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I've read descriptions of DCA as buying more of something when it's cheap, and less when it's expensive. In contrast, if you buy much of that thing all at once, you may be buying the whole load at a peak or trough price, i.e., you're either way worse off or way better off. This means it's more of a gamble due to its uncertainty. In a sense, with DCA, you end up buying at the temporally local average price.

As a conceptual toy problem, I pondered what would be a good frequency at which to make DCA purchases. I haven't been able to see an intuitive answer over the years, but I'm wondering if this next idea might be a good rough guide.

The fluctuations in the price of a thing to buy has a slow and fast variations. You'll never average out the slower fluctuations unless you intend to make DCA purchases forever. Would it be a good idea to look at the autocorrelation of the price function in time, gauge the time interval that it takes to fall "relatively" flat, then choose a DCA purchase interval to be that time? My thinking is that, with purchases made at that interval, the prices are uncorrelated, so you end up averaging out the faster fluctuations.

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    This is the Vanguard study on dollar cost averaging indicating if the money is going to be invested you should just invest it as a lump sum. personal.vanguard.com/pdf/s315.pdf What you're talking about is no different than any other form of market timing.
    – quid
    Commented Jul 19, 2019 at 1:40
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    With DCA in uniform dollar amounts, your average price is lower than the temporal average price, because you buy more when the price is lower.
    – nanoman
    Commented Jul 19, 2019 at 2:31
  • The Vanguard article refers to DCA as a form of market timing, which is quite different from saying that it is no different from any other form of market timing. I believe that it depends on how loosely one defines market timing. I see it as a day trader trying to divine when to buy/sell based on knowledge/news of what is going on in the world, including based on emotion. Making regular fixed transactions seems the very opposite of that, so to me, it's a stretch to call it market timing.
    – user2153235
    Commented Jul 19, 2019 at 4:53
  • I would have preferred if the article ground out a probability distribution of the difference in outcome between the different strategies. That would take into account the deepness of the difference, and not just how often one beats the other. In any case, the intuition is described as obvious up front for up-trending markets. For down-trending markets, lump-sum at the end of the DCA period would beat the DCA plan. Admittedly, markets tend to trend up. I guess I should have described the fact that I was trying to attenuate the uncertainty rather than beat lump sum in an up-trend.
    – user2153235
    Commented Jul 19, 2019 at 4:57
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    I said what YOU are talking about is no different than market timing, because you are adding a decision algorithm. Over the full history of the market it has been in an uptrend.
    – quid
    Commented Jul 19, 2019 at 14:48

2 Answers 2

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Market prices approximate Brownian motion, which has no intrinsic time scale (it is self-similar, with fluctuations on all time scales). The autocorrelation of price never falls off because the expectation value of the price at any future time is tied to the current price (modulo interest, dividends, etc.) -- a martingale-like process.

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  • I spent the evening reviewing Martingale processes. Great for investments, but doesn't the scale-less fluctuations translate into the fact that the "noise" is both slow and fast? I was simply trying to avoid the greater uncertainty due to noise. With DCA over a finite period, I can't beat slow noise, but I can avoid the uncertainty from fast noise. Given that as the goal, it seems that choosing a DCA purchase interval averages out the fast noise in the frequencies above 1/(interval), leaving the uncertainty from the slow noise.
    – user2153235
    Commented Jul 19, 2019 at 5:03
  • The disturbing thing is that I can't use ACF die-out period to estimate the DCA purchase interval, if it never falls off. I haven't looked at how ACFs look when there is a gross trend. I get traumatic flashbacks of reading about time series with unit roots and such. Though in time series (which I've never actually done), we remove the trend and periodic pieces to leave only the stationary noise. It assumes that the nonrandom components are recognizable, for removal.
    – user2153235
    Commented Jul 19, 2019 at 5:04
  • @user2153235 I suspect what's being said is that there will be slow noise, fast noise, and all speeds in between noise. If so, you can't simply separate out the slow from the fast... it's may be there's a way to apply the equivalent of a "low pass filter", to reduce the effects of fast noise, but I've no idea whether what you're proposing would do this.
    – TripeHound
    Commented Jul 19, 2019 at 10:33
  • Yes, the fast and slow noise was simpler than saying a noise spectrum. And temporal averaging is just low pass filtering. So I guess the question has more to do with choosing the sample interval, and it assumed that the ACF decayed, which means that the noise bandwidth is approxiimately the inverse of the decay interval (which itself is eyeballed). If the sample interval was wide enough, the samples being averaged would be relatively uncorrelated, thus filtering away the high frequency noise. But you would sitll be at the mercy of the temporally local variation.
    – user2153235
    Commented Jul 19, 2019 at 13:27
  • Which still reduces the uncertainty. While this was the motive for the question, I guess it is a secondary effect of DCA.
    – user2153235
    Commented Jul 19, 2019 at 13:35
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Serial correlation and stock returns

