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Proceedings of the 2014 Winter Simulation Conference
A. Tolk, S. Y. Diallo, I. O. Ryzhov, L. Yilmaz, S. Buckley, and J. A. Miller, eds.
DOLLAR COST AVERAGING VS LUMP SUM: EVIDENCE FROM INVESTING
SIMULATIONS ON REAL DATA
Ugo Merlone
Department of Psychology
University of Torino
via Verdi 10
Torino, I 10124, ITALY
Denis Pilotto
ADB–Analisi Dati Borsa S.p.A.
Corso Duca degli Abruzzi 65
Torino, I 10123, ITALY
ABSTRACT
Dollar Cost Averaging is a periodic investment of equal dollar amounts in stocks which allegedly
can reduce (but not avoid) the risks of security investment. Even if some academic contributions
questioned the alleged benefits, several professional investment advisors and websites keep on sug-
gesting it. In this paper we use simulation to analyze Dollar Cost Averaging performance and
compare its results to Lump Sum investment. We consider 30 international funds and 30 stocks to
simulate investing over different period windows in order to assess whether this strategy is better
than investing the whole available sum at time 0.
1 INTRODUCTION
Decision-making is a complex process which is often plagued by errors leading to poor decisions
(Bazerman and Moore 2013). Although important contributions suggest approaches to make better
decisions (see, for instance Hammond, Keeney, and Raiffa 1999), biases and heuristics are likely
to affect the judgement of all types of professionals (Bazerman and Moore 2013). A heuristic can
be defined as a “rule of thumb” that provides a best-guess solution to a problem (Goldstein 2005).
In particular, when decisions are made under uncertainty, heuristics have been well documented
(Tversky and Kahneman 1974). Since investment decisions are often based on beliefs concerning
the likelihood of uncertain events, it is not surprising that different heuristics have been proposed.
Among the different investment strategies, Dollar Cost Averaging (DCA) (Pye 1971) seems to be
quite popular. Although several academic studies have pointed to the underperformance of DCA
especially when compared with simple lump sum (LS) (see Greenhut 2006 for a review), financial
advisors keep on suggesting this passive investment strategy. Greenhut reports to have found as
many as 250 sites discussing DCA with more than half providing illustrations of the “cost benefit” of
DCA. Since 2006 something has changed: a recent search of “Dollar Cost Averaging” on Google.com
(Google.com ) has provided about 1,070,000 results and among the first 30 results as many as 12
sites illustrate “the benefits of Dollar Cost Averaging”.
By contrast, in Italy DCA seems to remain quite popular. In fact, a recent search of “Piani di
accumulo capitale” on Google.it (Google.it ) has provided about 184,000 results and as many as 23
sites advocating this investing strategy among the first 30 results. It is surprising that among these
we can find some of the major Italian banks.
In this paper we use simulation to compare the performance of DCA to LS, considering 30
investment funds and 30 Italian stocks. The paper is organized as follows. In Section 2 the DCA
strategy is exposed. In Section 3 we describe the simulation we have considered to compare DCA
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Merlone, and Pilotto
performance to LS, then in Section 3 the results of our analysis are summarized and discussed.
Finally, the last section is devoted to conclusions and further research.
2 DOLLAR COST AVERAGING
Dollar Cost Averaging (DCA) is an investing strategy which, over a given time interval, calls for the
periodic investment of a fixed amount of money in a stock or portfolio at each period. Quite often
this strategy is recommended over investing the whole amount in a lump sum (LS) at time zero
(Brennan, Li, and Torous 2005). Brokerage firms, mutual funds and professional financial advisors
have been suggesting this strategy for a long time in spite of several academic studies which have
pointed to underperformance of DCA when compared to LS. As mentioned in the Introduction, it
is possible to find several websites claiming “The Benefits of Dollar Cost Averaging” and stating
that, with this strategy, “you buy more shares of an investment when prices are low and less when
they are high”. Also, some sites claim that in such way the investor avoids “the difficult or even
impossible task of trying to figure out the exact best time to invest”. Furthermore, some sites even
provide examples similar to the one illustrated in Table 1. In this hypothetical example, assuming
that fractional shares may be purchased, the investor used a dollar cost averaging approach, making
regular investments of $100 each month. When the share prices were higher, the investor bought
fewer shares. And, when the share prices were lower, the investor bought more shares.
