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Lump Sum Investing and Regular Investing

Radim Gottwald

Mendel University in Brno Department of Finance

Brno, Czech Republic radim.gottwald@mendelu.cz

Abstract—The paper is focused on current topic lump sum investing and regular investing. Author compares lump sum investing with regular investment strategies dollar cost averaging and dollar value averaging. These strategies are compared within five-year and ten-year investment horizon in the framework of the whole period 10 years, in detail from 1st January 2003 to 31st December 2012 and applied to stock market of the United States of America, the Japan and the United Kingdom. Author uses corresponding indexes Standard & Poor´s 500, Nikkei 225 and FTSE 350 and he finds out which strategy is optimal according to the yield-to-risk ratio. The trend of used stock market indexes is graphically analysed. Results show interesting findings. Maximums of all three used indexes are reached during autumn 2007, just at the beginning of the financial crisis. The yield-to-risk ratio of dollar value averaging is found to be the highest of ratios for five-year and ten-year investment. So, the dollar value averaging is found to be an optimal strategy. Author also compares found results with results of other authors. This paper could inspire investors to assemble their investment portfolios and create investment strategies. Thus, the contribution of the paper can be deducted.

Keywords-lump sum investing, regular investing, investing, dollar cost averaging, dollar value averaging, yield-to-risk ratio

I. INTRODUCTION

Many investors invest in stock markets in an effort to achieve optimal investment. They should find out important characteristics of international markets before each investment. In connection with stock trading in stock markets, investors use various investment strategies. Principles of different strategies are also different, so investors can realize different profits using different strategies. In general, the market timing is very important for investors. They want to find out the right time to maximize the profit. Gladiš (2005) describes that investors monitor the whole market and try to estimate what will be the future market trend. Finding the right time when to buy or sell stocks is rather difficult. Mašek (2010) points out that retail investors sometimes unfortunately miss the ideal time when to buy stocks in order to time the investment on the market. Market bubble could be used within market timing, it could be considered as the signal to sell. Investors could identify the market bubble when stock price increases too fast and too long without any economic reason. The end of the market bubble leads to decrease of many stock prices.

The aim of the paper, detailly described in the Chapter “Methodology”, relates to lump sum investing, dollar cost averaging and dollar value averaging. The content of this paper is especially the comparison of these strategies within chosen

horizons over the chosen period. This paper follows in a number of empirical studies focused on the investment strategies. Some of these studies are quoted in this paper.

The rest of this paper is organized as follows. Chapter „Literary Survey“ is focused on investment strategies in detail. Especially, the dollar cost averaging and the dollar value averaging are at the centre of attention of the author. The principles of these strategies are described. Empirical studies focused on various investment strategies, especially mentioned two strategies are quoted, too. Author points out in the Chapter „Methodology“ the way of how the used investment strategies are compared. Used stock market indexes and indicators necessary to identify the optimal strategy are described, too. Chapter „Results“ contains the graphical analysis of the trend of chosen stock market indexes. Tabular comparison of strategies according to indicators is also in this chapter. Author examines, what investment strategy is optimal. The paper added value is emphasized in the Chapter „Conclusions“. Author proposes, how the research in this current economic field can continue. Chapter „Conclusions“ summarizes interesting findings related to this paper.

II. LITERARY SURVEY

The comparison of investment strategies is one of interesting economic topics. Strategies can be compared according to several criteria. Investors can invest by various ways including lump sum investing and regular investing. Lump sum investing requires the investors to use the whole money to purchase assets up front. Low transaction costs are the advantage of lump sum investing. According to Wilson (2011), most of share fund managers require only entry fee calculated as the ratio from the deposit. The risk of wrong investment timing is one of the disadvantages of lump sum investing. Investors may inadvertently commit the most or all of their money at a market high.

Kohout (2010) characterizes regular investing as the passive investment strategy. Such passive investors are too conservative and they are too risk-averse. The advantage of regular investing for investors is that investors can buy stocks regardless of current increasing or decreasing market trend. Thus, the risk of wrong investment timing is reduced. Given low regular deposits is regular investing acceptable for most of the investors.

