Lump Sum Investing and Regular Investing

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1 December, Lump Sum Invesing and Regular Invesing Radim Gowald Mendel Universiy in Brno Deparmen of Finance Brno, Czech Republic Absrac The paper is focused on curren opic lump sum invesing and regular invesing. Auhor compares lump sum invesing wih regular invesmen sraegies dollar cos averaging and dollar value averaging. These sraegies are compared wihin fiveyear and enyear invesmen horizon in he framework of he whole period 10 years, in deail from 1s January 2003 o 31s December 2012 and applied o sock marke of he Unied Saes of America, he Japan and he Unied Kingdom. Auhor uses corresponding indexes Sandard & Poor s 500, Nikkei 225 and FTSE 350 and he finds ou which sraegy is opimal according o he yieldorisk raio. The rend of used sock marke indexes is graphically analysed. Resuls show ineresing findings. Maximums of all hree used indexes are reached during auumn 2007, jus a he beginning of he financial crisis. The yieldorisk raio of dollar value averaging is found o be he highes of raios for fiveyear and enyear invesmen. So, he dollar value averaging is found o be an opimal sraegy. Auhor also compares found resuls wih resuls of oher auhors. This paper could inspire invesors o assemble heir invesmen porfolios and creae invesmen sraegies. Thus, he conribuion of he paper can be deduced. Keywordslump sum invesing, regular invesing, invesing, dollar cos averaging, dollar value averaging, yieldorisk raio I. INTRODUCTION Many invesors inves in sock markes in an effor o achieve opimal invesmen. They should find ou imporan characerisics of inernaional markes before each invesmen. In connecion wih sock rading in sock markes, invesors use various invesmen sraegies. Principles of differen sraegies are also differen, so invesors can realize differen profis using differen sraegies. In general, he marke iming is very imporan for invesors. They wan o find ou he righ ime o maximize he profi. Gladiš (2005) describes ha invesors monior he whole marke and ry o esimae wha will be he fuure marke rend. Finding he righ ime when o buy or sell socks is raher difficul. Mašek (2010) poins ou ha reail invesors someimes unforunaely miss he ideal ime when o buy socks in order o ime he invesmen on he marke. Marke bubble could be used wihin marke iming, i could be considered as he signal o sell. Invesors could idenify he marke bubble when sock price increases oo fas and oo long wihou any economic reason. The end of he marke bubble leads o decrease of many sock prices. The aim of he paper, deailly described in he Chaper Mehodology, relaes o lump sum invesing, dollar cos averaging and dollar value averaging. The conen of his paper is especially he comparison of hese sraegies wihin chosen horizons over he chosen period. This paper follows in a number of empirical sudies focused on he invesmen sraegies. Some of hese sudies are quoed in his paper. The res of his paper is organized as follows. Chaper Lierary Survey is focused on invesmen sraegies in deail. Especially, he dollar cos averaging and he dollar value averaging are a he cenre of aenion of he auhor. The principles of hese sraegies are described. Empirical sudies focused on various invesmen sraegies, especially menioned wo sraegies are quoed, oo. Auhor poins ou in he Chaper Mehodology he way of how he used invesmen sraegies are compared. Used sock marke indexes and indicaors necessary o idenify he opimal sraegy are described, oo. Chaper Resuls conains he graphical analysis of he rend of chosen sock marke indexes. Tabular comparison of sraegies according o indicaors is also in his chaper. Auhor examines, wha invesmen sraegy is opimal. The paper added value is emphasized in he Chaper Conclusions. Auhor proposes, how he research in his curren economic field can coninue. Chaper Conclusions summarizes ineresing findings relaed o his paper. II. LITERARY SURVEY The comparison of invesmen sraegies is one of ineresing economic opics. Sraegies can be compared according o several crieria. Invesors can inves by various ways including lump sum invesing and regular invesing. Lump sum invesing requires he invesors o use he whole money o