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Dollar-cost averaging may not be rational behavior,
is petjktly normal behavior.
nvestors with cash that
destined for stocks often
use a dollar-cost averaging plan. They divide the
cash into segments, and convert one segment at
time from cash
The popularity of dollar-cost averaging can be
mined schedule. The alternative to dollar-cost averag-
ing is lump-sum investment.
cussions in Ketchum
And that popularity has never waned.
For example, Clements
ordinary investors who
want to get their finances going in the right direction”:
buy more. One
whch involves shoveling,
ing to stock and bond prices
While popular, the practice of dollar-cost aver-
inconsistent with :standard finance. This has
been demonstrated by Ccinstantinides
shows, within a theoretical li-amework, that dollar-cost
averaging plans are suboptimal. It has
strated by Rozeff
who shows using simulation
that dollar-cost averaging
An analysis of dollar-cost averaging
for at least
reasons, one related to an understandmg
of the behavior of investors, and the other related to the
effects of investor tradmg on security prices. Standard
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
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-
the overall construction of portfolios.
This article offers
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
work is part of
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 ), the reluctance to reahze losses ,
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
“Behavioral investors” make choices in
tematic, if suboptimal, fashion. This is not to advocate
the selection of suboptimal portfolios. But
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
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  and Sharpe’s
for investing the
same dollar amount, rather than the same number of
shares, each period. Thus,
investor buys more shares when the price is low than
when the price is high.
Weston  writes:
cost-averaging, its merit is urged
the basis of
relationship that holds without exception:
shares held is less than
Weston exposes the irrelevance of
crucial test is whether the shares held can
any time be
For ths to be possible, average cost must
be less than the current market price per share’’
Similarly, Sharpe  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
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
the world of
frame invariance. Investors care about cash flows, but are
indlfferent among frames of cash flows. The pricing of
good example. The price of
call option on
stock is determined by the fact that the cash flows of
the option can be replicated by the cash flows of
ticular dynamic combination of
bond and the under-
lying stock. The fact that in the
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
world of frame invariance.
Although the literature of standard finance has
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,
itive theory of choice by Kahneman and Tversky
, and with it I begin the construction of the
behavioral framework within whch dollar-cost averag-
ing takes place.
Choices of standard finance investors conform
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
Kahneman and Tversky find that
the sure amount, in the first problem set.
Yet, 69% of subjects chose
the gamble, in the sec-
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
and B, in problem
overall choice is between:
A3: A sure gain of $1,500 (the
of the initial
B3: A 50% chance to gain
and the sure $500), and
chance to gain
Similarly, once the initial $2,000 is integrated
into the choice between A, and
in problem 2, the
overall choice is between:
of net cash flows
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
losses. (See Exhibits
The origins of prospect theory
development is the work of Kahneman
and Tversky . To understand the features of
prospect theory, consider an experiment by Kahneman
and Tversky. One group of subjects receives problem
In addition to whatever you
been given $1,000. You are now asked to choose
chance to gain $1,000 and
chance to gain nothing.
Another group of subjects receives problem 2:
2. In addition
whatever you own, you have
50% chance to lose $1,000 and
chance to lose nothing.
sure gain of $11,500, and
B4: A 50% chance
The two problems
identical in net cash flows.
Period Invested Share Shares Bought
$1,000 $50.00 20
Average Cost of Shares Held:
Average Price per Share Over
the Two Periods:
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
application of specific decision rules to the accounts.
The initial amount, $1,000 in problem
stripped away and framed into
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
the prospect function in
the domain of losses leads to a preference of the gam-
ble over the sure $500
a choice consistent with
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
each, investing one in period
and the second in peri-
od 2. The price per share of stock in period
and it turns out that the price per share in period 2
$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
total of $1,250. The
Framing the problem as the proponents of dol-
lar-cost averaging would have
the investor bought
the shares at an average cost of $20, while the average
price per share over the
periods was $31.25. The
investor has a clear gain. Indeed, framed in the behav-
ioral way, the problem shows
when the stock price never changes. It
true that the behavioral frame is misleading. It is equal-
ly true that the behavioral frame persists.
no comprehensive theo-
ry that explains what makes some frames more com-
pekng the others. (See Fischhoff .) However, the
persistence of the behavioral frame of dollar-cost aver-
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.
