UMP SUM BEATS DOLLAR-COST AVERAGING

by Richard E. Williams and Peter W. Bacon

This article compares the annualized re- turns from various dollar-cost averaging strategies with those produced by lump- sum investingfrorn 1926 to 1991. For all time periods and averaging strategies in- vestigated, lump-sum investing produced superior returns to dollar-cost averaging, and in all but one instance, the differences were significant at the .005 level. Based on these results, financial planners should advise clients wishing to make sizable cash investments in the market to invest as soon as possible. Dollar-cost averaging is un- likely to produce superior results to lump- sum investing.

A n important question facing many financial planners is what advice to give clients who wish to make a sizable investment of cash in the stock market. The cash may have come from a lump-sum retirement dis- tribution, court settlement, or inherit- ance. Should the funds be immediately invested in stocks or should the money be gradually invested in the market over time?

Theoretical arguments notwith- standing,[4] the conventional wisdom among financial planners seems to be that the lump sum should be gradually moved into stocks to avoid the risk of investing the entire amount at a market high. [ 1,3] Such advice amounts to a form of dollar-cost averaging (DCA), a strategy long recommended by invest- ment textbooks. [8] According to its proponents, the benefits of investing equal dollar amounts over time include a lower average price per share and, presumably, a higher realized rate of return. [7] Surprisingly, however, very little empirical evidence exists to sup- port the DCA strategy.

This article fills a void in the litera- ture by reporting the results of an em-

64

RICHARD E. WILLIAMS is asso- ciate dean of business and admin- istration at Wright State Univer- sity in Dayton, Ohio.

PETER W. BACON is a professor of finance at Wright State Univer- sity.

pirical study that compares the efficacy ofa DCA strategy with that of lump-sum (LS) investing. 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 is gradually shifted into the stock market in periodic equal dollar amounts. The more com- mon DCA assumption is that the inves- tor accumulates wealth by diverting a constant amount each period from cur- rent income into the market.

The results of this comparison strongly suggests that conventional wis- dom is wrong. Nearly two thirds of the time, according to our study, a lump- sum strategy significantly outperformed a dollar-cost-averaging approach.

Methodology

The study is based on monthly total rates of return for the Standard & Poor's 500 Stock Index (S&P 500) and 90-day Treasury bills from 1926 to 1991 as reported in Ibbotson Associates' 1992 Yearbook.[5] The LS strategy assumes that the entire lump sum is invested in the stock market at the beginning of a 12-month holding period. For the DCA strategy we assume that the fund is initial-

Near ly two thirds of the time, according to our

study, a lump-sum strategy signif icantly outperformed

a dol lar-cost-averaging approach.

ly invested in 90-day T-bills and then shifted in equal monthly installments into our market proxy, the S&P 500. Returns are then calculated and com- pared for each strategy at the end of 12- month holding periods. Taxes and transaction costs are ignored.

Journal of Financial Planning

The computational procedure can be illustrated with an example that as- sumes an available lump sum of $120,000 and monthly return data for January- December 1988 as set forth in Table 1. Under a lump-sum strategy, the entire $120,000 would be invested on January 1 in the S&P 500. After monthly com- pounding, the $120,000 would have a value of $140,172 at the end of Decem- ber 1988. The annualized holding pe- riod return (AHPR) would be:

$140,172 AHPR = -1 = 16.81%

$120,000 For a 12-period DCA strategy, we

assume that 1/12 of the $120,000 would be invested in the market index on Janu- ary 1,1988, and the balance of $110,000 would remain 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. On March 1, a third installment of $10,000 plus 2 month's interest would be invested in the S&P 500 for 10 months. This process is re- peated for the entire 12-month period. Thus, by December 1, the entire $120,000 has been shifted from T-bills into the market. By December 31,1988, the com- pounded value of the investment for DCA was $131,616 and the AHPR was computed as:

$131,611 AHPR = - 1 = 9.68%

$120,000 We also investigated the effects of

both a six-month and a three-month DCA installment period. For the six- month strategy, one sixth of the initial endowment would be invested for 12 full months in the S&P 500. Another one-sixth would be invested in T-bills for 1 month and then in the market for 11 months, and so on.

For the three-month strategy, one third of the endowment is immediately invested in the S&P 500 for 12 full months. Another third is invested in T- bills for 1 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 DCA strategies, annualized holding period returns were computed for every possible starting month (January 1926, February 1926 ..... December 1990) ~a total of 780 twelve- month periods.