purchase asses up fron. Low ransacion coss are he advanage of lump sum invesing. According o Wilson (2011), mos of share fund managers require only enry fee calculaed as he raio from he deposi. The risk of wrong invesmen iming is one of he disadvanages of lump sum invesing. Invesors may inadverenly commi he mos or all of heir money a a marke high. Kohou (2010) characerizes regular invesing as he passive invesmen sraegy. Such passive invesors are oo conservaive and hey are oo riskaverse. The advanage of regular invesing for invesors is ha invesors can buy socks regardless of curren increasing or decreasing marke rend. Thus, he risk of wrong invesmen iming is reduced. Given low regular deposis is regular invesing accepable for mos of he invesors. Invesmen sraegy dollar cos averaging is characerisic for a fixed amoun of money invesed regularly and periodically regardless of sock price, he invesmen frequency and he ime horizon over which invesmens are made. The 3rd year of hp:// 144

2 December, Invesors do no inves enire sum a a marke high and so regres heir invesmen decision ex pos. This sraegy leads o more socks being purchased when heir price is low and fewer when hey are expensive. I lowers he oal average cos of he invesmen, giving he invesor a lower overall cos for he shares purchased over whole period. This sraegy minimizes downside risk and i reduces he impac of volailiy on large purchases of socks. I increases reurns while reducing he invesor s exposure o risk. I also behaves more like lump sum invesing wih a shorer ime horizon. Invesors using he dollar cos averaging sraegy can profi from he relaionship beween he value of a currency and a sock. I is raher conservaive sraegy bes suied for invesors who are ineres in a forced savings plan ha avoids he consumpion of earnings. Malkiel (2012) menions ha he longer invesmen horizon is chosen by invesor, he higher profi will he invesor realize, because average price decreases in ime. Simple principle is he advanage of his sraegy. Invesors need no monior marke rends. Disadvanage of his sraegy relaes o siuaion when invesors sar invesing a he beginning of longerm decrease of sock prices. Leggio and Lien (2003) measures he effeciveness of he dollar cos averaging. Analysing he values of he Sandard & Poor s 500 Composie from 1926 o 1999 hey calculae indicaors he Upside Poenial raio and he Sorino raio. They also es his sraegy for alernaive asse invesmens. Their resuls show ha he dollar cos averaging consisenly remains an inferior invesmen sraegy o lump sum invesing when riskadjused performance measures are used. Some researchers have empirically compared his sraegy o alernaive invesmen echniques. The dollar cos averaging and lump sum invesing is compared by Sovall (2012). Specifically, he compares following sock marke indexes: Sandard & Poor s 500 and Sandard & Poor s 500 Dividend Arisocras over he period from 1999 o Furher, he examines, wheher high dividend yield can be he sole reason for he ouperformance of dollar cos averaging versus lump sum invesing. Using cumulaive oal reurns from he whole period, i is clear ha descending sor of all index secors deermines in 8 of 10 cases he line beween lump sum invesing and dollar cos averaging. Ulbrich (2013) compares reurns and risk for dollar cos averaging wih lump sum invesing He calculaes reurns of Dow Jones Indusrial Average 30 over he period from 1934 o His resuls show ha lump sum reurns for 40 year ime horizons oversae regular conribuor yields by 1.4 percenage poins implying a 40 % higher erminal value. Increasing conribuions deeriorae reurns and risk. The dollar cos averaging is compared wih lump sum invesing by Rozeff (1994), oo. Based on calculaed reurns of Sandard & Poor s 500 over he period from 1926 o 1990 his resuls show ha lump sum invesing provides a higher reurn using he Sandard & Poor s 500 in 40 of 65 years. He also saes ha if he marke has an expeced posiive risk premium, hen lump sum invesing is meanvariance superior o dollar cos averaging. Similarly, Williams and Bacon (1993) compare he reurns achieved by dollar cos averaging and by lump sum invesing. They calculae reurns of Sandard & Poor s 500 over he subperiods from 1926 o 1991, from 