Why Dollar Cost Averaging Cannot Be Compared as One Fixed Strategy
Summary
The discussion asks whether random-walk assumptions imply that dollar cost averaging must always underperform a lump-sum investment. The responses distinguish the broad idea of investing gradually from any particular schedule or stock-selection rule. A comparison between one timed contribution plan and immediate investment cannot establish a universal result for every strategy that might be called dollar cost averaging.
One response argues that strategy details matter: staged purchases could be tied to valuation or price declines, while other implementations may perform poorly. A second response adds a decision-theoretic qualification: in the class of models discussed by Constantinides, dollar cost averaging can be suboptimal for a utility-maximizing investor because an alternative strategy is preferred. That alternative need not be a lump-sum purchase. The document provides no derivation of the cited result and does not specify the models or investor preferences in detail, so its conclusions should not be generalized beyond the stated framing.
Key ideas
- Dollar cost averaging describes a family of investment approaches rather than one fixed schedule.
- A comparison of one contribution schedule with lump-sum investing cannot prove a universal ranking.
- The responses emphasize that asset selection and purchase rules can change an approach's performance.
- A cited theoretical result describes dollar cost averaging as suboptimal under a class of models and utility preferences.
- The preferred alternative in that result need not be a lump-sum investment.
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Full text
# Proof showing that dollar cost averaging always worse than lump sum alternative # Proof showing that dollar cost averaging always worse than lump sum alternative I am referring to the article here. In a nutshell the article says that using data based on S&P 500 index going back as far as to 1950, dollar cost averaging is performing worse than a lump sump investment. My question is, assuming that the market works according to random walk hypothesis, is it possible to show mathematically that dollar cost averaging is always worse than lump sum investment, as far as the return on investment goes? ## Answer by Matt Wolf (score 3) https://quant.stackexchange.com/a/3540 You did not carefully read the article you yourself linked to. Dollar cost averaging is a generalized concept. What the author compares is a full-sized investment or time-specific partial investments. So, dca is a concept and you draw conclusions from one single approach to dca. There is no mathematical proof that dca works or not because it is one single concept that is only part of the overall investment process. Its as if I tell you that getting higher education does not pay off because those who undergo it and become philosophers do not recoup their investment. I did not include those who become lawyers, doctors, financiers,...the same applies to this article. What if I told you that dca hugely outperforms a lump-sum investment approach if instead of investing the parts at time-shifted periods you instead disregards time and buy companies with great fundamentals but depressed stock prices because of overall market sentiment. Each time the stock price trades another 2% below your previous investment you invest another portion. It is one alternative approach from many but it clearly demonstrates that you are comparing apples and oranges here. Another example to debunk the point made in the link is if I claimed trend following strategies do not work because the market is 70% of times range-bound and the strategy cannot make money in a range bound environment thus it has to be inferior to a range-bound strategy approach. Hope you got my point. So, in short, there is no mathematical proof. I could specify a strategy approach that hugely under-performs when investing in a dca way and another strategy that hugely outperforms a lump sum investment approach. ## Answer by amgc (score 2) https://quant.stackexchange.com/a/3542 There are a number of papers in the literature which show that Dollar Cost Averaging is suboptimal, in the sense that, given a DCA investment strategy, then there exists an alternative investment strategy which will be strictly preferred by a utility maximising agent. This preferred strategy may not necessarily be a "lump-sum" strategy, but a better strategy can be given that beats DCA for any utility maximising investor. I think that the original paper on this was by Constantinides, "A note on the suboptimality of dollar-cost averaging as an investment policy" http://www.jstor.org/stable/2330513 (edit: The class of models that Constantinides considers is large, and should include the ones you want.)
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