Table 1: A typical example illustrating the alleged benefits of DCA.
Date Shares Price Investment Amount Shares Purchased
January $25 $100 4
February $25 $100 4
March $22 $100 4.55
April $20 $100 5
May $18 $100 5.56
June $17 $100 5.88
July $15 $100 6.67
August $15 $100 6.67
September $16 $100 6.25
October $20 $100 5
November $25 $100 4
December $28 $100 3.57
Total $1,200 61.15
Average Cost Per Share $19.62
Usually, this result is compared to what the result would have been investing $1200 in a lump
sum, namely buying 48 shares at an average cost per share of $25. It is immediate to show that with
DCA the investors end up with more shares than with LS, even over periods of time in which stock
market is low. Usually, the websites end with providing the usual caveats and disclaimers about
investment risks.
As mentioned in the Introduction several major Italian banks are quite enthusiastic in suggesting
that DCA increases portfolio value and in claiming that this approach helps reducing market volatility.
3 COMPARING DCA TO LS THROUGH SIMULATION
Given the popularity of DCA with Italian websites we used simulation to compare DCA to LS
considering thirty U.S. mutual funds that can be subscribed to in Italy. The sample of funds we
considered mainly consisted of euro traded retail funds, which are managed by some of the major
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banks and asset managers such as JP Morgan, Goldman Sach, Blackrock and Templeton. The mixed
sample we considered consisted of funds that invest in the stock market, bonds, cash and mixed
(stocks and bonds). For the sake of comparison, we also considered a sample of 30 stocks of major
Italian companies, even if we were well aware of “of the inefficiency of a single security portfolio”
(Brennan, Li, and Torous 2005, p.532). The funds and stocks we considered are reported in Table 2.
Table 2: The set of funds and stocks considered in the analysis
Funds Stocks
BGF Euro Markets E2 EUR A2A
Templeton EuroLand N Cap. EUR Autogrill
BGF Asian Dragon E2 EUR Astaldi
BGF Pacific Eq. E2 EUR Beghelli
BGF Emerging Europe E2 EUR Banca Intermobiliare
JPM Europe Equity D Acc EUR Monte dei Paschi di Siena
Templeton European N Cap. EUR Banco Popolare Societ`a Cooperativa
Templeton Eastern Europe N Cap. EUR Brembo
Franklin Templeton Japan N Cap. EUR Cattolica Assicurazioni
BGF Japan Small & MidCap Opportunities E2 EUR Centrale del Latte di Torino
BGF Global Opportunities E2 EUR Banca Carige
BGF Emerging Markets E2 EUR Datalogic
Templeton Growth (Euro) N Cap. EUR De’Longhi
BGF New Energy E2 EUR ENEL
BGF World Gold E2 EUR ENI
BGF US Basic Value E2 EUR EXOR
BGF US Small & MidCap Opportunities E2 EUR FIAT Group
Templeton Global Balanced N Cap. EUR Gabetti
BGF Global Allocation E2 EUR Indesit
BGF Flexible Multi Asset E2 EUR Interpump Group
BGF Euro Bond E2 EUR Italcementi
Fidelity Euro Bond A Dis EUR Luxottica
BGF Euro Short Duration Bond E2 EUR Mondadori
AXA WF Euro Bonds A Cap. EUR Mediaset
BGF Global High Yield Bond Eur Hedged E2 EUR Pininfarina
Templeton Euro High Yield N Cap. EUR Saipem
Fidelity European High Yield A Dis EUR Tenaris
BNY Mellon Global Bond A EUR Tiscali
GS US Fixed Income E Cap EUR Telecom
Fidelity Us High Yield A Dis EUR Zucchi
We considered quotations from January 2003 through December 2012, i.e., ten years. In such way,
we could investigate whether the–still popular–suggestion to use DCA strategy was supported by
recent actual performances. Both samples were selected among those traded in Italy. In particular,
stocks were selected among the largest Italian companies. Moreover, in order to increase comparability,
funds were selected among those investing in stocks. For each fund we thus considered the different
length investment windows from 1 month width, ie., buying at the beginning of the first month and
evaluating the portfolio value at beginning of the next month, up to 120 months, with DCA, the
investment is spread over 119 periods and at period 120 the portfolio is evaluated. For all the possible
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investment windows the beginning dates were considered within the 10 interval we analyzed. For each
investment, we thus consider 119 1-period investment windows, 118 2-period investment windows
up to 1 119-period investment window, for a total amount of 7140 comparisons. Furthermore, we
assumed that the money was kept on a saving account with zero interest rate, which is consistent
to the Italian bank situation for private small investors (for some of the consequences of zero lower
bound on nominal interest rate, see Ullersma 2002). Finally, we observe that our comparison made
sense when the investor had sufficient money to invest at the beginning, otherwise several options
are available to find money in one’s budget for investing, see, e.g., (Bajtelsmit 2006, p.350).