1950 o 1991 and from 1970 o For all ime subperiods, he lump sum invesing produces superior reurns o he dollar cos averaging, bu a higher levels of he risk. Furhermore, he reurns for dollar cos averaging increase as he number of dollar cos averaging insallmens is reduced. Brennan, Li and Torous (2005) ry o explore wheher he dollar cos averaging is an invesmen heurisic ha has survival value in an environmen in which securiy prices exhibi mean reversion behavior or wheher his sraegy is anoher insance of irraional behavior by individual invesors. Their resuls show ha he uninformed individual invesors who follow he dollar cos averaging in purchasing individual socks o add o some exising porfolio are beer off han if hey followed such sraegies, which are radiionally recommended by academics. Edleson (2006) claims ha he principle of he dollar value averaging is more difficul han he one of he dollar cos averaging. Invesors using he dollar value averaging increase he cumulaive value of heir invesmen by a se amoun every period. This sraegy is suied raher for volaile invesmens. Iniial sum, regular sum and invesmen goal are deermined before he sar of his sraegy, as Marshall (2006) menions. Porfolio balance increases by a se amoun, regardless of sock prices. In periods of marke climbs, invesors conribue less, while in periods of marke declines, invesors conribue more. Invesors may acually be required o wihdraw from he porfolio in some periods. Chopade (2013) compares dollar cos averaging wih dollar value averaging using daa of 5 Indian equiy muual funds over he period from 2008 o The dollar value averaging provides an advanage over he radiionally followed dollar cos averaging. He also finds ou ha he average cos of acquisiion of muual fund unis is lower in dollar value averaging when compare o dollar cos averaging. Invesors using he dollar value averaging sraegy inves more when he sock prices fall and less when he sock prices rise. They carry ou raher simple and mechanical ype of marke iming ha helps hem o minimize iming risk. According o Marshall (2000), invesors should keep invesmen plan even when sock prices increase very fas. Markese, Bajkowski and Thorp (2011) consider dollar value averaging o be more risky han dollar cos averaging, because of wo reasons. The firs, regular sum is no limied by dollar value averaging. The second, dollar value averaging relaes o acive porfolio syle. Hayley (2013) shows ha he inernal rae of reurn is a biased indicaor of expeced profis for dollar value averaging and for any oher dynamic sraegy which is based on a profi level or arge reurn, or which akes profis or doubles down following losses. The choice of invesors wha invesmen sraegy o use, could depends on heir aiude o a risk. According o he risk rae, which hey could accep, invesors could be considered o be aggressive or conservaive. A number of researchers examine invesmen sraegies mosly used by aggressive or conservaive invesors, oo. The 3rd year of hp:// 145

3 December, III. METHODOLOGY The aim of he paper is o assess he comparison of he lump sum invesing wih regular invesing. Lump sum invesing is compared wih regular invesmen sraegies dollar cos averaging and dollar value averaging. These hree sraegies are compared wihin fiveyear and enyear invesmen horizon in he framework of he whole period 10 years, in deail from 1s January 2003 o 31s December Auhor applies hem o sock marke of he Unied Saes of America, he Japan and he Unied Kingdom. These sock markes are ones of he greaes sock markes in he world. Imporan indicaors of hese markes are also used, namely Sandard & Poor s 500, Nikkei 225 and FTSE 350. Auhor idenifies such a sraegy, which is opimal according o he yieldorisk raio calculaed as he raio of yield and he sandard deviaion of yield. Yields and risks of sraegies are expressed in ables as percenages. The parameers of he chosen invesmen sraegies are described in deail, so he research could be replicaed in similar or differen conex. Iniial invesed sums of money and he ways how o calculae he yield and risk are described. Lump sum invesing is deermined by invesed USD in case of fiveyear invesmen and USD in case of enyear invesmen. The final sum equals o he produc