Investment strategy dollar cost averaging is characteristic for a fixed amount of money invested regularly and periodically regardless of stock price, the investment frequency and the time horizon over which investments are made.

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Investors do not invest entire sum at a market high and so regrets their investment decision ex post. This strategy leads to more stocks being purchased when their price is low and fewer when they are expensive. It lowers the total average cost of the investment, giving the investor a lower overall cost for the shares purchased over whole period. This strategy minimizes downside risk and it reduces the impact of volatility on large purchases of stocks. It increases returns while reducing the investor´s exposure to risk. It also behaves more like lump sum investing with a shorter time horizon.

Investors using the dollar cost averaging strategy can profit from the relationship between the value of a currency and a stock. It is rather conservative strategy best suited for investors who are interest in a forced savings plan that avoids the consumption of earnings. Malkiel (2012) mentions that the longer investment horizon is chosen by investor, the higher profit will the investor realize, because average price decreases in time. Simple principle is the advantage of this strategy. Investors need not monitor market trends. Disadvantage of this strategy relates to situation when investors start investing at the beginning of long-term decrease of stock prices.

Leggio and Lien (2003) measures the effectiveness of the dollar cost averaging. Analysing the values of the Standard & Poor´s 500 Composite from 1926 to 1999 they calculate indicators the Upside Potential ratio and the Sortino ratio. They also test this strategy for alternative asset investments. Their results show that the dollar cost averaging consistently remains an inferior investment strategy to lump sum investing when risk-adjusted performance measures are used.

Some researchers have empirically compared this strategy to alternative investment techniques. The dollar cost averaging and lump sum investing is compared by Stovall (2012). Specifically, he compares following stock market indexes: Standard & Poor´s 500 and Standard & Poor´s 500 Dividend Aristocrats over the period from 1999 to 2012. Further, he examines, whether high dividend yield can be the sole reason for the outperformance of dollar cost averaging versus lump sum investing. Using cumulative total returns from the whole period, it is clear that descending sort of all index sectors determines in 8 of 10 cases the line between lump sum investing and dollar cost averaging. Ulbricht (2013) compares returns and risk for dollar cost averaging with lump sum investing He calculates returns of Dow Jones Industrial Average 30 over the period from 1934 to 2013. His results show that lump sum returns for 40 year time horizons overstate regular contributor yields by 1.4 percentage points implying a 40 % higher terminal value. Increasing contributions deteriorate returns and risk. The dollar cost averaging is compared with lump sum investing by Rozeff (1994), too. Based on calculated returns of Standard & Poor´s 500 over the period from 1926 to 1990 his results show that lump sum investing provides a higher return using the Standard & Poor´s 500 in 40 of 65 years. He also states that if the market has an expected positive risk premium, then lump sum investing is mean-variance superior to dollar cost averaging. Similarly, Williams and Bacon (1993) compare the returns achieved by dollar cost averaging and by lump sum investing. They calculate returns of Standard & Poor´s 500 over the subperiods from 1926 to 1991, from 1950 to 1991 and from 1970 to 1991.

For all time subperiods, the lump sum investing produces superior returns to the dollar cost averaging, but at higher levels of the risk. Furthermore, the returns for dollar cost averaging increase as the number of dollar cost averaging installments is reduced.

Brennan, Li and Torous (2005) try to explore whether the dollar cost averaging is an investment heuristic that has survival value in an environment in which security prices exhibit mean reversion behavior or whether this strategy is another instance of irrational behavior by individual investors. Their results show that the uninformed individual investors who follow the dollar cost averaging in purchasing individual stocks to add to some existing portfolio are better off than if they followed such strategies, which are traditionally recommended by academics.

