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Dollar Cost Averaging, The Myth and the reality
Chapman, Spira & Carson - Disscusion

From: Chapman Spira and Carson
Date: 4/12/99
Time: 8:57:31 AM
Remote User:


I don't know that there is an exact definition for dollar cost averaging, either it is a misnomer and the investment clubs are correct and it means taking a fixed amount of money from a number of people and investing that sum, in an analytically determined group of securities over a long but indefinite period of time in the stock market or for that matter in anything else. This discussion deals more with taking a predetermined, available sum of money to be invested in the stock market for a finite period of time. The results are startling, but we wanted to make some observations before you jump into the pool.

For years we have believed that "dollar cost averaging" would bring a improved total return than investing all your money at once. An overlooked 1993 study by Richard E. Williams and Peter W. Bacon thoroughly examined the issue and establish that what we believed in, within the same breath, as motherhood and blueberry pie was an old wives tale. We have enclosed the study for you to take a look at but before we burst your bubble there are a few comments that should be made.

One of the most important aspects of dollar cost averaging is the fact that it creates discipline, a prerequisite for success in any endeavor. I firmly believe that almost any reasonable strategy will succeed as long as it is followed rigorously. As in other arenas, the meanderer is eaten alive in the market. The focused individual generally seems to succeed. Another victim is the tip recipient who is always looking for a faster way to make it big. The tipster usually loses big instead. Whatever else may be mathematically true about dollar cost averaging, the psychological variant cannot be measured. In time there may be studies that will classify humanity into personality types and then we may be able to predict the relative success of a "type A personality" investing in dollar cost averaging or lump sum investing. Then we would go down the line and compare type "B", "C" and on down until we have covered the universe of types. The study does the best it can by lumping us all in one homogeneous mold and looking at humanity from a disparate point of view.

From a purely mathematical point of view, it would appear commonsensical that, assuming a person starts with a sum certain, in an up (bull market) market, securities will provide a greater return than fixed income instruments such as treasury bills which were the comparison used in the study. During the studies time frame, markets for the most part went straight up so that whenever you choose to invest, was probably the right time and that by only investing money in, a portion at a time, you would be paying higher and higher prices and the commissions that you would be generating for you friendly broker would be infinitely higher. The study being a pure mathematical work did not deal with that aspect. .

The study would have looked very different if the market had been down as frequently as it was up during the period in question. Unless you started from an exceedingly high base, if everything else is equal, inflation literally rules against the success of dollar cost averaging. A market that stays virtually unchanged in real terms is in actuality going up faster than inflation just to keep up with the loss in the dollar's purchasing power. When you add the type of efficiency that our industries have been able to squeeze out, the plant become leaner and meaner and most important, more profitable. While the study gives credit for alternative use of money such as treasury bills during the accumulation period, thus has the dividends of the S&P been included in the study, dollar cost averaging for the most part would have come out somewhat better, with the exception of investments in utilities during the period covered.

Over recent years, U. S. industry has been able to make tremendous progress in cutting unnecessary expenses. Listed companies today don't have any resemblance to they predecessors of only a decade ago as modern economical approaches along with lower bulk communicates and transportation expenses have been utilized by more informed management's. One could wonder than, what will happen now that much of the fat has already been squeezed out and inflation has drifted into a non-event. Will future gains be harder to come by. Much of today's market gains have become anticipatory, thus when there is little left to anticipate and no more inflation to worry about, what will be the result?

Another factor that should be carefully considered by investors is the prodigious number of new issues coming out skewed toward the Internet. More and more people see the Net as where the future will be and indeed they are probably right. Not all of these issues are going to succeed and many of them have capitalization's greater than that of a good sized country. As the amount of money that they are sopping up continues to increase, it reeks of a giant Ponzi Pyramid, which must topple from the weight, created at the top. The Ponzi pyramid did not collapse because someone found him out, it collapsed because not enough new investors could be found to keep repaying the old ones. Ultimately this will occur in the Internet stock as well. The old saw that the majority of the people are always wrong at the top has not yet been disproved. The only question left to answer is, just where is the top and for that answer, your guess is as good as mine.

All that aside, this following is easily both the most consistent and mathematically accurate model on the subject that we have ever seen and do not in a general sense dispute any of its findings. Until we have been able to place humanity into categories and then do the analysis again using that variable, this will have to stand is the best effort to date. Chapman

Dollar Cost Averaging vs. Lump-Sum Investing By Richard E. Williams and Peter W. Bacon

Should you invest a lump sum gradually, or all at once? The historical record suggests that investing it all at once may provide higher returns, if you are investing over long time periods—and are willing to accept the risk.