Lump-Sum Strategy Superior

The results of the analysis are sum- marized in Tables 2, 3, and 4. Three time periods are shown in each table: 1926- 91, 1950-91, and 1970-91. The first pe-

riod represents the extent of the Ibbotson Associates' database. The second period encompasses the post-World War II era, while the third covers a more recent period of investment experience, includ- ing the unhappy investment decade of the 1970s and the extended bull market

April 1993 65

of the 1980s. Table 2 shows the mean annualized

returns for each strategy for each time period. For all time periods, the LS strat- egy produced superior returns to the DCA strategies. Also of interest is the fact that the returns for dollar-cost aver- aging increase as the number of DCA installments is reduced. Clearly, the

66

sooner the entire endowment is fully invested in the market, the higher the realized return.

Table 3 summarizes the number of time periods that the LS strategy pro- duced higher returns than the DCA strat- egy. As illustrated, LS outperformed DCA nearly two thirds of the time. The suc- cess of lump-sum investing was some-

what less during the 1970-91 period because of the poor performance of the stock market during much of the 1970s. When coupled with the high interest rates that prevailed from the mid-1970s to early 1980s, the success of a DCA strategy improved. However, even un- der these market conditions, the lump- sum strategy still outperformed the averaging strategy nearly six out of ten times.

Finally, Table 4 summarizes the dif- ference in the mean annualized returns for the three time periods. For all time periods the difference between LS and DCA was positive and, in all but one instance, statistically significant at the .005 level as measured by the T-test for paired differences. As expected, the dif- ferences diminish with the number of DCA periods but still remain significant except for the 3-month DCA for the 1970-91 period. Again, these results strongly support a lump-sum invest- ment strategy over a dollar-cost-averag- ing strategy.

What is the practical significance of the superiority of LS over DCA invest- ing? Consider the 1950-91 period and a $100,000 initial investment. According to Table 2, the initial $100,000 would be worth, on the average, $113,370 ($100,000 x 1.1337) after one year of being fully invested in the market. Fol- lowing a DCA strategy for 12 months would result in an average compound value of $109,630 ($100,000 x 1.0963), a difference of $3,740 after 1 year. After 10 years, assuming an average return of 13.37%, the difference would compound to $13,118. After 20 years, the differ- ence in accumulated wealth would be $46,008 - - an amount equal to 46 per- cent of the initial investment.

Conclusion

This article has examined a com- mon problem facing many investors, namely whether to invest a large cash endowment immediately in stocks or to use a dollar-cost-averaging approach to gradually shift the funds into the mar- ket. The DCA approach has received wide acceptance in the literature 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

Journal of Financial Planning

perspective. Given a lump sum, is it better to invest the entire amount imme- diately, or spread it out in equal install- ments?

Based on historical evidence, the major conclusion of our study is that the odds strongly favor investing the lump sum immediately. This conclusion emerges after comparing annualized monthly returns for both DCA and LS strategies for all possible 12-month peri-

Based on the historical record, financial planners would be well advised to encourage their clients to invest in the stock market

as soon as poss ib le !

ods from 1926 to 1991. For the entire 65-year period, the LS strategy produced superior returns approximately two thirds of the time, and the superior re- turns were statistically significant.

How do we account for these re- sults? The primary explanation seems to center on the positive risk premium that exists in the great majority of time peri- ods. Thus, there is normally a relatively high opportunity cost associated with holding the uninvested portion of an endowment in a risk-free asset. Approxi- mately one third of the time, however, DCA did produce superior results to LS investing. The authors are currently ex- amining those time periods for common causal factors.

There is, of course, no assurance that the past pattern of stock market and T-bill returns will persist in the future. Nonetheless, based on the historical record, financial planners would be well advised to encourage their clients to invest in the stock market as soon as possible! Dollar-cost averaging is un- likely to produce superior results to lump-sum investing.

References

1. Lynn Asinof, "Do's and Don'ts of Early Pension Money," The Wall Street Journal, September 24, 1991, p. C1.

2. Kirt C. Butler and Dale L. Domian, "Risk, Diversification, and the In-

vestment Horizon," Journal of Port- folio Management, Spring 1991, pp. 41-47.

3. Jonathan Clements, "Why It's Risky Not to Invest More In Stocks," The Wall Street Journal, February 11, 1992, p. C1.

4. GeorgeM. Constantinides, "ANote on the Suboptimality of Dollar-Cost Averaging as an Investment Policy," Journal of Financial and Quantitative Analysis, XlV, June, 1979, pp. 443- 50.

5. Roger G. Ibbotson and Rex A. Sinquefield, Stocks, Bonds, Bills and Inflation 1992 Yearbook, (Chicago: Ibbotson Associates).

6. Wayne Y. Lee, "Diversification and Time: Do Investment Horizons Matter?" Journal of Portfolio Man- agement, Spring 1990, pp. 21-26.

7. Burton G. Malkiel, A Random Walk Down Wall Street, (W.W. Norton & Company), 1991, pp. 344-47.

8. Richard K. Smith, Dennis L. Proffitt, and Alan A. Stephens, Investments, (West Publishing Company, 1992), pp. 13-14, 613-14.

April 1993 67