Edleson (2006) claims that the principle of the dollar value averaging is more difficult than the one of the dollar cost averaging. Investors using the dollar value averaging increase the cumulative value of their investment by a set amount every period. This strategy is suited rather for volatile investments. Initial sum, regular sum and investment goal are determined before the start of this strategy, as Marshall (2006) mentions. Portfolio balance increases by a set amount, regardless of stock prices. In periods of market climbs, investors contribute less, while in periods of market declines, investors contribute more. Investors may actually be required to withdraw from the portfolio in some periods. Chopade (2013) compares dollar cost averaging with dollar value averaging using data of 5 Indian equity mutual funds over the period from 2008 to 2013. The dollar value averaging provides an advantage over the traditionally followed dollar cost averaging. He also finds out that the average cost of acquisition of mutual fund units is lower in dollar value averaging when compare to dollar cost averaging.

Investors using the dollar value averaging strategy invest more when the stock prices fall and less when the stock prices rise. They carry out rather simple and mechanical type of market timing that helps them to minimize timing risk. According to Marshall (2000), investors should keep investment plan even when stock prices increase very fast. Markese, Bajkowski and Thorp (2011) consider dollar value averaging to be more risky than dollar cost averaging, because of two reasons. The first, regular sum is not limited by dollar value averaging. The second, dollar value averaging relates to active portfolio style. Hayley (2013) shows that the internal rate of return is a biased indicator of expected profits for dollar value averaging and for any other dynamic strategy which is based on a profit level or target return, or which takes profits or “doubles down” following losses.

The choice of investors what investment strategy to use, could depends on their attitude to a risk. According to the risk rate, which they could accept, investors could be considered to be aggressive or conservative. A number of researchers examine investment strategies mostly used by aggressive or conservative investors, too.

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III. METHODOLOGY

The aim of the paper is to assess the comparison of the lump sum investing with regular investing. Lump sum investing is compared with regular investment strategies dollar cost averaging and dollar value averaging. These three strategies are compared within five-year and ten-year investment horizon in the framework of the whole period 10 years, in detail from 1st January 2003 to 31st December 2012. Author applies them to stock market of the United States of America, the Japan and the United Kingdom. These stock markets are ones of the greatest stock markets in the world. Important indicators of these markets are also used, namely Standard & Poor´s 500, Nikkei 225 and FTSE 350. Author identifies such a strategy, which is optimal according to the yield-to-risk ratio calculated as the ratio of yield and the standard deviation of yield. Yields and risks of strategies are expressed in tables as percentages.

The parameters of the chosen investment strategies are described in detail, so the research could be replicated in similar or different context. Initial invested sums of money and the ways how to calculate the yield and risk are described.

Lump sum investing is determined by invested 100 000 USD in case of five-year investment and 200 000 USD in case of ten-year investment. The final sum equals to the product of initial invested sum and closing index value to the end of investing divided by closing index value to the beginning of investing.

Dollar cost averaging is determined by invested 5 000 USD each quarter in case of five-year investment and 2 500 USD each quarter in case of ten-year investment. The final sum equals to the product of total bought shares and closing index value to the end of investing. It is clear that stocks are bought or sold only within quarters. Corresponding prices are quarter closing prices of indexes.

Dollar value averaging is determined by invested 5 180.66 USD each quarter in case of five-year investment and 2 886.86 USD each quarter in case of ten-year investment. Certain share is bought at the first quarter. Shares according to current index values are bought and sold within each quarter in order to keep investment goal. The final sum equals to the product of total bought shares and closing index value to the end of investing. Investment goals are calculated with regard to annual interest rate 1.7 % p.a. in order to maintain similar real values as follows:

n

r PV

FV  1      

whereas FV is the future value (investment goal), PV is the initial value, r is the annual interest rate and n is the number of interest periods.

Thus, investment goal in case of five-year investment is 108 794 USD, while the ratio of this value and 21 is mentioned invested 5 180.66 USD. Analogically, investment goal in case of ten-year investment is 118 361 USD. The database of Yahoo Finance (2014) is used as the data source. The values of the stock market indexes Standard & Poor´s 500, Nikkei 225 and FTSE 350 are collected.

IV. RESULTS

A. The Trends of the Indexes

The trends of chosen stock market indexes are analysed. Fig. 1 points out the trends of indexes Standard & Poor´s 500, Nikkei 225 and FTSE 350 from 1st January 2003 to 31st December 2012.

