Within-Horizon Exposure to Loss for Dollar Cost Averaging and Lump Sum Investing

Abstract

Abstract Based on a statistic known as first-passage time that accounts for exposure to loss during the entire investment horizon, it is shown that dollar cost averaging relative to lump sum investing can significantly reduce the magnitude, and duration of enduring a large loss. This is especially relevant to investors with minimum loss thresholds, possible interim withdrawal needs, changing asset allocations, and/or an uncertain retirement date. For investing in stocks with a 5-year horizon, the probability of enduring a loss can be reduced from over 90% to less than 50%, the dollar amount of the conditional expected shortfall can be reduced by 65%, and the expected time one may have to endure a loss is reduced from 1.5 years to 4 months. © 2005 Academy of Financial Services. All rights reserved. JEL classifications: C15; G11 Keywords: Dollar cost averaging; Within-horizon risk; Continuous risk 1. Introduction It is not often investors are saddled with the enviable problem of investing large lump sums (LS), but with an aging population that has more wealth than ever before, large inheritances will become increasingly more common for the next generation of investors. Many of these heirs will decide to invest these sums for their own future retirement plans and deciding whether to invest it all at once or employ dollar cost averaging (DCA) will be a major conundrum. The major advantage of DCA over LS investing touted by many financial planners is that it allows investors to gradually invest in the stock market or some other risky asset while reducing the risk of buying completely in at a market high. One need only do a quick search on Google to find a variety of sites expounding this advantage, including such notables as Wells Fargo, Met Life, and CNN Money. Even Burton Malkiel's classic text A Random Walk Down Wall Street discusses this advantage (Malkiel, 2003). However, most studies suggest implementing DCA reduces returns without a large enough reduction in risk to justify it relative to lump sum (LS) investing. Constantinides (1979) first demonstrated the inferiority of DCA relative to LS investing when the decision is based solely on expected return. On a risk-return basis, the answer is not as obvious, but a substantial amount of empirical research agrees that DCA is suboptimal relative to LS investing, (Knight & Mandell, 1993; Williams & Bacon, 1993; Rozeff, 1994; Leggio & lien, 2003). In DC A's defense, some empirical studies have suggested that DCA has merit in some narrowly defined circumstances, (Israelsen, 1999; Abeysekera & Rosenbloom, 2000; Milevsky & Posner, 2003). More recently, using an option theory framework, Dubil (2004) finds DCA can reduce the expected dollar amount of shortfall upon liquidation of the investment, although the probability of shortfall is found to be approximately the same for both strategies, and the difference in shortfall amounts tends to disappear as the investment horizon is extended. Thus, even the support for DCA had not been overwhelming. However, previous studies have never directly addressed the risk of loss during the investment horizon that DCA is tailored made to mitigate. This study remedies this oversight and addresses the question as to whether DCA can reduce the probability of loss throughout the investment horizon substantially enough to justify its use. Using a statistic known as first-passage time probability, the results of this study show that DCA can significantly reduce the magnitude, and duration of enduring a large loss anytime within the investment horizon. Inputting returns and standard deviations based loosely on the U.S. stock market, it is found that, for a 10-year time horizon, a 5-year DCA averaging strategy can reduce the probability of ever experiencing a loss from over 90% to less than 60%, reduce the conditional mean expected shortfall by 45%, and reduce the expected time one has to weather a loss during the investment horizon from over 22% to less than 10%. …