What do you do when you want to invest a sizable amount of cash in the stock market?

The cash may have come from a lump-sum retirement distribution, court settlement or inheritance, but the question investors face is the same: Should the funds be immediately invested in a diversified stock portfolio all at once or should the money be gradually invested in the market over time?

The conventional wisdom, at least among professional investment advisers, is that the lump sum should be gradually moved into stocks in order to reduce the risk that you are investing the entire amount at a market high. Such advice really amounts to a form of dollar cost averaging, a strategy long recommended by investment textbooks.

This article fills a void in the literature by reporting the results of an empirical study that compares the efficacy of a dollar cost averaging strategy with that of lump-sum investing over a long-term historical time period. The averaging strategy examined here differs from the kind usually discussed in investment texts in that we assume a lump sum initially invested in Treasury bills and gradually shifted into the stock market in periodic equal dollar amounts. The more common assumption is that the investor accumulates wealth by diverting a constant amount each period from current income into the market.

The Study The study is based on monthly total rates of return for the Standard & Poor’s index of 500 stocks (S&P 500) and 90-day Treasury bills over the period 1926 through 1991 as reported in Ibbotson Associates’ "Stocks, Bonds, Bills & Inflation—1992 Yearbook." The lump-sum strategy assumed that the entire amount was invested in the stock market at the beginning of a 12-month holding period. For the dollar cost averaging strategy, we assumed that the total amount was initially invested in 90-day Treasury bills and then shifted in equal monthly installments into our proxy for the stock market, the S&P 500. Returns were then calculated and compared for each strategy at the end of 12-month holding periods. Taxes and transaction costs were ignored.

Table 1. 1988 Monthly Returns: An Example Monthly Returns (%) Month

                    90-Day Treasury Bills              S&P 500

January               0.29                                             4.27

February            0.46                                             4.70         

March                 0.44                                           -3.02

April                   0.46                                             1.08

May                    0.51                                             0.78

June                    0.49                                              4.64

July                     0.51                                             -0.40

August                0.59                                             -3.31

September         0.62                                              4.24

October             0.61                                              2.73

November          0.57                                            -1.42

December          0.63                                              1.81

The computational procedure can be illustrated with an example that assumes an original lump sum of $120,000 and monthly return data for January through December 1988, as set forth in Table 1. Under the lump-sum strategy, the entire $120,000 would be invested on January 1 in the S&P 500. After monthly compounding, the $120,000 would have a value of $140,172 at the end of December 1988. The annualized holding-period return would be:


________ - 1 = 16.81%


For a 12-period dollar cost averaging strategy, we assumed that one-twelfth of the $120,000 would be invested in the market index on January 1, 1988 and the balance of $110,000 invested in T-bills. On February 1, a second installment of $10,000 plus one month’s accumulated interest would be invested in the S&P 500 for 11 months. This process is repeated for the entire 12-month period. Thus, by December 1, the entire $120,000 is invested in the market index. By December 31, 1988, the value of the dollar cost averaging portfolio would be $131,616, and the annual holding-period return would be:

$131,616 - 1

_________ = 9.68%


We also investigated the effects of both a six-month and a three-month dollar cost averaging installment period. For the six-month strategy, one-sixth of the initial amount was invested for 12 full months in the S&P 500. Another one-sixth was invested in T-bills for one month and then in the market for 11 months, etc.

For the three-month strategy, one-third of the initial amount is immediately invested in the S&P 500 for 12 full months. Another third is invested in T-bills for one month and then switched to the S&P 500 for 11 months. The final installment of one-third is in T-bills for two months before being invested in the S&P 500 for ten full months. For each of the three dollar cost averaging strategies, annual holding period returns were computed for every possible starting month (January 1926, February 1926, etc., through December 1991), a total of 780 12-month periods.

The Results The results of the analysis are summarized in Tables 2 and 3. Three time periods are shown in each table: 1926 through 1991; 1950 through 1991 and 1970 through 1991. The first period represents the extent of the database. The second period encompasses the post-World War II era while the third covers a more recent period of investment experience and includes both the unhappy investment decade of the 1970s and the extended bull market of the 1980s.