prominent feature of dollar-cost averaging
recommended with equal force to investors
with cash who consider converting cash into stock and
investors with stock who consider converting stock into
usehl in highlighting the difference
in framing and choice between standard finance and
19791, who analyzes dollar-
cost averaging within the framework of standard
Where, then, does the intuitive rationale of dol-
rationale is that the
major gamble on
bles and thus diversifies risk. The fault of
argument is misrepresentation of
decision is made. Dollar-cost-
averaging implies that
A is in
from an investor with all
B, but otherwise identical. Dollar-cost-averaging
the simple fact that the latter investor
his endowment from asset
B before he considers the optimal
investment decision. Both investors face the
irrespective of the composition
their endowment, and any claims
simply fallacious (pp.
Imagine two investors, A and
who are iden-
tical except that
in cash and
choice between keeping his wealth
or converting it into stock while
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
can costlessly convert her initis stock
endowment into cash. Therefore, their choices are
predcted to be identical.
The frames and choices of
are likely to
be difierent within the framework of behavioral
finance. The two are identical in their beliefs,
agree that the return on cash is zero, and that the value
with equal prob-
abilities, either increase to $1,300 or decrease to $860.
The expected gain on stocks is $80, while the expect-
on cash is zero.
How would A frame the choice? Assume that
the reference point for A is the $1,000 in cash,
tion he has adapted to, and that he frames the choice in
terms of gains and losses relative to the $1,000 reference
Cash A. A sure gain of zero, and
chance to gain $300 and
chance to lose
Assume that the reference point for
position she has adapted to.
Cash A. A
chance for an (opportunity)
50% chance for
an (opportunity) loss of
A sure (opportunity) gain of zero.
The problems faced by A and
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
to hold onto his cash, and it is likely to cause
hold o’nto her stock.’
The purported advantages
leading frames. Framed in the standard finance way,
dollar-cost averaging investor only replaces one
major gamble, embedded in
number of smaller gambles, embedded in dol-
lar-cost averaging. But frames are important, and
they a:ffect choice.
The purchase of stock for
will result in
at the end of the period, or it will result in $860.
The monetary gain is
and the monetary
but monetary gains and losses are not
affects choice. The joy of pride and the pain of regret
matter. Kahneman and Tversky E19821 describe regret
the frustration that comes, ex post, when
purchase of stocks results in
monetary gain is supplemented with
the pride that comes from what is framed
$1,300 worth of stock for
chase of stocks results in $800, the
is supplemented with the regret that comes from what
buying $860 worth of stock for
The dstinction between
gains and losses in
terms of money and 2) gains and losses in terms of
pride and regret is akin to Thaler’s  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
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
association between regret and the level
choice. Actions taken under duress entail little
responsibility and bring little regret. Following
one way to reduce responsibihty. Choice under
rule is choice under duress. Dollar-cost averaging
strict rule that specifies amounts
particular points of tinie. The abdity of
cost averaging plan to reduct: responsibdity is especially
helpful for investors who are concerned about their
exposure to regret.2
Dollar-cost averaging is
non-contingent investment policy. The non-sequential
nature of dollar-cost averaging is manifested in
the initiation of the plan to invest
ular amount in each subsequent period, regardless of
any information that might become available after the
initiation of the investment plan. Constantinides
notes that the non-sequential nature of dollar-
cost averaging is considered by its proponents
key to its success.
shows that dollar-cost
averaging is dominated by
sequential optimal invest-
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
they follow the
inferior non-sequential investment policy.
policy that is suboptimal within standard
finance might nevertheless be attractive to behavioral
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
reduction in responsibility.
The rules of dollar-cost averaging serve to combat laps-
es in self-control
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
ed by Constantinides
engage in dollar-cost-averaging
and the courage
continue buying in
declining market when
may seem bleak.