No, it does not make sense. Stock prices do not have reliable serial correlation at frequencies that will matter to you, so you will not be able to find a frequency at which movements tend to cancel each other out going forward.

Any serial correlation happening with actionable frequency would imply a trading pattern that someone could use to make a ton of money. Doing so would dampen the pattern out. Even though your intent is not to "beat the market," the type of pattern you are looking for would lend itself to this.

It is easy to find serial correlation and other patterns in any given historical sample, but you will find that when you use them out-of-sample, whether as a statistical arbitrage rule or as an "improvement" to a rule like DCA, it will not reliably give you the results you are seeking. In other words, if you implement DCA at a given frequency, you will find that it will outperform other frequencies only according to chance, despite any optimization you did to choose that frequency.

Nanoman's answer says this same thing, but some of the consequences of that answer may not have been obvious.

Dollar Cost Averaging

Another point: DCA reduces risk relative to an up-front investment only because your money spends less time invested. Its reduction in expected return is proportional to the reduction in risk. The idea that 'buying more when cheap' outperforms 'buying it all up front' in a risk-adjusted sense is incorrect. There's no theoretical advantage to DCA over simply making a proportionally smaller investment up front and leaving it. The reason DCA is relevant to our world is that it matches what people do when they make monthly investments out of their paycheck.

Best not to take timing advice from anyone who suggests that DCA has any theoretical advantage over all-at-once investment. I say this knowing full well that most retail-level financial advisors and virtually all internet warriors do exactly this.

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  • Hi, farnsy, not sure if I was sufficiently clear about this, but I'm not trying to capitalize on correlations. I'm trying to determine how the spacing of purchases that minimize correlations, at least as indicated by the autocorrelation function. Perhaps the use of the term DCA was misleading, as it implies trying to beat upfront lump sum?
    – user2153235
    Commented Aug 25, 2019 at 19:56
  • In contrast, I'm looking at a more general buying situation, e.g., perhaps even buying products rather than investments, or transferring funds between investments. The aim is to avoid the uncerntainty in fluctations and realize the local average. I'm wondering if we might be speaking about different problems.
    – user2153235
    Commented Aug 25, 2019 at 19:56
  • For a given asset, there is a tradeoff between volatility/risk and expected return. You have described your problem in terms of minimizing the volatility/risk caused by purchase timing. This is equivalent to getting a better expected return for a given volatility--they require the same information. Neither is possible unless there is a consistent/persistent pattern in returns, which there is not.
    – farnsy
    Commented Aug 25, 2019 at 20:03
  • You will certainly reduce your uncertainty and realize the local average by using any kind of trading pattern that buys over time instead of at once. But you will lose the associated expected return. Statistically this is no better than just buying up front, in a lesser amount.
    – farnsy
    Commented Aug 25, 2019 at 20:05
  • Yes, but spacing the purchases in time is not arbitrary. One has to choose the spacing to avoid the high frequency fluctuations, though you will still be subjected to the low frequency. If spacing is too small, you avoid most of neither. As for expected returns, I'm less concerned about that if I'm timing (say) consumer product purchases or transferring funds between investment vehicles rather than having cash sit in a 0-return account. I don't treat expected returns as the only consideration, otherwise I'd do a lump sum upfront purchase of something with very high risk and return.
    – user2153235
    Commented Aug 25, 2019 at 20:18

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