesis in an experiment.
While my focus here is on investor behavior,
not on security prices, the practice of dollar-cost aver-
aging has important implications for pricing. It is by
now well established that investment flows, even in the
absence of information, affect prices. For example, the
work of Warther [1994] reveals
a
strong link between
cash flows into and out of mutual funds and the returns
to stocks held by the funds. Iiivestors who practice dol-
lar-cost averaging are more likely than other investors
to continue to buy stocks afier
a
period
of
declines in
stock prices and less likely to accelerate buying after
a
period of increases in stock prices. I hypothesize that
an increase in dollar-cost averaging leads to a decrease
in volatility.
Dollar-cost averaging is indeed suboptimal
within the choice set facing
a
fully rational investor in
standard finance. But the interpretation of rationality
is
a
delicate task. Consider, for example, the equity
risk premium (Mehra and Prescott [1985]). The exis-
tence of an equity premium puzzle suggests that
investors invest too little in stock, and investment
advisors might wish to guide their clients to convert
some cash into stock.
Compare an advisor who counsels
a
client to
convert cash into stock in
a
lump
sum
to
an advisor
who counsels the client
to
use dollar-cost averaging.
Lump-sum conversion from cash to stock might be
optimal, but such conversion is unappealing to investors
who are deterred from action
as
they contemplate the
regret that they will experience if the stock market
were to crash
as
soon
as
the cash is converted into stock.
Dollar-cost averaging is indeed
a
second-best solution,
but it might start an investor on
a
road that leads to
allo-
cation of
a
portion of wealth to stocks.
As Samuelson
[
19941 writes about dollar-cost
averaging, he notes that it
is
one of dozens of rules
76
A
BEHAVIORAL
FRAMEWORK
FOR
DOLLAR-COST
AVERAGING
FALL
1995
whose merit has nothing to do with improving risk-
adjusted returns or mean-variance optimization. He
adds that, at least for fiduciary trustees, using such rules
is
a
blunder, if not
a
crime. Yet the fact that many com-
mon investment rules are inconsistent with standard
finance is evidence that standard finance does not do
well
as
a
positive theory.
Standard finance is inconsistent with the exis-
tence of an investment advising industry where rules
such
as
dollar-cost averaging are
a
mainstay. Standard
finance is inconsistent with the existence of
a
mutual
fund industry where, on average, money managers fail
to outperform indexes (see Malkiel
[1995]),
and stan-
dard finance is inconsistent with the existence of an
investment newsletter industry where newsletter writ-
ers provide useless asset allocation advice (see Graham
and Harvey
[1995]).
It might be time to move on to
a
positive the-
ory that is consistent with the evidence, and to
remember that
a
normative theory is useless if
investors cannot be persuaded to follow it.
Meanwhile,
I
offer an hypothesis. The practice of dol-
lar-cost averaging will persist.
ENDNOTES
The author thanks Hersh She& and Atulya
Sarin
for help-
ful
discussions, and the Dean Witter Foundatiop for financial support.
‘The choice problem
of
B is equivalent to the choice prob-
lem of a money manager whose performance is evaluated relative to a
benchmark identical to B’s portfolio. The benchmark serves
as
the ref-
erence point, and
gains
and losses are measured relative to it. (See Roll
[1992] and Clarke, Krase, and Statman [1994].)
2For a “mini-max” policy, where considerations of regret
lead investors to choose dollar-cost averaging, see Pye
[1972].
REFERENCES
Clarke, Roger G., Scott Krase, and Meir Statman. “Tracking Errors,
Regret, and Tactical Asset Allocation.”
Journal
of
Porttlio Management,
Spring 1994, pp. 16-24.
Clements, Jonathan. “Expect Some Bumps, and Hang
On
For the Long
Haul.”
Wall
StreetJournal,
October 24, 1994, p.
C1.
Cohen, Jerome B., Edward D. Zinbarg, and Arthur Zeikel.
Investment
Analysis
and
Portfolio Management.
Homewood,
IL
Irwin,
1977.
Constantinides, G.M. “A Note
on
the Suboptimality of Dollar-Cost
Averaging
as
an
Investment Policy.”Journal
of
Financial and Quantitative
Analysis,
XIV, 2 (June 1979), pp. 443-450.
Cottle, C. Sidney, and W.T. Whitman. “Formula Plans and the
Institutional Investor.”
Harvard
Business Review,
28,
4
(July 1950), pp.
84-96.
Fischhoff, Baruch. “Predicting Frames.”