of iniial invesed sum and closing index value o he end of invesing divided by closing index value o he beginning of invesing. Dollar cos averaging is deermined by invesed USD each quarer in case of fiveyear invesmen and USD each quarer in case of enyear invesmen. The final sum equals o he produc of oal bough shares and closing index value o he end of invesing. I is clear ha socks are bough or sold only wihin quarers. Corresponding prices are quarer closing prices of indexes. Dollar value averaging is deermined by invesed USD each quarer in case of fiveyear invesmen and USD each quarer in case of enyear invesmen. Cerain share is bough a he firs quarer. Shares according o curren index values are bough and sold wihin each quarer in order o keep invesmen goal. The final sum equals o he produc of oal bough shares and closing index value o he end of invesing. Invesmen goals are calculaed wih regard o annual ineres rae 1.7 % p.a. in order o mainain similar real values as follows: n FV PV 1 r whereas FV is he fuure value (invesmen goal), PV is he iniial value, r is he annual ineres rae and n is he number of ineres periods. Thus, invesmen goal in case of fiveyear invesmen is USD, while he raio of his value and 21 is menioned invesed USD. Analogically, invesmen goal in case of enyear invesmen is USD. The daabase of Yahoo Finance (2014) is used as he daa source. The values of he sock marke indexes Sandard & Poor s 500, Nikkei 225 and FTSE 350 are colleced. IV. RESULTS A. The Trends of he Indexes The rends of chosen sock marke indexes are analysed. Fig. 1 poins ou he rends of indexes Sandard & Poor s 500, Nikkei 225 and FTSE 350 from 1s January 2003 o 31s December Index value Source: Own calculaions using Yahoo Finance (2014) I is clear ha indexes are sensiive o sock marke flucuaions. Maximums of all hree indexes are reached during auumn 2007, a he beginning of he financial crisis. The rend since auumn 2007 ill spring 2009 is mosly increasing, however since spring 2009 raher sable or increasing. While he financial crisis sared in he Unied Saes, res wo sock markes were affeced by crisis in a shor ime, oo. Growh of Nikkei 225 wihin he whole period is 24 % bu growhs of res wo indexes are 62 %. B. The Unied Saes Sock Marke Table 1 repors indicaors relaed o fiveyear and enyear invesmen on he Unied Saes sock marke. TABLE I. INDICATORS RELATED TO FIVEYEAR AND TENYEAR INVESTMENT ON THE UNITED STATES STOCK MARKET Indicaor Lump sum invesing Dollar cos averaging Dollar value averaging Yield (5) % % % Yieldorisk raio (5) Yieldorisk raio (10) S&P 500 Nikkei 225 FTSE 350 Figure 1. The Trends of Chosen Indexes % % % % % % % % % Source: Own calculaions using Yahoo Finance (2014) Period I is clear ha yieldorisk raio of lump sum invesing is for fiveyear and enyear invesmen higher han dollar cos averaging bu lower han dollar value averaging. This raio of The 3rd year of hp:// 146

4 December, lump sum invesing is higher for fiveyear invesmen han enyear invesmen. Higher yields of lump sum invesing han oher yields are mosly conneced wih higher risks. Thus, invesors can realize high yield only a he cos of high risk. C. The Japan Sock Marke Table 2 repors indicaors relaed o fiveyear and enyear invesmen on he Japan sock marke. TABLE II. Indicaor Yield (5) Yieldorisk raio (5) Yieldorisk raio (10) INDICATORS RELATED TO FIVEYEAR AND TENYEAR INVESTMENT ON THE JAPAN STOCK MARKET Lump sum Dollar cos Dollar value invesing averaging averaging % % % % 3.66 % 3.83 % % % 5.32 % % 5.00 % 5.02 % Source: Own calculaions using Yahoo Finance (2014) I is clear ha yieldorisk raio of lump sum invesing is for fiveyear and enyear invesmen lower han dollar value averaging. This raio is always higher for fiveyear invesmen han enyear invesmen. D. The Unied Kigdom Sock Marke Table 3 repors indicaors relaed o fiveyear and enyear invesmen on he Unied Kingdom sock marke. TABLE III. INDICATORS RELATED TO FIVEYEAR AND TENYEAR INVESTMENT ON THE UNITED KINGDOM STOCK MARKET Indicaor Yield (5) Yieldorisk raio (5) Yieldorisk raio (10) Lump sum Dollar cos Dollar value invesing averaging averaging % % % % % % % % 3.10 % % % 2.84 % Source: Own calculaions using Yahoo Finance (2014) I is clear ha yieldorisk