Source: Own calculations using Yahoo Finance (2014) It is clear that indexes are sensitive to stock market fluctuations. Maximums of all three indexes are reached during autumn 2007, at the beginning of the financial crisis. The trend since autumn 2007 till spring 2009 is mostly increasing, however since spring 2009 rather stable or increasing. While the financial crisis started in the United States, rest two stock markets were affected by crisis in a short time, too. Growth of Nikkei 225 within the whole period is 24 % but growths of rest two indexes are 62 %.

B. The United States Stock Market

Table 1 reports indicators related to five-year and ten-year investment on the United States stock market.

TABLE I. INDICATORS RELATED TO FIVE-YEAR AND TEN-YEAR

INVESTMENT ON THE UNITED STATES STOCK MARKET Indicator Lump sum

investing

Dollar cost averaging

Dollar value averaging

Yield (5) 66.89 % 29.90 % 26.45 %

Yield (10) 62.10 % 24.28 % 35.81 %

Risk (5) 43.82 % 69.27 % 16.63 %

Risk (10) 80.12 % 35.60 % 12.20 %

Yield-to-risk ratio (5)

1.53 0.43 1.59

Yield-to-risk ratio (10)

0.78 0.68 2.93

Source: Own calculations using Yahoo Finance (2014) It is clear that yield-to-risk ratio of lump sum investing is for five-year and ten-year investment higher than dollar cost averaging but lower than dollar value averaging. This ratio of

Figure 1. The Trends of Chosen Indexes 0

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

2003 . 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Index value

Period

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lump sum investing is higher for five-year investment than ten-year investment. Higher yields of lump sum investing than other yields are mostly connected with higher risks. Thus, investors can realize high yield only at the cost of high risk.

C. The Japan Stock Market

Table 2 reports indicators related to five-year and ten-year investment on the Japan stock market.

TABLE II. INDICATORS RELATED TO FIVE-YEAR AND TEN-YEAR

INVESTMENT ON THE JAPAN STOCK MARKET Indicator Lump sum

investing

Dollar cost averaging

Dollar value averaging

Yield (5) 83.04 % 28.46 % 25.72 %

Yield (10) 24.30 % -3.66 % 3.83 %

Risk (5) 80.25 % 10.20 % 5.32 %

Risk (10) 104.49 % 5.00 % 5.02 %

Yield-to-risk ratio (5)

1.03 2.79 4.84

Yield-to-risk ratio (10)

0.23 -0.73 0.76

Source: Own calculations using Yahoo Finance (2014) It is clear that yield-to-risk ratio of lump sum investing is for five-year and ten-year investment lower than dollar value averaging. This ratio is always higher for five-year investment than ten-year investment.

D. The United Kigdom Stock Market

Table 3 reports indicators related to five-year and ten-year investment on the United Kingdom stock market.

TABLE III. INDICATORS RELATED TO FIVE-YEAR AND TEN-YEAR

INVESTMENT ON THE UNITED KINGDOM STOCK MARKET Indicator Lump sum

investing

Dollar cost averaging

Dollar value averaging

Yield (5) 73.15 % 36.95 % 33.89 %

Yield (10) 62.89 % 21.19 % 28.42 %

Risk (5) 37.92 % 39.73 % 3.10 %

Risk (10) 73.19 % 16.86 % 2.84 %

Yield-to-risk ratio (5)

1.93 0.93 10.93

Yield-to-risk ratio (10)

0.86 1.26 10.00

Source: Own calculations using Yahoo Finance (2014) It is clear that yield-to-risk ratio of lump sum investing is for five-year and ten-year investment lower than dollar value averaging. This ratio of lump sum investing and dollar value averaging is higher for five-year investment than ten-year investment.

Found data related to the United States stock market, the Japan stock market and the United Kingdom stock market can be summarized. Important findings can be deducted from the data of Yahoo Finance (2014). The yield-to-risk ratio of dollar value averaging is the highest of ratios for five-year and ten-year investment. Thus, this investment strategy can be

considered to be optimal according to the yield-to-risk ratio. The strategy leads to the most intensive elimination of risk of wrong investment timing. Yield-to-risk ratio of lump sum investing is always higher for five-year investment than ten-year investment.