Journal
of
Experimental
Psychology, Learning, Memory
and
Cognition,
9,
1
(January 1983), pp.
103-116.
Graham, J.R., and C.R. Harvey. “Market Timing Ability and Volatility
Implied in Investment Newsletters’ Asset Allocation Recommenda-
tions.”
Workmg paper, University of Utah, 1995.
Kahneman, D., and
A.
Tversky. “Prospect Theory: An Analysis of
Decision Malung Under Risk.”
Econometrica,
1979, pp. 263-291.
-.
“The Psychology of Preferences.”
Scient$c American,
246 (1982),
pp. 167-173.
Ketchum, M.D. “Investment Management Through Formula Timing
P1ans:’Journal
ofBusiness,
XX
(July 1982), pp. 157-158.
Malkiel, B. “Returns From Investing in Equity Mutual Funds 1971-
1991.”Journal
ofFinance,
50 (June 1995), pp. 549-572.
Markowitz, H. “The Utility
of
Wealth.”Journal
ofPolitical Eronomy,
60
(1952),
pp. 151-158.
Mehra,
R.,
and E.C. Prescott. “The Equity Premium Puzzle.”Journal
ofMonetory Economics,
40, 2 (1985), pp. 145-161.
F‘ye, Gordon. “Minimax Policies for Sehng an Asset and Dollar
Averaging.”
Management Science,
17,
7
(March 1985), pp. 379-393.
Roll,
R.
“A MeanNariance Analysis of Trackmg Error.”
Journal
of
Portfolio
Management,
Summer 1992,
pp.
13-22.
RozeK, Michael. “Lump-Sum Investing Versus Dollar-Averaging.”
Journal
of
Portfolio Management,
Winter 1994, pp. 45-50.
Samuelson, Paul. “The Long-Term Case for Equities.” Journal
of
Porlfolio
Management,
Fall 1994, pp. 15-24.
Sharpe, W.F.
Investmenfs.
Englewood CS, NJ: Prentice-Hall, 1981.
Shefiin, Hersh, and Meir Statman. “Behavioral Aspects of the Design
and Marketing of Financial Products.”
Financial Management,
22, 2
(1993),
pp.
123-134.
-
. “Behavioral Capital Asset Pricing Theory.”
Journal ofFinancial and
Quantitative Analysis,
29, 3 (1994), pp. 323-349.
-
.
“Behavioral Portfolio Theory.” Working paper, Santa Clara
University,
1995a.
-.
“The Disposition to Sell Winners Too Early and Ride Losers
Too Long: Theory and Evidence.”Journal
ofFinance,
40 (July 1985), pp.
777-790.
-. “Explaining Investor Preference for Cash Dividends.”
Journal
of
Financial Economics,
13 (June 1984), pp. 253-282.
-. “How Not to Make Money in the Stock Market.”
Psychology
Today,
20, 2 (February 1986), pp. 52-57.
-
. “Making Sense of Beta, Size, and Book-to-Market.’’ Journal
of
Porlfoolio Management,
Winter 1995b, pp. 26-34.
FALL
1995
THE
JOURNAL
OF
PORTFOLIO MANAGEMENT
77
Solomon, Ezra. “Are Formula
Plans
What They Seem
To
Be?’Joumal
ofBusiwsz,
XXI
(April 1948), esp. pp. 96-97.
Solt, Michael
E.,
and Meir
Statman.
“How Usem
is
the Sentiment
Index?”
Finanrial
AnalptsJoumal,
SeptemberIOctober 1988, pp. 45-55.
Thaler, Richard. “Mental Accounting and Consumer Choice.”
Marketing
Science,
4,
3
(Summer 1994), pp. 199-214.
Warther, V.A. “Mutual Fund Flows and Security Returns.” Working
paper, University
of
Southern California, 1994.
Weston,
J.F. “Some Theoretical Aspects
of
Formula Timing
Plans.”
journal
ofBusiness,
XXII,
4 (October 1949), pp. 249-270.
Acknowledgments
In addition
to
our Editorial Advisory Board, the following
have been most helpful in providing reviews of manuscripts
submitted to
us
in recent months:
Clifford Asness (Goldman Sachs Asset Management)
Josef Lakonishok (University of Illinois)
Michael Rosenberg (Merrill
Lynch)
78
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BEHAVIORAL
FRAMEWORK
FOR
DOLLAR-COST AVERAGING
FALL
1995
This article was published in The Journal of Portfolio Management, Fall 1995.
It is reproduced with permission of Institutional Investor, Inc.,
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