For each security we plotted the mean obtained by DCA and LS and also the mean plus/minus
one standard deviation, as illustrated in Figures 1, 2 and 3. For some funds the average portfolio value
with LS outperforms DCA (Figure 1), on the contrary, for some others the opposite is true (Figure
2); finally, in other cases the result depends on the width of the window. Actually, these results are
consistent with the fact that DCA is suboptimal when the market is in an uptrend (Greenhut 2006).
0 20 40 60 80 100 120
5000 15000 25000 35000
BGF Emerging Europe E2 EUR
Investment periods
Average +/− Sdev
LS
DCA
Figure 1: Portfolio value with DCA and LS at the end of investment period when investing in BGF
Emerging Europe E2 EUR.
To obtain a wider perspective about the two samples of funds we have considered, some descriptive
statistics are reported in Table 3.
Table 3: Portfolio value descriptive statistics with DCA and LS
strategy average standard deviation
Funds DCA 10510.16 1797.386
LS 11388.31 3916.935
Stocks DCA 9747.364 5012.186
LS 10702.641 9994.872
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0 20 40 60 80 100 120
9000 9500 10000 10500
Fidelity Euro Bond A Dis EUR
Investment periods
Average +/− Sdev
LS
DCA
Figure 2: Portfolio value with DCA and LS at the end of investment period when investing in Fidelity
Euro Bond A Dis EUR.
0 20 40 60 80 100 120
6000 8000 12000
BGF Japan Small & MidCap Opportunities E2 EUR
Investment periods
Average +/− Sdev
LS
DCA
Figure 3: Portfolio value with DCA and LS at the end of investment period when investing in BGF
Japan Small & MidCap Opportunities E2 EUR.
We can see that with both strategies the average portfolio value is larger than the invested
capital, nevertheless with LS the standard deviation is larger than with DCA. This larger variability
may suggests that, in principle, DCA could be superior to LS for more risk averse investors, yet the
actual reason might be that such investors should not be investing the whole of their wealth in the
market portfolio, as correctly pointed out by Brennan, Li, and Torous (2005).
As the distribution of the end period value is not normal and the difference between DCA and LS
is not symmetrical around the median, we cannot use either the Student’s t-test nor the Wilcoxon
rank-sum test, therefore we use graphical analysis as suggested by Loftus (1993). Therefore, we plot
the final portfolio values considering DCA and LS strategies for each of the 7140 windows in Figure
4.
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Figure 4: Funds: portfolio value with DCA and LS at the end of investment period.
The point corresponding to the average portfolio values with DCA and LS is depicted in red and
the dashed lines determine four regions. In the top right region we find investments for which both
DCA and LS provided a final value larger than the respective averages; in the top left region we
find investments for which LS provided a final value larger than the average and DCA a final value
lower than the average; similar considerations hold for the other regions. It can be observed that
most of the points lie above the 45 degrees line. As for the stocks this phenomenon is less evident,
as illustrated in Figure 5.
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Figure 5: Stocks: portfolio value with DCA and LS at the end of investment period.
For each of these securities we also computed the percentage of time in which DCA outperforms
LS. These results are presented in Tables 4 and 5. From these figures, we see that DCA outperformed
LS only 35.97% of the times for funds and 53.38%, as stocks are concerned. This can be confirmed by
the fact the market for stocks was less uptrend than the funds market in the period we considered.