Table 2. Lump-Sum Strategy vs. Dollar Cost Averaging: Return and Risk Average Annual Return (%) Variation* (%)                                                               1926-1991

Lump-Sum Strategy              12.75                                              22.81

12-Month Averaging              8.50                                               13.21

6-Month Averaging                9.97                                               16.81

3-Month Averaging              11.10                                               19.40


Lump-Sum Strategy              13.37                                              16.39

12-Month Averaging              9.63                                                 9.83

6 Month Averaging               10.97                                              12.91

3-Month Averaging               12.00                                              14.61




Lump-Sum Strategy        13.28                                              16.84

12-Month Averaging       10.80                                              10.56

6-Month Averaging         11.84                                              13.80

3-Month Averaging         12.51                                              15.40 *

As measured by standard deviation. The figure represents the amount by which most returns varied around the average return.

Table 2 shows the average annual returns for each strategy for each time period, as well as the risk as measured by variability (the amount by which most actual returns varied around the average). For all time periods, the lump-sum strategy produced superior returns to the dollar cost averaging strategies, but at higher levels of risk. Also of interest is the fact that the returns for dollar cost averaging increase as the number of dollar cost averaging installments is reduced. Clearly, the sooner the entire amount is fully invested in the market, the higher is the realized return.

Table 3. Lump-Sum Strategy vs. Dollar Cost Averaging (DCA) Percent of Time Lump-Sum Outperformed DCA (%)

Dollar Cost Averaging Strategy 1926-1991     1950-1991      1970-1991

12-Month                                      64.5                  66.3                  59.5

6-Month                                        62.4                  63.2                  56.7

3-Month                                        60.5                  62.2                  57.5

Table 3 summarizes the number of time periods that the lump-sum strategy produced higher returns than the dollar cost averaging strategy. As can be seen, the lump-sum strategy outperformed dollar cost averaging nearly two-thirds of the time. The success of the lump-sum strategy dropped, however, during the 1970 through 1991 period because of the poor performance of the stock market during much of the 1970s, coupled with the high interest rates that prevailed from the mid-1970s to the early 1980s, which improved the success of a dollar cost averaging strategy.

What is the practical significance of the superiority of lump-sum investing over dollar cost averaging? Consider the 1950-91 period and a $100,000 initial endowment. According to Table 2 the initial $100,000 would be worth, on the average, $100,000 � (1.1337) = $113,370 after one year of being fully invested in the market. Following a dollar cost averaging strategy for 12 months would result in an average compound value of $100,000 � (1.0963) = $109,630, a difference of $3,740 after one year. After 10 years, assuming an average return of 13.37%, the difference would compound to $13,118. After 20 years, the difference in wealth would be $46,008 or an amount equal to 46% of the initial amount.

Conclusions This article has examined a common problem facing many investors, namely whether to invest a large cash amount immediately in a diversified stock portfolio or to use a dollar averaging approach to gradually shift the funds into the market. The dollar cost averaging approach has received wide acceptance when the assumption is that equal dollar amounts, taken from current income, are invested periodically in stocks, thus avoiding the possibility of investing all the money at a market high.

Our study looks at the problem from a different perspective. Given a lump sum, is it better to invest the entire amount immediately, or spread it out in equal installments?

Based on historical evidence, the major conclusion of our study is that an investor is better off investing the lump sum immediately, if he is willing to assume the greater risks in terms of variability of return. This conclusion emerges after calculating annualized monthly returns for three averaging strategies for all possible 12-month periods from 1926 to 1991 and comparing the results with those from investing the entire amount immediately in the market at the beginning of each period. For all time periods and averaging strategies, the lump-sum strategy produced superior returns, albeit at greater levels of risk.

These results should not be too surprising. In the great majority of time periods, diversified stock portfolios produce a higher return than Treasury bills—while stocks are riskier in terms of return variability, the market over the long term compensates investors for that risk. Thus, there is normally a relatively high opportunity cost associated with holding the uninvested portion of an amount in a risk-free asset.

Of course, the theory behind dollar cost averaging is that an investor does not know in advance what the stock market is going to do. Dollar-cost averaging lowers the risk of investing the original amount at a high point, and selling at a low point. The actual outcome of such a strategy, however, depends on the movement of the stock market. If the market rises, dollar cost averaging will result in a lower return than a lump-sum investment strategy, while if the market drops, it will result in a higher return.

There is, of course, no assurance that the past pattern of stock market and Treasury bill returns will persist in the future. Nonetheless, based on the historical record, investors who can overlook the risk may prefer to invest in the stock market as soon as possible.

Richard E. Williams and Peter W. Bacon are professors in the Department of Finance at Wright State University, Dayton, Ohio. This article originally appeared in the April 1993 issue of the Journal of Financial Planning.

� AAII Journal June 1993, Volume XV, No. 5

Last changed: March 17, 2000