Furthermore, lump sum investing mostly leads to higher yield but also higher risk. This investment strategy is suitable rather for investors that accept risk, thus aggressive investors. The shorter is the investment horizon, the higher is mostly yield. The highest yield-to-risk ratio is on the United Kingdom stock market, then the Japan stock market and finally the United States stock market.

V. DISCUSSION

The results can be compared with the results presented by other authors. Author finds out that dollar value averaging is optimal according to the yield-to-risk ratio. This fact is in accordance with results presented by Varga (2011). He compares lump sum investing with dollar cost averaging and dollar value averaging. Based on calculated internal rate of returns of Standard & Poor´s 500 over the period from 1927 to 2011, he concludes that dollar value averaging is the most favourable strategy. Yields of dollar cost averaging are mostly positive in this paper, which is in accordance with results of Edleson (2006).

Sharma (2011) compares dollar cost averaging with dollar value averaging and volatility pumping. He uses Monte Carlo simulation and widely available asset classes to study the behavior of these strategies under different scenarios. For large cap and small stock portfolios it is clear that constant proportion investing dominates dollar cost and dollar value averaging. By simulating extreme scenarios dollar value averaging dominates both constant proportion investing and dollar cost averaging due to the condition that positive cashflows above the value path are invested in a risk free asset. Furthermore, all three investment strategies perform better than the individual assets themselves. In general, an effort of many researchers to examine the investment strategies is clear.

Found results can be discussed in other ways, too. Based on the fact that lump sum investing mostly leads to higher yield but also higher risk, individual investment recommendations could be created for individual types of investors. For example, conservative investors prefer low risk level. The differences between results in individual stock markets could be added by total market capitalizations of these markets.

As for the limitations of the analysis, presented results are determined by used stock markets, stock market indexes and time period. The choice of other markets, indexes and periods could bring a little different results because some great unexpected events can affect the investor behaviour.

The search could be replicated in the future in order to assess various investment strategies under changed conditions. Research in this topical economic field can continue in several directions. Other investment strategies could be chosen. These strategies could be applied within other time periods to other stock markets. Other stock market indexes, invested money, investing periods and indicators could be chosen. Thus, various preferences of investors could be taken into consideration.

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VI. CONCLUSIONS

In the past few decades, the comparison of investment strategies has become the subject of interest of many researchers. Numerous studies investigating what investment strategy is optimal have been published. Author assesses the comparison of the lump sum investing with regular investing. Publications focused on these forms of investing are cited in the paper. Three investment strategies are compared within five-year and ten-year investment horizon in the framework of the period from 1st January 2003 to 31st December 2012. Indexes Standard & Poor´s 500, Nikkei 225 and FTSE 350 are chosen as indicators of stock market of the United States, the Japan and the United Kingdom. Strategies are compared according to yields, risks and yield-to-risk ratios.

Presented results show that dollar value averaging is optimal strategy according to the yield-to-risk ratio. Investors preferring this strategy should not panic when stock prices substantially decrease, because low stock prices lead to buying of higher pieces of stocks which can be sold in the future at higher prices. Investors and financial analysts can use results of this paper when they create their investment strategies.

The paper added value is clear from following facts. Author finds out what yields, risks and yield-to-risk ratios relate to lump sum investing, dollar cost averaging and dollar value averaging. Based on these facts, investors can assemble their investment portfolios and create investment strategies. Many recent publications including this paper are focused on lump sum investing and regular investing, which means that this economic field is currently analysed. Investing by such a strategy, which can eliminate the risk of wrong investment timing could be very interesting for investors. Right investment timing leads to higher yields for investors.

ACKNOWLEDGMENT

The paper was compiled in terms of Thematic direction 02 solution of Research plan FBE MENDELU in Brno MSM No. 6215648904/02 named „Main tendencies in the development of a competitive environment within the integration and globalisation processes, and the adaptation of business entities to the new conditions of the integrated market“ realized by means of financial support of state resources through Ministry of Education, Youth and Sports.