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Table 4: Portfolio value comparison for funds
Fund % DCA >LS
AXA WF Euro Bonds A Cap. EUR 9.89
BGF Asian Dragon E2 EUR 24.52
BGF Emerging Europe E2 EUR 29.26
BGF Emerging Markets E2 EUR 22.58
BGF Euro Bond E2 EUR 29.02
BGF Euro Markets E2 EUR 29.02
BGF Euro Short Duration Bond E2 EUR 7.34
BGF Flexible Multi Asset E2 EUR 32.87
BGF Global Allocation E2 EUR 24.79
BGF Global High Yield Bond Eur Hedged E2 EUR 24.68
BGF Global Opportunities E2 EUR 32.94
BGF Japan Small & MidCap Opportunities E2 EUR 55.80
BGF New Energy E2 EUR 36.43
BGF Pacific Eq. E2 EUR 34.30
BGF US Basic Value E2 EUR 43.96
BGF US Small & MidCap Opportunities E2 EUR 35.53
BGF World Gold E2 EUR 17.80
BNY Mellon Global Bond A EUR 17.49
Fidelity Euro Bond A Dis EUR 71.64
Fidelity European High Yield A Dis EUR 59.02
Fidelity Us High Yield A Dis EUR 72.86
Franklin Templeton Japan N Cap. EUR 53.03
GS US Fixed Income E Cap EUR 66.30
JPM Europe Equity D Acc EUR 34.41
Templeton Eastern Europe N Cap. EUR 33.42
Templeton Euro High Yield N Cap. EUR 29.87
Templeton EuroLand N Cap. EUR 37.41
Templeton European N Cap. EUR 36.40
Templeton Global Balanced N Cap. EUR 34.71
Templeton Growth (Euro) N Cap. EUR 41.83
Average 35.97
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Table 5: Portfolio value comparison for stocks
Stock % DCA >LS
A2A 44.96
Autogrill 33.42
Astaldi 55.24
Beghelli 61.85
Banca Intermobiliare 54.83
Monte dei Paschi di Siena 65.49
Banco Popolare Societ`a Cooperativa 36.50
Brembo 30.60
Cattolica Assicurazioni 57.76
Centrale del Latte di Torino 61.09
Banca Carige 39.24
Datalogic 57.44
De’Longhi 58.28
ENEL 43.43
ENI 18.00
EXOR 34.47
FIAT Group 69.79
Gabetti 75.64
Indesit 36.68
Interpump Group 52.25
Italcementi 31.83
Luxottica 74.15
Mondadori 75.67
Mediaset 64.31
Pininfarina 72.76
Saipem 17.13
Tenaris 76.67
Tiscali 30.04
Telecom 90.43
Zucchi 81.54
Average 53.38
Finally, by comparing the distribution graph of portfolio values with different strategies it is
clear that LS provides a higher expected value and, at the same time, it displays a larger dispersion
than DCA. This is evident for both funds and stocks, as illustrated in Figures 6 and 7. Graphical
analysis confirms the descriptive statistics reported in Table 3.
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Figure 6: Funds: distribution of portfolio value with DCA and LS at the end of investment period.
Figure 7: Stocks: distribution of portfolio value with DCA and LS at the end of investment period.
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Even if we were considering the Italian Stock market only, our results are in line with (Brennan,
Li, and Torous 2005), therefore there is no particular reason for the popularity of this strategy among
Italian financial advisors.
4 CONCLUSION
Analysis of the simulations shows that the claim that DCA yields a higher portfolio value–as suggested
by several websites–seems not to hold.
On the contrary, LS yields a higher portfolio value, especially when funds are considered. Since
usually DCA is suggested to investors when subscribing to investment funds, our results highlight
that this may not be a good strategy. This aspect has been already proved using optimal control
techniques by Merlone (1993) and, from the viewpoint of a rational investor with a von Neumann-
Morgenstern utility function, by Brennan, Li, and Torous (2005). As for stocks, in the timeframe we
considered, DCA strategy seems to provide higher final value, even if it seems unadvisable to apply
this strategy to a single stock when taking into the underdiverisification effect of buying a single
stock, see for example (Brennan, Li, and Torous 2005). Another important aspect are transaction
costs. In our study, we have not considered transaction costs–which in the case of DCA may offset
profits (Bajtelsmit 2006). Obviously, had other stocks and funds been chosen, the results may have
been different, yet, as it is well known “By its nature all stock is risky.. . . In addition, the actual
return on your investment will vary over time and with economic conditions” (Bajtelsmit 2006, p.