raio of lump sum invesing is for fiveyear and enyear invesmen lower han dollar value averaging. This raio of lump sum invesing and dollar value averaging is higher for fiveyear invesmen han enyear invesmen. Found daa relaed o he Unied Saes sock marke, he Japan sock marke and he Unied Kingdom sock marke can be summarized. Imporan findings can be deduced from he daa of Yahoo Finance (2014). The yieldorisk raio of dollar value averaging is he highes of raios for fiveyear and enyear invesmen. Thus, his invesmen sraegy can be considered o be opimal according o he yieldorisk raio. The sraegy leads o he mos inensive eliminaion of risk of wrong invesmen iming. Yieldorisk raio of lump sum invesing is always higher for fiveyear invesmen han enyear invesmen. Furhermore, lump sum invesing mosly leads o higher yield bu also higher risk. This invesmen sraegy is suiable raher for invesors ha accep risk, hus aggressive invesors. The shorer is he invesmen horizon, he higher is mosly yield. The highes yieldorisk raio is on he Unied Kingdom sock marke, hen he Japan sock marke and finally he Unied Saes sock marke. V. DISCUSSION The resuls can be compared wih he resuls presened by oher auhors. Auhor finds ou ha dollar value averaging is opimal according o he yieldorisk raio. This fac is in accordance wih resuls presened by Varga (2011). He compares lump sum invesing wih dollar cos averaging and dollar value averaging. Based on calculaed inernal rae of reurns of Sandard & Poor s 500 over he period from 1927 o 2011, he concludes ha dollar value averaging is he mos favourable sraegy. Yields of dollar cos averaging are mosly posiive in his paper, which is in accordance wih resuls of Edleson (2006). Sharma (2011) compares dollar cos averaging wih dollar value averaging and volailiy pumping. He uses Mone Carlo simulaion and widely available asse classes o sudy he behavior of hese sraegies under differen scenarios. For large cap and small sock porfolios i is clear ha consan proporion invesing dominaes dollar cos and dollar value averaging. By simulaing exreme scenarios dollar value averaging dominaes boh consan proporion invesing and dollar cos averaging due o he condiion ha posiive cashflows above he value pah are invesed in a risk free asse. Furhermore, all hree invesmen sraegies perform beer han he individual asses hemselves. In general, an effor of many researchers o examine he invesmen sraegies is clear. Found resuls can be discussed in oher ways, oo. Based on he fac ha lump sum invesing mosly leads o higher yield bu also higher risk, individual invesmen recommendaions could be creaed for individual ypes of invesors. For example, conservaive invesors prefer low risk level. The differences beween resuls in individual sock markes could be added by oal marke capializaions of hese markes. As for he limiaions of he analysis, presened resuls are deermined by used sock markes, sock marke indexes and ime period. The choice of oher markes, indexes and periods could bring a lile differen resuls because some grea unexpeced evens can affec he invesor behaviour. The search could be replicaed in he fuure in order o assess various invesmen sraegies under changed condiions. Research in his opical economic field can coninue in several direcions. Oher invesmen sraegies could be chosen. These sraegies could be applied wihin oher ime periods o oher sock markes. Oher sock marke indexes, invesed money, invesing periods and indicaors could be chosen. Thus, various preferences of invesors could be aken ino consideraion. The 3rd year of hp:// 147

5 December, VI. CONCLUSIONS In he pas few decades, he comparison of invesmen sraegies has become he subjec of ineres of many researchers. Numerous sudies invesigaing wha invesmen sraegy is opimal have been published. Auhor assesses he comparison of he lump sum invesing wih regular invesing. Publicaions focused on hese forms of invesing are cied in he paper. Three invesmen sraegies are compared wihin fiveyear and enyear invesmen horizon in he framework of he period from 1s January 2003 o 31s December Indexes Sandard & Poor s 500, Nikkei 225 and FTSE 350 are chosen as indicaors of sock marke of he Unied Saes, he Japan and he Unied Kingdom. Sraegies