1

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.

user2153235
  • 197
  • 5

2 Answers2

1

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.

nanoman
  • 30,218
  • 3
  • 75
  • 92
0

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.

farnsy
  • 15,118
  • 31
  • 51