Cohen, Zinbarg, and Zeikel note, investors
find it dfficult to continue to buy stocks following
stock price declines. But why do investors find it
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
reflection of representative-
cognitive error, and that tendency is well-docu-
mented. For example, Solt and Statman
investment advisors become optimistic about the
prospep of stocks after increases in stock prices and
pessimistic after declines. They
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.
dollar-cost averaging investor starts
the investment plan with the expectation that there
an equal chance for an up-market or down-market in
the coming period. Once several down-periods occur,
the investor revises the probabilities
that the proba-
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-
useful in enforcing
savings plan. Shefrin and Statman
“consume from dividends, but don’t dip
into capital” help investors manage the self-control
myopic “agent” within the individu-
al wants to consume now, but
“principal” considers savings for the future
current consumption. “Don’t dip into capital” is
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
period of losses, whch
when the strict rules of dollar-cost averaging are most
effective. The rules of dollar-cost averaging help
investors “continue buying in
declining market when
prospects may seem bleak.”
Investors who employ dollar-cost averaging have
their wealth in one asset, such
cash, and consider
transferring it into another asset, such
can transfer wealth from one asset to the other in
lump sum. Instead, they transfer wealth in increments
over time according to
It has been known
least since Weston
that the practice of dollar-cost averaging is inconsistent
with standard finance. Yet dollar-cost averaging seems
ever. The persistence of dollar-cost
averaging is an embarrassment to the role of standard
positive theory of financial behavior.
:Dollar-cost averaging is significant even if it is
followed only by small investors,
the aggregate of
small investors is large. Moreover, the early literature on
dollar-cost averaging, such
Cottle and Whtman
, suggests that dollar-cost averaging plans were
then popular among institutional investors. There is no
decline in that popularity.
Dollar-cost averaging is consistent with the pos-
itive framework of behavioral finance. I have described
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
stock price declines, and the need for rules to
facilitate self-control explains the non-sequential
of the rules that govern dollar-cost averaging.
.Dollar-cost averaging joins financial products
covered calls and LYONS, described by Shefrin
and Statman ,
standard finance yet fit well with behavioral finance.
Indeed, it belongs in the general area
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.
dollar-cost averaging takes place in
framework where choice is not explicit.
the implementation of defined-contribution pension
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,
only implicit because employees
are not given an explicit choice between contributions
in portions over the cause of
point during the year.
Suppose an employer does offer employees
choice between dollar-cost averaging contributions
coinciding with payroll days during
time lump-sum contribution of the total annual
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
know of no employer who offers such
present, it should be possible to test
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  reveals
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
stock prices and less likely to accelerate buying after
period of increases in stock prices. I hypothesize that
an increase in dollar-cost averaging leads to a decrease
Dollar-cost averaging is indeed suboptimal
within the choice set facing
fully rational investor in
standard finance. But the interpretation of rationality
delicate task. Consider, for example, the equity
risk premium (Mehra and Prescott ). 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
convert cash into stock in
who counsels the client
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
they contemplate the
regret that they will experience if the stock market
were to crash
the cash is converted into stock.
Dollar-cost averaging is indeed
but it might start an investor on
road that leads to
portion of wealth to stocks.
19941 writes about dollar-cost
averaging, he notes that it
one of dozens of rules
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
blunder, if not
crime. Yet the fact that many com-
mon investment rules are inconsistent with standard
finance is evidence that standard finance does not do
Standard finance is inconsistent with the exis-
tence of an investment advising industry where rules
dollar-cost averaging are
finance is inconsistent with the existence of
fund industry where, on average, money managers fail
to outperform indexes (see Malkiel
dard finance is inconsistent with the existence of an
investment newsletter industry where newsletter writ-
ers provide useless asset allocation advice (see Graham
It might be time to move on to
ory that is consistent with the evidence, and to
normative theory is useless if
investors cannot be persuaded to follow it.
offer an hypothesis. The practice of dol-
lar-cost averaging will persist.
The author thanks Hersh She& and Atulya
discussions, and the Dean Witter Foundatiop for financial support.
‘The choice problem
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
erence point, and
and losses are measured relative to it. (See Roll
 and Clarke, Krase, and Statman .)
2For a “mini-max” policy, where considerations of regret
lead investors to choose dollar-cost averaging, see Pye
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our Editorial Advisory Board, the following
have been most helpful in providing reviews of manuscripts
in recent months:
Clifford Asness (Goldman Sachs Asset Management)
Josef Lakonishok (University of Illinois)
Michael Rosenberg (Merrill
This article was published in The Journal of Portfolio Management, Fall 1995.
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