are compared according o yields, risks and yieldorisk raios. Presened resuls show ha dollar value averaging is opimal sraegy according o he yieldorisk raio. Invesors preferring his sraegy should no panic when sock prices subsanially decrease, because low sock prices lead o buying of higher pieces of socks which can be sold in he fuure a higher prices. Invesors and financial analyss can use resuls of his paper when hey creae heir invesmen sraegies. The paper added value is clear from following facs. Auhor finds ou wha yields, risks and yieldorisk raios relae o lump sum invesing, dollar cos averaging and dollar value averaging. Based on hese facs, invesors can assemble heir invesmen porfolios and creae invesmen sraegies. Many recen publicaions including his paper are focused on lump sum invesing and regular invesing, which means ha his economic field is currenly analysed. Invesing by such a sraegy, which can eliminae he risk of wrong invesmen iming could be very ineresing for invesors. Righ invesmen iming leads o higher yields for invesors. ACKNOWLEDGMENT The paper was compiled in erms of Themaic direcion 02 soluion of Research plan FBE MENDELU in Brno MSM No /02 named Main endencies in he developmen of a compeiive environmen wihin he inegraion and globalisaion processes, and he adapaion of business eniies o he new condiions of he inegraed marke realized by means of financial suppor of sae resources hrough Minisry of Educaion, Youh and Spors. REFERENCES [1] M. J. Brennan, F. Li and W.N. Torous, Dollar Cos Averaging, Review of Finance, vol. 9, no. 4, pp , Winer [2] C. Chopade, An Empirical Sudy of Value Averaging Vs. Cos Averaging Using Diversified Equiy Funds in India, Indian Journal of Research, vol. 2, no. 9, pp , Sepember [3] M. E. Edleson, Value Averaging. The Safe and Easy Sraegy for Higher Invesmen Reurns. New York: Wiley, 2006, pp [4] D. Gladiš, Nauče se invesova. Praha: Grada, 2005, pp [5] S. Hayley. (2013). Value Averaging and How Dynamic Sraegies Bias he IRR and Modified IRR. [Online]. Available: hp://papers.ssrn.com/sol3/papers.cfm?absrac_id= [6] P. Kohou, Invesiční sraegie pro řeí isícileí. Praha: Grada, 2010, pp [7] K. B. Leggio, D. Lien, An Empirical Examinaion of he Effeciveness of Dollarcos averaging Using Downside Risk Performance Measures, Journal of Economics and Finance, vol. 27, no. 2, pp , Summer [8] B. G. Malkiel, Náhodná procházka po Wall Sree: Časem prověřená sraegie úspěšného invesování. Praha: Pragma, 2012, pp [9] J. Markese, J. Bajkowski, W. Thorp. (2011). Value Averaging Spreadshee. Compuerized Invesing. Available a: hp:// [10] P. S. Marshall, A mulimarke, hisorical comparison of he invesmen reurns of value averaging, dollar cos averaging and random invesmen echniques, Academy of Accouning and Financial Sudies Journal, vol. 16, no. 1, pp. 116, Sepember [11] P. S. Marshall, A saisical comparison of value averaging vs. Dollar cos averaging and random invesmen echniques, Journal of Financial and Sraegic Decisions, vol. 13, no. 1, pp. 8799, Spring [12] F. Mašek. (2010). Jak dobře koupi a proda akcie. Available a: hp:// [13] M. S. Rozeff, LumpSum Invesing versus DollarAveraging, The Journal of Porfolio Managemen, vol. 20, no. 2, pp. 4550, Winer [14] D. Sharma. (2011). Sysems Approach o Invesmen Managemen: Does Consan Proporion Invesmen Bea Volailiy Pumping? [Online]. Available: hp://papers.ssrn.com/sol3/papers.cfm?absrac_id= [15] S. Sovall, Should You Dollar Cos Average or LumpSum Inves?, American Associaion of Individual Invesors Journal, vol. 17, no. 4, pp. 16, April 2012 [16] D. Ulbrich, Sock Invesmens for OldAge: Less Reurn, More Risk, and Unexpeced Timing, Deusches Insiu für Wirschafsforschung Discussion Paper no. 1324, pp. 116, [17] M. Varga, Jednorázová invesice se aké vyplaí, Fond Shop, vol. 13, no. 6, pp. 2021, March [18] R. E. Williams, P.W. Bacon, Dollar Cos Averaging vs. LumpSum Invesing, The American Associaion of Individual Invesors, vol. 15, no. 5, pp. 13, June [19] J. Wilson. (2011). Advanage of Lump Sum Invesing. [Online]. Available: hp://personalwm.com/2011/03/03/advanagesoflumpsuminvesing/. [20] Yahoo Finance. (2014). Yahoo Finance. Available a: hp://finance.yahoo.com/. The 3rd year of hp:// 148