401). Nevertheless, our conclusions are in line with some of the suggestions (Bazerman and Moore
2013) given in order to avoid common investment mistakes. That is, taking the time to formulate
an asset allocation and avoiding to pay high fees, commissions and transaction costs. In this sense,
while diversification presents its advantages in terms of risk reduction, asset allocation diversification
seems to be a less controversial suggestion than temporal diversification. Finally, Bazerman and
Moore (2013) warn against external sources encouraging investors’ natural optimism. In fact, often,
these sources “remind us of the wise advice they provided in the past, but generally neglect to
mention advice that were flat-out wrong” (Bazerman and Moore 2013, p.166). Therefore, we would
not suggest to invest money just looking at a well crafted example and forgetting transaction costs
that are not mentioned. This, of course, applies to all the cases in which the same commission has
to be paid for each purchase. Given the results of our analysis, the diffusion of such a scheme in the
Italian websites seems to be the result of ill-conceived financial advice.
ACKNOWLEDGMENTS
We are grateful to Davide Dalmasso at ADB - Analisi Dati Borsa S.p.A. and to FIDA - Finanza
Dati Analisi Srl for the help and the contributions to this paper. In particular, FIDA Srl for the
database and the information provided, and Davide for the selection of the samples. We are also
grateful to Gabriella Valentino for helpful suggestions. Usual caveats apply.
REFERENCES
Bajtelsmit, V. 2006. Personal Finance. Hoboken, NJ: Wiley.
Bazerman, M. H., and D. A. Moore. 2013. Judgement in Managerial Decision Making. Wiley.
Brennan, M. J., F. Li, and W. N. Torous. 2005. “Dollar Cost Averaging”. Review of Finance 9:509–535.
Goldstein, B. E. 2005. Cognitive Psychology. Belmont, CA: Thompson, Wadsworth.
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Greenhut, J. G. 2006, October. “Mathematical Illusion: Why Dollar Cost Averaging Does Not Work”.
Journal of Financial Pianning XIX (10): 76–83.
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Hammond, J. S., R. L. Keeney, and H. Raiffa. 1999. Smart Choices. Boston, MA: Harvard Business
School Press.
Loftus, G. R. 1993. “Visual data representation and hypothesis testing in the microcomputer age”.
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Merlone, U. 1993. “Scelte dinamiche ottime di investimento”. In Atti del XVII Convegno A.M.A.S.E.S.
Ischia, September 8-11: Istituto Italiano per gli Studi Filosofici.
Pye, G. 1971, March. “Minimax Policies for Selling an Asset and Dollar Averaging”. Management
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Tversky, A., and D. Kahneman. 1974. “Judgment under uncertainty: Heuristics and biases”. Sci-
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AUTHOR BIOGRAPHIES
UGO MERLONE (Ph.D. in Applied Mathematics, University of Trieste, Italy) is Associate Pro-
fessor at the Psychology Department, University of Torino, Italy. His main area of interest is
the modeling of human behavior and organizations. On these topics he has published on journals
such as European Journal of Operational Research,Physica A,Journal of Economic Behavior &
Organization,Journal of Mathematical Sociology,International Game Theory Review,Organiza-
tion Science,Journal of Artificial Societies and Social Simulation,Mathematics and Computers
in Simulation, and Communications in Nonlinear Science and Numerical Simulation. Further de-
tails can be found on his homepage www.ugomerlone.net. His email address is ugo.merlone@unito.it.
DENIS PILOTTO holds a bachelor’s degree in Business Management and a master’s degree in
Business Administration from the University of Turin. After an initial experience in Pricewaterhouse
Coopers he started working at ADB - Analisi Dati Borsa S.p.A. as a financial analyst. He has a
particular interest in the decision theory and in behavioral psychology for investment choices. His
email address is d.pilotto@adb.it.
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