REFERENCES

[1] M. J. Brennan, F. Li and W.N. Torous, “Dollar Cost Averaging“, Review of Finance, vol. 9, no. 4, pp. 509-535, Winter 2005.

[2] C. Chopade, “An Empirical Study of Value Averaging Vs. Cost Averaging Using Diversified Equity Funds in India“, Indian Journal of Research, vol. 2, no. 9, pp. 151-152, September 2013.

[3] M. E. Edleson, Value Averaging. The Safe and Easy Strategy for Higher Investment Returns. New York: Wiley, 2006, pp. 25-55

[4] D. Gladiš, Naučte se investovat. Praha: Grada, 2005, pp. 11-34. [5] S. Hayley. (2013). Value Averaging and How Dynamic Strategies Bias

the IRR and Modified IRR. [Online]. Available: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1606347.

[6] P. Kohout, Investiční strategie pro třetí tisíciletí. Praha: Grada, 2010, pp. 191-205.

[7] K. B. Leggio, D. Lien, “An Empirical Examination of the Effectiveness of Dollar-cost averaging Using Downside Risk Performance Measures“, Journal of Economics and Finance, vol. 27, no. 2, pp. 211-223, Summer 2003.

[8] B. G. Malkiel, Náhodná procházka po Wall Street: Časem prověřená strategie úspěšného investování. Praha: Pragma, 2012, pp. 20-33. [9] J. Markese, J. Bajkowski, W. Thorp. (2011). Value Averaging

Spreadsheet. Computerized Investing. Available at: http://www.aaii.com/computerized-investing/article/value-averaging-spreadsheet?forceFull.

[10] P. S. Marshall, “A multi-market, historical comparison of the in-vestment returns of value averaging, dollar cost averaging and random investment techniques“, Academy of Accounting and Financial Studies Journal, vol. 16, no. 1, pp. 1-16, September 2006.

[11] P. S. Marshall, “A statistical comparison of value averaging vs. Dollar cost averaging and random investment techniques“, Journal of Financial and Strategic Decisions, vol. 13, no. 1, pp. 87-99, Spring 2000. [12] F. Mašek. (2010). Jak dobře koupit a prodat akcie. Available at:

http://www.penize.cz/akcie/90889-jak-dobre-koupit-a-prodat-akcie. [13] M. S. Rozeff, “Lump-Sum Investing versus Dollar-Averaging“, The

Journal of Portfolio Management, vol. 20, no. 2, pp. 45-50, Winter 1994. [14] D. Sharma. (2011). Systems Approach to Investment Management: Does Constant Proportion Investment Beat Volatility Pumping? [Online]. Available: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1839984. [15] S. Stovall, “Should You Dollar Cost Average or Lump-Sum Invest?“, American Association of Individual Investors Journal, vol. 17, no. 4, pp. 1-6, April 2012

[16] D. Ulbricht, “Stock Investments for Old-Age: Less Return, More Risk, and Unexpected Timing“, Deutsches Institut für Wirtschaftsforschung Discussion Paper no. 1324, pp. 1-16, 2013.

[17] M. Varga, “Jednorázová investice se také vyplatí“, Fond Shop, vol. 13, no. 6, pp. 20-21, March 2011.

[18] R. E. Williams, P.W. Bacon, “Dollar Cost Averaging vs. Lump-Sum Investing“, The American Association of Individual Investors, vol. 15, no. 5, pp. 1-3, June 1993.

[19] J. Wilson. (2011). Advantage of Lump Sum Investing. [Online]. Available: http://personalwm.com/2011/03/03/advantages-of-lump-sum-investing/.

[20] Yahoo Finance. (2014). Yahoo Finance. Available at: http://finance.yahoo.com/.

Figure

Fig. 1 points out the trends of indexes Standard & Poor´s 500,  Nikkei  225  and  FTSE  350  from  1st  January  2003  to  31st  December 2012
TABLE II.   I NDICATORS  R ELATED TO  F IVE - YEAR AND  T EN - YEAR

References

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